Made available in DSpace on 2014-07-29T15:08:17Z (GMT). No. of bitstreams: 1 Dissertacao Flavio Geraldo Coelho Rocha.pdf: 3399518 bytes, checksum: feb6250bd7ead671989ce282786ce64e (MD5) Previous issue date: 2011-03-29 / In this dissertation, the multifractal analysis is used in the context of traffic modeling of communications networks by proposing algorithms and techniques for improving the performance of these networks. Thus, in order to better describe traffic networks, a model based on multifractal multiplicative cascade that uses autoregressive processes for multipliers modeling is proposed, the model is called CMAM (Multifractal Cascade with Multipliers Autoregressive Modeling). Simulations are carried out to evaluate the model performance on describing real video traffic traces and wired and wireless real network traffic traces. In addition, considering data loss probability as an important quality of service measure, a mathematical expression for estimating loss probability that takes into account wavelet coefficients associated to the traffic process is proposed. The expression is evaluated, among other ways, through simulations in a wireless network scenario based on OFDM / TDMA technologies. Then, an admission control scheme for network flows which is based on the proposed loss probability estimation is presented and applied to the scenario considered. Simulations show efficiency of the proposed scheme in comparison to other approaches found in the literature. In addition, an adaptive transmission rate allocation scheme that considers the characteristics of multifractal network traffic is proposed, which one is compared to an approach that considers the monofractal traffic properties. Finally, using CMAM for video traffic modeling, a rate control algorithm for video traffic in the source is presented based on exponential modeling of the scale function associated with the quantization parameter Q of the video encoder. / Nesta dissertação, a análise multifractal é utilizada no contexto de modelagem do tráfego de redes de comunicações, propondo algoritmos e técnicas para a melhoria do desempenho destas redes. Assim, com o propósito de descrever melhor o tráfego de redes, propõe-se um modelo multifractal baseado em cascata multiplicativa que utiliza processos autorregressivos para modelagem dos multiplicadores da cascata, o modelo é chamado de CMAM (Cascata Multifractal com Modelagem Autorregressiva para os Multiplicadores). Simulações utilizando o CMAM são conduzidas para avaliar o desempenho deste modelo em descrever séries reais de tráfego de vídeo, de redes com fio, e de redes sem fio. Adicionalmente, considerando a probabilidade de perda de dados como uma importante métrica de qualidade de serviço, uma expressão matemática para estimação de probabilidade de perda, que leva em consideração coeficientes wavelets associados ao processo de tráfego, é proposta. Os resultados da expressão proposta são analisados, dentre outras formas, por meio de simulações realizadas em um cenário de rede sem fio baseado no OFDM/TDMA. Em seguida, é apresentado um esquema de controle de admissão de fluxos baseado na expressão para estimação de probabilidade de perda proposta e aplicado ao cenário considerado. Simulações comprovam a eficiência do esquema proposto em comparação com outras abordagens presentes na literatura. Além disso, um esquema de alocação adaptativa de taxa de transmissão que considera as características multifractais do tráfego de redes é proposto, o qual é comparado com uma abordagem existente na literatura que considera as propriedades monofractais do tráfego. Por fim, utilizando o CMAM para modelagem multifractal do tráfego de vídeo, um algoritmo de controle de taxa de tráfego de vídeo na fonte é apresentado com base na modelagem exponencial da função de escala associada ao parâmetro de quantização Q do codificador de vídeo.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-22T10:13:08Z No. of bitstreams: 2 Dissertação - Diego Cruz Abrahão - 2015.pdf: 9765017 bytes, checksum: 6f29592215e8451edda4aa5ad24238f4 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-22T10:15:40Z (GMT) No. of bitstreams: 2 Dissertação - Diego Cruz Abrahão - 2015.pdf: 9765017 bytes, checksum: 6f29592215e8451edda4aa5ad24238f4 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-10-22T10:15:40Z (GMT). No. of bitstreams: 2 Dissertação - Diego Cruz Abrahão - 2015.pdf: 9765017 bytes, checksum: 6f29592215e8451edda4aa5ad24238f4 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-03-19 / In this paper we propose two schemes for allocating resource blocks for transmission LTE downlink to maximize the throughput of the system, to guarantee QoS (Quality of Service) parameters for the users and reduce the data loss rate of network. The first proposed scheme uses the Max-min criterion and the second employs a fuzzy inference system to calculate the priorities of users and make scheduling decisions. Both schemes use an estimated effective bandwidth of traffic flows of users. The effective bandwidth of a traffic flow is the rate required to meet a criterion of probability of data loss rate. In this work, the effective