Antenas fractais são estruturas irradiadoras geradas recursivamente a partir da aplicação reiterada de um fator de conjunto gerador, possuindo a característica marcante de ser auto semelhante. São baseadas na teoria dos fractais desenvolvida por Mandelbrot e cuja aplicação se encontra presente em quase todos os ramos da ciência. Tais antenas possuem hoje inúmeras aplicações, de celulares a antenas de satélites, e têm se mostrado uma alternativa atraente para aplicações que requeiram característica de multibanda associada a alto ganho e miniaturização. O presente trabalho procura apresentar de forma sistemática a teoria básica envolvendo antenas fractais, tendo-se por base não apenas as contribuições pioneiras de pesquisadores no mundo todo, mas também a teoria básica de antenas, a partir das quais é possível chegar-se a formulações importantes na área. O foco é para antenas de microfita, dada a grande popularidade que têm encontrado nas últimas décadas. Além de vasta bibliografia, contou-se com o auxílio da ferramenta computacional HFSS da Ansoft®, um software que simula estruturas em alta frequência. Este programa é utilizado para simular uma antena fractal de microfita proposta pelo autor, e os resultados são analisados tendo-se um duplo propósito: exemplificar o uso de uma antena fractal, por um lado, e fornecer um protótipo que porventura poderá ser utilizado em aplicações especiais, por algum projetista de antenas. Os principais parâmetros fundamentais de antenas são analisados, como Perda de Retorno, VSWR, Ganho, etc., mas será dada ênfase especial à aplicação de estruturas fractais de microfita em dois tipos de aplicações: antenas eletricamente pequenas e antenas independentes da frequência. / Fractal Antennas are radiating structures generated recursively from the reiterated application of a generating array, having the remarkable feature of being self similar. They are based on the theory of fractal developed by Mandelbrot and whose application is present in almost every branches of science. Such antennas have many applications today, from cell phones to satellite antennas, and have proved to be an attractive alternative for applications that required multiband characteristic associated with high gain and miniaturization. This paper aims do present systematically the basic theory involving fractal antennas, and is based not only on the pioneering contributions of researchers around the world, but also the basic theory of antennas, from which is possible to reach important formulations in the area. Besides the extensive bibliography, was used the computational tool HFSS by Ansoft®, a software that simulates high frequency structures. This program is used to simulate a fractal microstrip antenna proposed by the author, and the results are analyzed, having a dual propose: to exemplify the use of fractal antenna on the one hand, and providing a prototype which could possible be used in special applications, for some designer of antennas. The main fundamental parameters of antennas are analyzed, such as Return Loss, VSWR, Gain, etc., but special emphasis will be given to the application of fractal microstrip structures in two kinds of applications: electrically small antennas and frequency independent antennas. / Dissertação (Mestrado)

Given a very large dataset of moderate-to-high dimensionality, how to mine useful patterns from it? In such cases, dimensionality reduction is essential to overcome the well-known curse of dimensionality. Although there exist algorithms to reduce the dimensionality of Big Data, unfortunately, they all fail to identify/eliminate non-linear correlations that may occur between the attributes. This MSc work tackles the problem by exploring concepts of the Fractal Theory and massive parallel processing to present Curl-Remover, a novel dimensionality reduction technique for very large datasets. Our contributions are: (a) Curl-Remover eliminates linear and non-linear attribute correlations as well as irrelevant attributes; (b) it is unsupervised and suits for analytical tasks in general not only classification; (c) it presents linear scale-up on both the data size and the number