bandwidth is estimated adaptively by the parameters of multifractal modeling βMWM (β-Multifractal Wavelet Mode). Are made simulations of the algorithms proposed, considering different propagation models with multipath fading and with different numbers of users in the network. The simulation results are compared with other algorithms presented in the literature, using parameters such as: throughput of the system, data loss rate and fairness index. It is also proposed to use predict of the SNR (Signal-to-Noise Ratio) of users, in the scheduling algorithms, using linear prediction of multi-step filter, in view of the delay in receipt of the channel quality information of the users in the base station and the variation of the signal propagation conditions. The multi-step prediction filter is used with the algorithms of allocation of resource blocks proposed in this work to estimate the signal-to-noise-ratio of users and set well, modulation schemes and code to be used in the LTE network. / Neste trabalho são propostos dois esquemas de alocação de blocos de recurso para a transmissão de downlink LTE, visando maximizar a vazão de dados total do sistema, garantir parâmetros de QoS (Quality of Service) dos usuários e diminuir a taxa de perda de dados da rede. O primeiro esquema proposto utiliza o critério Max-min e o segundo emprega um sistema de inferência fuzzy para calcular as prioridades dos usuários e tomar decisões de escalonamento. Ambos os esquemas utilizam estimações de banda efetiva dos fluxos de tráfego dos usuários. A banda efetiva de um fluxo de tráfego é a taxa necessária para atender a um critério de probabilidade de perda de dados. Neste trabalho, a banda efetiva é estimada de forma adaptativa, através dos parâmetros da modelagem multifractal βMWM (β-Multifractal Wavelet Mode). São realizadas simulações dos algoritmos propostos de alocação de blocos de recurso, considerando diferentes modelos de propagação com desvanecimento de multipercursos e com diferentes quantidades de usuários na rede. Os resultados das simulações são comparados com outros algoritmos apresentados na literatura, através de parâmetros, como: vazão de dados do sistema, taxa de perda de dados e índice de justiça. É proposta ainda, a utilização da predição da relação sinalruído (SNR - Signal-to-Noise Ratio) dos usuários nos algoritmos de escalonamento, utilizando filtro de predição linear de multi-passos, tendo em vista o atraso no recebimento da informação da qualidade do canal dos usuários na estação base e a variação das condições de propagação do sinal. O filtro de predição de multi-passos é utilizado junto com os algoritmos de alocação de blocos de recurso propostos neste trabalho, para estimar a relação sinal-ruído dos usuários e definir, assim, os esquemas de modulação e código a serem utilizados na rede LTE.

L'objectif principal de cette thèse était de parvenir à un outil de gestion fiable des bassins de rétention d'eaux pluviales en utilisant les données radar en bande X. Il s’est avéré que cela nécessite plusieurs développements de recherche. Le cas d’étude considéré comprend un bassin de 10000 m3 situé en Val-de-Marne et construit en aval d'un bassin versant urbain de 2.15 km2. Il assure un double rôle de traitement des eaux pluviales et de prévention des inondations par stockage du volume. Opérationnellement les modes de gestion associés à chacun de ces objectifs sont antagonistes si bien qu’une gestion prédictive a été mise en place ; exploitation routinière en mode anti-pollution et basculement vers le mode anti-inondation en cas de besoin. Il doit se faire sur la base d’une connaissance sûre de la situation pluvieuse prévue à court terme. Une façon courante de répondre aux besoins opérationnels de la gestion prédictive est de mettre en place un système d’alerte basé sur l’utilisation des données radar. Le système CALAMAR par exemple, repose sur l’utilisation des données radar brutes à mono polarisation du réseau radar de Météo-France; traitées avec des méthodes de conversion classiques Z-R et une calibration avec des pluviomètres. Cependant, la fiabilité de ce système fait débat, notamment vis-à-vis de la qualité de la mesure radar obtenue. Une nouvelle méthodologie de comparaison de produits radar a été développée au cours de cette thèse. Elle repose sur le cadre théorique des multifractals et permet une comparaison de la structure et de la morphologie des champs de précipitations dans l'espace et le temps à travers les échelles. Cette méthode a d'abord été appliquée sur les produits CALAMR et Météo-France, puis, pour confirmer certains des résultats, sur les premières données d’un radar bande X, acquis par l’Ecole des Ponts ParisTech dans le cadre du projet Européen RainGain et fournissant des mesures de précipitations à des échelles plus fines (jusqu’à 100m en espace et 1 min en temps). Les résultats obtenus mettent en évidence non seulement l'influence cruciale des méthodes de traitement des données brutes sur la variabilité spatio-temporelle à travers les échelles, mais permettent également de prédéfinir les conditions dans lesquelles la calibration CALAMAR peut aggraver la qualité des mesures. Elles