of machines used; (d) it does not require the user to guess the number of attributes to be removed, and; (e) it preserves the attributes semantics by performing feature selection, not feature extraction. We executed experiments on synthetic and real data spanning up to 1.1 billion points, and report that our proposed Curl-Remover outperformed two PCA-based algorithms from the state-of-the-art, being in average up to 8% more accurate. / Dada uma grande base de dados de dimensionalidade moderada a alta, como identificar padrões úteis nos objetos de dados? Nesses casos, a redução de dimensionalidade é essencial para superar um fenômeno conhecido na literatura como a maldição da alta dimensionalidade. Embora existam algoritmos capazes de reduzir a dimensionalidade de conjuntos de dados na escala de Terabytes, infelizmente, todos falham em relação à identificação/eliminação de correlações não lineares entre os atributos. Este trabalho de Mestrado trata o problema explorando conceitos da Teoria de Fractais e processamento paralelo em massa para apresentar Curl-Remover, uma nova técnica de redução de dimensionalidade bem adequada ao pré-processamento de Big Data. Suas principais contribuições são: (a) Curl-Remover elimina correlações lineares e não lineares entre atributos, bem como atributos irrelevantes; (b) não depende de supervisão do usuário e é útil para tarefas analíticas em geral não apenas para a classificação; (c) apresenta escalabilidade linear tanto em relação ao número de objetos de dados quanto ao número de máquinas utilizadas; (d) não requer que o usuário sugira um número de atributos para serem removidos, e; (e) mantêm a semântica dos atributos por ser uma técnica de seleção de atributos, não de extração de atributos. Experimentos foram executados em conjuntos de dados sintéticos e reais contendo até 1,1 bilhões de pontos, e a nova técnica Curl-Remover apresentou desempenho superior comparada a dois algoritmos do estado da arte baseados em PCA, obtendo em média até 8% a mais em acurácia de resultados.

Orientador: Marcio Luiz de Andrade Netto / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-08T10:53:36Z (GMT). No. of bitstreams: 1 Peres_SarajaneMarques_D.pdf: 11492142 bytes, checksum: 7eeb4f81f681e145111b43ccfdde2b7e (MD5) Previous issue date: 2006 / Resumo: Redes Neurais Artificiais Auto-Organizáveis (RNA-AO), introduzidas por Teuvo Kohonen na década de 60, constituem uma poderosa ferramenta para análise de dados, mais especificamente para análise de agrupamentos, visualização e aproximação de superfícies. Nesta tese definiu-se uma nova forma para determinar a dimensão topológica do espaço de saídada RNA-AO a partir da análise do conjunto de dados a ser explorado pela rede, realizada como apoio combinado da Teoria de Fractais e do Raciocínio Aproximado Fuzzy. Ao combinar essas duas teorias, concebeu-se uma nova medida de dimensão fractal, a medida de Dimensão Fractal Fuzzy Significativa (DFFS) de um conjunto de dados. Tanto o processo de determinação da DFFS quanto sua aplicação como inferência da dimensãotopológica para a RNA-AO foram validados neste trabalho. O primeiro por meio de sua aplicação ao problema de Tendência a Agrupamentos e o segundo por meio da análise de qualidade das RNAs-AO projetadas segundo tal inferência / Abstract: Self Organizing Maps (SOM), introduced by Teuvo Kohonen during the decade of 1960's, is a powerful tool for data analysis, mainly for clustering analysis and surface approximation. In this thesis, we have defined a new way to determine the output space topological dimension of the SOM using the analysis of the dataset to be explored by the map. This analysis is carried out with the combined support of the Fractal Theory and the Fuzzy Approximated Reasoning, deriving a new fractal dimension measure: the Meaningful Fractal Fuzzy Dimension - DFFS (of the Portuguese "Dimensão Fractal:..Fuzzy Significativa"). The DFFS determination process and its application as an inference to the SOM topological dimension have been both validated in this work. The former has been carried out through its application to the Clustering Tendency Analysis and the latter through the quality analysis of the SOM designed by such inference / Doutorado / Engenharia de Computação / Doutor em Engenharia Elétrica

FundaÃÃo de Amparo à Pesquisa do Estado do Cearà / Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / In this work a procedure is studied for pattern classification related to different types of data, namely: (1) signals obtained from ultrasonic testing ( pulse-echo technique) and magnetic signals obtained from BarkhÃusen noise in samples of ferritic-pearlitic carbon steel tubes which, due to temperature effects, have shown microstructural changes as consequence of the total or partial transformation of the pearlite into spherodite; (2) images built from TOFD ultrasonic testing and 8 bit digital radiographic images obtained from carbon steel 1020 sheets, with different welding defects. From the data obtained, images have been considered with the defects as lack of fusion, lack of penetration, porosity and images without defect. For this aim, non-conventional mathematical techniques have been used for the preprocessing of the data, namely, the statistical analyses, Hurst analysis (RSA) and detrended fluctuation analysis (DFA), and fractal analyses, box counting analysis (BCA) and minimal cover analysis (MCA). The curves obtained with the initial mathematical treatment, discrete functions of the temporal window width, have been handled with the supervised and non-supervised pattern recognition techniques known as principal component analysis and Karhunen-LoÃve (KL) transformation analysis respectively. With respect to the magnetic signals, the KL classifier has been shown to be very efficient when applied to DFA obtained from the magnetic flux, with a success rate around 94%. On the other hand, for the magnetic noise signals we have not obtained an acceptable success rate independently of the pre-processing used. However, when were considered the curves obtained by concatenating all curves of the pre-processing was obtained a consistent average success rate of 85%. As far as the rate of success of the PCA classifier is concerned, an excellent success of 96% has been reached for concatenated curves of selected data of magnetic noise only. As far as the analyses of the backscattered ultrasonic signals is concerned, it was not possible to classify the different stages of the microstructural degradation by using KL or PCA independently of the pre-processing used. As far as the analyses of the D-scan images are concerned, by applying PCA a rate of success of 81% has been obtained with MCA data, 73% has been obtained by concatenating all curves from the different fractal and statistical analyses and around 85% when concatenating the best individual results (DFA and MCA). On the other hand, considering the KL classifier, high success rates have been verified for the training stage, between 96% and 99%, and a maximum success rate (100%), when concatenating all analyses. With respect to the testing results, the best success rate which has been reached was approximately 77%, when concatenating all the curves obtained from the statistical and fractal pre-processing. For the digitalized radiographic images, relevant individual rates of success (between 70% and 90%) for the training set (consisting of all data) have been obtained for the classifier KL only, and a 100% success rate, when concatenating all the curves obtained from the pre-processing of the images. / Neste trabalho estudou-se uma metodologia de classificaÃÃo de padrÃes relacionados a dois tipos de dados: (1) sinais obtidos atravÃs dos ensaios ultrassÃnicos (tÃcnica pulso-eco) e sinais magnÃticos obtidos atravÃs de ruÃdo Barkhausen realizados em amostras de tubos de aÃo carbono ferrÃtico-perlÃtico que devido aos efeitos da temperatura de trabalho apresentaram mudanÃas microestruturais decorrentes da transformaÃÃo parcial ou total da perlita em esferoiditas; e (2) imagens construÃdas a partir de ensaios ultrassÃnicos (tÃcnica TOFD) e imagens radiogrÃficas digitais de chapas de aÃo carbono 1020 soldadas, obtidas com resoluÃÃo de 8bits, nas quais foram inseridos diversos tipos de defeitos de soldagem. Dos dados gerados, foram estudadas