seraient très difficiles à détecter par les méthodes classiques largement répandues, n’impliquant qu’un nombre très limité de pixels radar (seulement ceux correspondants aux pluviomètres au sol). Des extensions de la méthodologie proposée ouvriront de nouveaux horizons pour la calibration des données de pluie. Alors que la littérature scientifique, notamment autour expériences TOMACS au Japon et CASA aux Etats-Unis, souligne l’importance opérationnelle d’une mesure de pluie plus détaillée grâce au radar en bande X, son impact sur les performances des modèles hydrologiques fait encore débat. Les recherches antérieures, basée pour la plupart sur des modèles conceptuels, ne sont pas concluantes. Ainsi pour dépasser ces limites, nous avons utilisé deux modèles impliquant des approches de modélisation différentes : CANOE (semi-distribué et conceptuel) et Multi-Hydro (distribué et à base physique ; développé à l’ENPC). Une version opérationnelle de CANOE et une nouvelle configuration plus fine améliorant considérablement la sensibilité du modèle à la variabilité de la pluie ont été utilisées. Plusieurs développements ont été apportés à Multi-Hydro, y compris une optimisation de sa résolution, ce qui améliore grandement l'ensemble de ses fonctionnalités. Il ressort de ce travail qu’en prenant en compte la variabilité spatio-temporelle des précipitations à petite échelle, la performance des modèles hydrologiques peut être augmentée jusqu'à 20%.Nous pensons que cette thèse a contribué à la mise au point de nouveaux outils opérationnels, fiables ayant la capacité de prendre en compte les données en bande X haute résolution / The main goal of this thesis was to achieve a reliable management tool of storm water storage basins using high resolution X-band radar. It turned out that it required several research developments. The analysed case study includes a retention basin of 10000 m3 located in Val de Marne county downstream of a 2.15 km2 urban catchment. It has a twofold goal: storm water decontamination and flood protection by volume storage. Operationally the management strategies associated with these two aims are conflicting; hence, a predictive management has been set up: a routine exploitation of the basin in the anti-pollution mode, and a switch to the flood protection mode when needed. It should be based a reliable knowledge of short-term rainfall forecasts. A common way to respond to operational needs of the predictive management is to set up a warning system based on the use of radar data. For example, the CALAMAR system relies on the use of single-polarization raw radar data, coming from Meteo-France radar network, being processed with the conventional Z-R conversion methods followed by a calibration with rain gauge. However, the reliability of such warning systems has been subject to debate, often due to a questionable quality of the resulting radar rainfall estimates, compared to local rain gauges. Therefore a new methodology for more meaningful comparison of radar rainfall field products was developed during this PhD project. Being rooted to the multifractal theory, it allows a comparison of the structure and the morphology of rainfall fields in both space and time through scales. It was initially tested on CALAMAR and Meteo-France rainfall products before being applied for results confirmation on initial data from a X band radar, acquired by Ecole des Ponts ParisTech in the framework of the European project RainGain and providing data at higher resolution (up to 100 m in space and 1 min in time). The obtained results not only highlight the crucial influence of raw data processing on the scaling behaviour, but also permit to pre-define the conditions when the CALAMAR optimization may worsen the quality of rainfall estimates. Such conditions would be very difficult to detect with widely used conventional methods, which rely on a very limited number of radar pixels (only those containing rain gauges). Further extensions of the proposed methodology open new horizons for the rainfall data merging. While the scientific literature, notably around the TOMACS experiment in Japan and CASA one in the United States, highlights the operational benefits of higher resolution rainfall measurements thanks to X-band radars, its impact on the performance of hydrological models still remains a subject of debate. Indeed previous research, mainly based on conceptual models remains inconclusive. To overcome these limitations, we used two models relying on two very distinct modelling approaches: CANOE (semi-distributed and conceptual) and Multi-Hydro (fully distributed and physically based research model developed at ENPC). An operational version of CANOE and a new much finer configuration, which increases the sensitivity of the model to spatio-temporal variability of small-scale rainfall, were used. Several extensions of the Multi-Hydro were developed, including an optimization of its resolution, which greatly improves its whole functionality. It appears from this work that by taking into account the spatial and temporal variability of small-scale rainfall, the performance of hydrologic models can be increased up to 20%.Overall, we believe that this dissertation contributes to the development of new, reliable, operational tools to use in their full extent the high-resolution X-band data

Les précipitations ont une très grande variabilité sur une large gamme d'échelles tant spatiale que temporelle. Cette variabilité est une source importante d'incertitude pour la mesure, les applications et la modélisation, et au-delà pour la simulation et la prévision. De plus, les précipitations sont des processus extrêmement intermittents et possèdent plusieurs régimes d’invariance d’échelle. Le générateur de champ précipitant développé au cours de la thèse est basé sur la modélisation statistique de l’hétérogénéité et de l’intermittence des précipitations à fine échelle. L’originalité de la modélisation repose en partie sur l’analyse de données observées par un disdromètre à très fine résolution. Cette modélisation qui diffère des modèles existants dont la résolution est plutôt de l’ordre de la minute, voire de l’heure ou du jour, permet d’obtenir des simulations dont les propriétés sont réalistes sur une large gamme d’échelle. Ce simulateur permet de produire des séries chronologiques dont les caractéristiques statistiques sont similaires aux observations aussi bien à l’échelle de simulation (15s) qu’après dégradation (1h et 1 jour). Les propriétés multi-échelles du simulateur sont obtenues grâce à une approche hybride qui repose sur une simulation à fine échelle des évènements de pluie par un générateur multifractal associé à une simulation du support basée sur une hypothèse de type Poissonienne. Une étape de re-normalisation des taux de pluie assure l’adaptation du générateur à la zone climatique considérée.Le simulateur permet la génération de cartes 2D de lames d’eau. La méthodologie développée pour les séries chronologiques est étendue au cas 2D. Le simulateur stochastique multi-échelle 2D ainsi développé reproduit les caractéristiques géostatistiques et topologiques à la résolution de 1x1 km2. Ce générateur est utilisé dans le cadre d’une étude de faisabilité d’un nouveau système d’observation des précipitations en milieu urbain. Le principe de ce système repose sur l’utilisation de mesures opportunistes de l’affaiblissement subit par les ondes radios émises par les satellites géostationnaires TV-SAT dans la bande 10.7-12.7 GHz. De façon plus spécifique on suppose que les terminaux de réception TVSAT installés en ville chez les particuliers sont capables de mesurer de tels affaiblissements. A ce stade de l’étude nous ne disposons pas de telles observations. L’étude s’appuie donc sur des cartes de précipitations issues du générateur 2D et d’un réseau de capteur hypothétique. Le système d’observation envisagé permettra d’estimer les champs de précipitation (30x30 Km2) et avec une résolution spatiale de 0.5x0.5 Km2. / Precipitations are highly variable across a wide range of both spatial and temporal scales. This variability is a major source of uncertainty for the measurement and modeling, also for the simulation and prediction. Moreover, rainfall is an extremely intermittent process with multiple scale invariance regimes. The rain-field generator developed during the thesis is based on the fine-scale statistic modeling of rain by the mean of its heterogeneity and intermittency. The modeling originality partially rest on the analysis of fine-scale disdrometer data. This model differs from other existing models whose resolution is roughly a minute or even an hour or a day. It provides simulations with realistic properties across a wide range ofscales. This simulator produces time series with statistical characteristics almost identical to the observations both at the 15s resolution and, after degradation, at hourly or daily resolutions. The multi-scale properties of our simulator are obtained through a hybrid approach that relies on a fine scale simulation of rain events using a multifractal generator associated with a rain support simulation based on a Poissonian-type hypothesis. A final re-normalization step of the rain rate is added in order to adapt the generator to the relevant climate area. The simulator allows the generation of 2D water-sheets. The methodology developed in the first part is extended to the 2 Dimension case. The multi-scale 2D stochastic simulator thus developed can reproduce geostatistical and topological characteristics at the spatial resolution of 1x1 km2.This generator is used in the scope of the feasability study of a new observation system for urban area. The principle of this system is based on the opportunistic use of attenuation measurements provided by geostationary TV satellites which radio waves lay in the 10.7 to 12.7 GHz bandwidth. More specifically it is assumed that the SAT-TV reception terminals installed in private homes are able to measure such attenuations. At this stage of the study we do not have such observations. The study is therefore based on rainfall maps generated using the 2D generator in addition to a hypothetical sensor network. The considered observation system will allow to estimate precipitation fields (30 x 30 km2) with a spatial resolution of 0.5x0.5 km2.