as imagens com os defeitos de falta de fusÃo (FF), falta de penetraÃÃo (FP), porosidade (PO) e uma classe designada como sem defeito (SD). Para tanto, utilizaram-se de tÃcnicas matemÃticas nÃo convencionais no prÃ-processamentos dos dados conhecidas como anÃlises estatÃsticas de Hurst (RSA) e flutuaÃÃo sem tendÃncia (DFA) e as anÃlises fractais de contagem de caixas (BCA) e de mÃnima cobertura (MCA). Em seguida as curvas obtidas desse tratamento matemÃtico inicial, funÃÃes discretas da largura da janela temporal, foram utilizadas na alimentaÃÃo das tÃcnicas de reconhecimento de padrÃes nÃo supervisionada e supervisionada conhecidas, respectivamente, como anÃlise de componentes principais (PCA) e anÃlise da transformaÃÃo de Karhunen-LoÃve (KL). Em relaÃÃo aos estudos dos sinais magnÃticos, o classificador KL mostrou-se eficiente quando aplicado Ãs DFA do fluxo magnÃtico, com uma taxa de sucesso em torno de 94%. Jà para os sinais do ruÃdo magnÃtico nÃo se obteve uma taxa de sucesso aceitÃvel, independente do prÃ-processamento utilizado. Entretanto quando todas as curvas de todas as anÃlises, dos dois tipos de sinais magnÃticos (ruÃdo e fluxo), foram concatenadas, obteve-se uma taxa mÃdia de sucesso consistente de aproximadamente 85%. No tocante Ãs taxas de sucesso do classificador PCA, somente para o ruÃdo magnÃtico e considerando todas as curvas concatenadas para um grupo de dados selecionados, conseguiu-se uma taxa de sucesso de 96%. A respeito das anÃlises dos sinais ultrassÃnicos retroespalhados, tambÃm nÃo foi possÃvel classificar, nem com a KL e nem com a PCA, os diferentes estÃgios de degradaÃÃo microestrutural, independemente do prÃ-processamento utilizado. No tocante Ãs analises das imagens D-scan, obteve-se com a PCA, taxas de sucesso de 81% considerando apenas os dados das MCA, 73% quando as curvas de todas as anÃlises estatÃsticas e fractais foram concatenadas, e em torno de 85%, quando apenas as curvas das melhores anÃlises (DFA e MCA) foram concatenadas. Jà considerando o classificador KL, verificaram-se taxas de sucesso na etapa de treinamento, entre 96% e 99%, e mÃxima taxa de sucesso (100%) no caso dos vetores de todas as anÃlises concatenados. Em relaÃÃo aos resultados dos testes, a melhor taxa de sucesso alcanÃada foi aproximadamente de 77% quando se concatenaram todas as curvas oriundas dos prÃ-processamentos estatÃsticos e fractais. Com respeito Ãs imagens radiogrÃficas digitalizadas somente com o classificador KL (na etapa de treinamento, com 100% dos vetores) obtiveram-se taxas de sucesso individuais entre 70 e 90% de acertos e 100% de sucesso na classificaÃÃo quando se concatenaram as curvas de todos os prÃ-processamentos das imagens.

Ce travail porte sur une étude comparative des huiles végétales (esters naturels) issues de différentes graines, esters synthétiques, et minérales sur la base des caractéristiques de génération et de propagation des streamers qui s’y développent, des tensions de claquage ainsi que des décharges se propageant sur un isolant solide en présence de ces huiles. Il ressort des résultats obtenus qu’en géométrie pointe – plan, sous tension continu, la tension de génération en polarité positive est toujours supérieure à celle mesurée en polarité négative et elle est plus élevée dans les huiles esters que dans les huiles minérales quelle que soit la polarité de l’électrode pointe. En ce qui concerne la propagation de streamers sous tension impulsionnelle de foudre, les longueurs finales (ou longueurs d’arrêt) Lf des streamers positifs sont environ10 fois supérieures à celles des streamers négatifs. Pour atteindre la même Lf, il faut beaucoup plus de tension en polarité négative qu’en polarité positive. Par conséquent, les tenues diélectriques sont plus élevées en polarité négative qu’en polarité positive. D’autre part, Lf est plus élevée dans les huiles végétales que dans certaines huiles minérales. La tension de claquage des huiles isolantes, déterminée selon la norme CEI 60156, suit généralement une distribution Normale. Les probabilités de claquage peuvent alors être déterminées suivant la distribution Normale en prenant un échantillonnage suffisamment grand (n>30). Il est également montré que les huiles végétales et l’ester synthétique présentent des tensions de claquage (U1%, U10% et U50%) plus élevées que les huiles minérales sous tension alternative. La tension de claquage moyenne est aussi plus élevée dans les esters que dans les huiles minérales sous tension impulsionnelle de foudre. La morphologie, la longueur d’arrêt et le courant des décharges se propageant sur un isolant solide (carton) immergé dans les liquides étudiés, dépendent de l’amplitude et de la polarité de la tension, de l’épaisseur du solide et de la nature des huiles. Lf augmente quasi-linéairement avec la tension appliquée et diminue lorsque l’épaisseur du solide augmente. Pour une tension et une épaisseur données, les décharges qui se développent sur l’interface carton/huile végétale sont plus longues que celles sur l’interface carton/huile minérale. Par ailleurs, Lf est plus élevé en polarité positive qu’en polarité négative, ce qui indique que la polarité la plus contraignante est la polarité positive. Ila été également mis en évidence l’existence d’une décharge secondaire de signe opposé à celui de la tension appliquée, résultat de l’accumulation de charges d’espace à la surface de l’isolant solide. Enfin, la dimension fractale D des décharges diminue lorsque l’épaisseur du solide augmente. Plus l’épaisseur du solide est grande, plus le degré de ramification des décharges est moins important. Pour une tension et une épaisseur données, D est généralement plus élevée dans l’huile minérale que dans l’huile végétale. / This work is aimed at the comparative study of vegetable oils (natural esters) issued from different seeds, synthetic ester oil and mineral oils, based on the characteristics of generation and propagation of streamers, breakdown voltages and creeping discharges propagating over solid insulator (pressboard) immersed in these oils. It has been shown that, in a point – plane electrode geometry, the DC threshold voltage Us is higher when the point is positive than when it’s negative; Us is higher in vegetable oils than in mineral oils for both polarities of voltage. Under lightning impulse voltage, the streamers are filamentary in all different tested oils whatever the polarity of voltage. The final (or stopping) length Lf of streamers are about ten times higher when the point is positive than when it’s negative. The voltage required to reach the same Lf is higher with a negative point than with a positive point.Thus the positive polarity is unfavourable for the industrial applications. In addition, Lf is longer in vegetable oils than in some mineral oils. The breakdown voltage of insulating oils, measured according to IEC 60156 standard specifications generally follows a normal distribution. The probability of breakdown can hence be determined according to the normal distribution with a large amount of samples (n>30). So, vegetable oils and synthetic ester have breakdown voltages (U1%, U10% and U50%) higher than mineral oils under AC; and the mean breakdown voltage is also higher in esters oils than in minerals oils under lightning impulse voltage. The morphology, final length Lf and current of discharges propagating over a solid insulator (pressboard) immersed in the liquid tested, depend on the amplitude and polarity of the voltage, the thickness of insulator as well as the nature of insulating oils. It has been shown that Lf increases quasi-linearly with the applied voltage and decreases when the thickness of insulator increases. For a given applied voltage and thickness of insulator, Lf is higher with a pressboard/vegetable oil interface than with a pressboard/mineral oil interface.In addition, Lf is also longer when the point is positive than when it’s negative. The recorded currents revealed the existence of a secondary discharge of opposite sign to that of the applied voltage. This phenomenon is due to the accumulation of charges at the surface of insulator.Finally, the fractal dimension D of creeping discharges decreases when the thickness of insulator increases. For a given applied voltage and thickness of solid, D is generally higher in mineral oils than in vegetable oils.

Le présent travail porte sur une étude comparative des caractéristiques optiques et électriques des décharges glissantes se propageant aux interfaces solide/gaz sur des isolateurs de verre, de Bakélite et de résine époxy en présence des gaz N2, CO2 et SF6 et des mélanges SF6/N2 et SF6/CO2, sous tension continue et alternative (50 Hz), en géométrie pointe - plan. L’objectif est de mieux comprendre les mécanismes impliqués dans l’initiation des décharges partielles et leur évolution et développement en décharges surfaciques (glissantes) lesquelles peuvent conduire au contournement des composants et systèmes haute tension. Les résultats obtenus montrent que la morphologie et la longueur finale (d’arrêt ou d’extension maximale) des décharges surfaciques dépendent de la forme et de l’amplitude de la tension, de l’épaisseur et de la nature du solide isolant, du type du gaz/mélange et de sa pression. Il est montré que la longueur finale des décharges Lf augmente quasi-linéairement avec la tension. Lf diminue lorsque la pression du gaz et/ou l’épaisseur du solide augmentent. Cette longueur est plus courte dans le SF6 que dans le CO2 ou le N2 ; et elle diminue significativement lorsque le taux du SF6 dans le mélange de gaz augmente. Par ailleurs, pour une tension donnée, Lf augmente avec la constante diélectrique de l’isolant solide. La longueur finale des décharges est nettement plus élevée sous tension alternative que sous tension continue. La morphologie des décharges glissantes générées sous tension continue et alternative est généralement non radiale; leur orientation est fortement influencée par la présence des charges d’espace présentes ou déposées sur la surface de l’isolateur. Une analyse fractale des décharges glissantes obtenues expérimentalement sous tension continue est également réalisée et une corrélation entre la dimension fractale, la pression du gaz, la constante diélectrique et l’épaisseur du matériau solide est mise en évidence. En particulier, la dimension fractale augmente lorsque la constante diélectrique augmente et/ou l’épaisseur de l’isolant solide diminue et/ou la pression du gaz diminue. / This work deals with a comparative study of optical and electrical characteristics of creeping discharges propagating at solid/gas interfaces on insulators made of glass, Bakelite and epoxy resin in the presence of N2, CO2 and SF6 gases and SF6/N2 SF6/CO2 mixtures, under DC and AC (50 Hz) voltage, using a point - plane electrode arrangement. The objective is to better understand the mechanisms involved in the initiation of partial discharges and their evolution and development into discharges surface (creeping discharges) that can lead to flashover of components and high voltage systems. The results show that the morphology and final length (maximum extension or stopping length) depend on the shape and amplitude of the voltage, the thickness and the nature of the solid insulator, type of gas / mixture and its pressure. It is shown that the final length Lf increases quasi-linearly with the voltage. Lf decreases as the gas pressure increases and/ or the thickness of the solid increases. Lf is shorter in SF6 than in CO2 or N2, and it decreases significantly when the rate of SF6 in the gas mixture increases. Moreover, for a given voltage, Lf increases with the dielectric constant of the solid insulation. The final length of the discharge is much higher under AC voltage than under DC voltage. The morphology of creeping discharges generated under DC and AC voltage is generally not radial; and their orientation is strongly influenced by the presence of space charges present or deposited on the surface of the insulator. A fractal analysis of creeping discharges experimentally obtained under DC voltage is also carried out and a correlation between the fractal dimension, the pressure of the gas, the dielectric constant and the thickness of the solid material is highlighted. In particular, the fractal dimension increases when the dielectric constant increases and / or thickness of the solid insulator decreases and / or pressure of the gas decreases.

En raison des changements climatiques actuels, il est primordial de comprendre comment les écosystèmes vont réagir et tout particulièrement comment les chaînes trophiques vont être impactées. Pour cela, le comportement des oiseaux marins peut être utilisé comme des indicateurs des changements se déroulant au sein de l’écosystème. Cependant, un des défis actuels dans l’étude du comportement animal est d’identifier comment la structure temporelle du comportement est dépendante des conditions intrinsèques et extrinsèques et comment la complexité de cette organisation comportementale évolue sur un gradient allant de la stochasticité au déterminisme en fonction des changements environnementaux. Ma thèse a donc pour objectif d’étudier si un comportement complexe est adapté pour faire face à une perturbation du système chez les oiseaux marins et plus particulièrement chez deux espèces de manchots étant exposées à des changements environnementaux. / Due to ongoing climate change, it is necessary to understand how ecosystems will react and more particularly, how species may cope with the challenges of living in unstable systems. Seabirds’ behavior provides a way to monitor changes occurring in the marine environment, but identifying how the temporal structure and complexity of behavior depend on intrinsic and extrinsic parameters are underexplored topics in the field of animal behavior. My thesis aims to investigate if behavioral organization, through a gradient of stochasticity-determinism complexity, allows little and adélie penguins to buffer changes in the environment under a fractal analysis approach.

Ce travail de thèse aborde le problème de l'alignement d'images 2D obtenues en tomographie électronique dans la perspective d'une reconstruction tridimensionnelle et la détection des ribosomes à partir de l'objet reconstruit. Une méthode d'optimisation globale est proposée pour minimiser un coût qui permet d'effectuer l'alignement 3D et la reconstruction de manière conjointe. La thèse traite également le problème de la segmentation des images 3D reconstruites avec une méthode de classification probabiliste. Cependant, la nature des images de cryo-tomographie révèle des problèmes de bruit et de contraste. Deux méthodes de filtrage 3D ont été proposées comme prétraitement du processus de segmentation. La première méthode est basée sur l'intégration fractionnaire. La seconde est basée sur l'analyse multi-fractale. L'institut de recherche biomédicale IGBMC de Strasbourg a fourni les images de projection utilisées dans cette thèse. / This thesis deals with the problem of the alignment of 2D images obtained by transmission electron microscopy in the perspective of a three-dimensional reconstruction and the detection of ribosomes from the reconstructed object. A global optimization method is proposed to minimize a cost that allows the 3D alignment and reconstruction to be carried out jointly. The thesis also deals with the problem of segmentation of reconstructed 3D images with a probabilistic classification method. However, the nature of cryo-tomography images reveals noise and contrast problems. For this reason, two methods of 3D filtering have been proposed as pre-processing of segmentation, one is based on fractional integration, and the other on a multi-fractal analysis. The institute of biomedical research IGBMC in Strasbourg provides the projection images used in this thesis.

Les marchés financiers occupent, depuis des décennies, une place importante dans notre société. Pourtant, ils présentent des risques accrus auxquels font face la majorité des institutions financières. Les crises, les krachs, les bulles et les turbulences financières jalonnent l’histoire de ces marchés et les déstabilisent fréquemment. En effet, l’existence des anomalies et des biais psychologiques, allant à l’encontre de l’hypothèse d’efficience, remettent en question la théorie financière et révèlent de façon rigoureuse les inefficacités des mécanismes de gestion financière et de contrôle du risque du marché. Confrontés à ces évolutions, le comité de Bâle II recommande la Value at Risk comme une nouvelle vision réglementaire des risques. Ce processus d’innovation financière, introduite par la banque JP Morgan dans les années 90, a connu une grande reconnaissance en finance, mais elle est aussi sujette à des controverses continuelles. Pour surmonter les limites de la VaR, nous proposons un nouveau cadre d’analyse de la VaR basé sur des processus fractals. Tenant compte des anomalies et des facteurs de risques du marché financier, qui induisent des rendements par nature non-gaussiens, nous introduisons la VaR en fonction du modèle multifractal à changements de régime markovien de Calvet et Fisher. L’approche VaR-MSM qui modélise la volatilité multifractale à différentes fréquences constitue un aperçu différent d’évaluation du risque du marché. En appliquant ce modèle sur l’indice boursier français le CAC 40, les résultats obtenus révèlent que la VaR-MSM a surpassé assez nettement les autres modèles d’évaluation de la VaR. / Financial markets occupy an important place in our society. However, they present increased risks to financial institutions. Crises, crashes, bubbles and financial turbulence often destabilize these markets. Indeed, the existence of different anomalies and psychological bias, going against the hypothesis of efficiency, put into question financial theory and present an inefficiency of financial and risk management. Faced with these effects, Bale II committee recommended Value at risk as a new financial instrument of risk management. Value at Risk, introduced by JP Morgan Bank in the 90, have a great recognition in finance, but it is also a subject of controversy. To overcome the VaR limits, we propose a new framework based on fractal process. Taking into account abnormalities and risk factors of financial markets, which induce non-Gaussian returns, we introduce the VaR with a Markov-switching multifractal model proposed by Calvet and Fisher. The VaR-MSM approach presents multifractal volatility at different frequencies. We apply this model to the France CAC 40 stock market index. The results clearly show the advantages of VaR-MSM compared with other models of VaR evaluation.

No description available.