Este trabalho fornece informações sobre uma questão importante que é a previsão de preços e apresenta um novo método para fazer previsão para o comportamento de séries temporais financeiras, que foi nomeado de FGAMP (Forecasting with a general average of the multifractal parameters). O novo método utiliza os parâmetros extraídos do momento 5 do método MFDFA (Multifractal Detrended Fluctuation Analysis) como marcador para reconhecer um padrão e realizar uma previsão. As séries temporais utilizadas para verificar a viabilidade do método consistiram de 6 cotações de preços de ativos de alta frequência - minuto a minuto - em um período de um ano, perfazendo aproximadamente 110.000 observações para cada ativo. Um deles é o índice Ibovespa e os outros 5 são ações de alta negociabilidade no mercado, que representam, aproximadamente 32% do próprio índice que é a principal carteira teórica de ações do mercado brasileiro. Um dos diferenciais deste método é que a previsão é realizada para um horizonte de tempo - chamado de janela posterior - aqui testada para 1 dia, 5 dias ou 10 dias. Procurou-se verificar se, em algum ou em alguns momentos, o preço do ativo irá subir - igual ou mais do que um percentual definido - em relação ao último ponto de um intervalo adjacente, chamado de janela anterior. A este percentual foi dado o nome de limiar. Os medidores de qualidade geralmente utilizados em finanças, como por exemplo, MAPE, MASE e RMSE, não são adequados para medir a qualidade deste tipo de previsão, pois verificam a dispersão do previsto em relação ao realizado, observando apenas um ponto. O medidor de qualidade aqui utilizado é o Valor Preditivo Positivo, amplamente difundido na área da saúde em tabelas de validação de diagnóstico e demonstra o grau de acerto do previsto acontecer em um horizonte de tempo determinado. O critério para a tomada de decisão foi baseado nos valores dos parâmetros numa primeira metade da série, aqui denominada de série de treinamento, sendo que os testes foram feitos na segunda metade da série, aqui denominada de série de teste. Os resultados encontrados apresentam 7 parâmetros que são bons marcadores para previsão: Hq(9), Hq(10), Hq(11), tq(11), hq(7), hq(8) e Dq(7), de acordo com a nomenclatura aqui adotada. Um tamanho de janela anterior - utilizada para o cálculo dos parâmetros - bastante eficiente é o de 540 pontos, sendo que são melhores para prever um horizonte de tempo de 10 dias (um tamanho também razoável encontrado para a janela posterior). O objetivo principal da pesquisa era o de estudar a viabilidade do uso destes parâmetros como marcadores do estado do sistema e verificar se conseguiam indicar o comportamento futuro com alguma eficiência. O resultado foi que o modelo FGAMP apresenta-se bastante viável, chegando a acertar até 97,54% das vezes quando afirma que o preço do ativo irá subir igual ou mais do que 1%, até 91,94% das vezes para uma subida de 2% ou mais e até 88,70% das vezes quando afirma uma subida de 3% ou mais. Foi definido como comparador de eficiência o percentual de acerto de quando é afirmado que o preço do ativo irá subir mais ou igual ao limiar em um ou alguns pontos para todas as janelas testadas (que seria uma solução trivial), sendo que aqui este percentual foi denominado de porcentagem real. Percebe-se que quanto maior o percentual que se quer prever (aqui testados 1%, 2% e 3%) maior é a eficiência do modelo FGAMP em relação à porcentagem real: o novo método chega a ser 128,65% mais eficiente. Isto demonstra a viabilidade do método e os resultados evidenciam que ele pode ser útil para investidores e analistas de mercado, no mínimo como uma nova ferramenta em Análise Técnica / This paper provides information about an important issue that is price forecasting and presents a new method to forecast financial time series behaviour, which was named FGAMP (Forecasting with a general average of the multifractal parameters). The new method uses the parameters extracted from moment 5 of the MFDFA (Multifractal Detrended Fluctuation Analysis) method as a marker to recognize a pattern and perform a prediction. The time series used to verify the viability of the method consisted of 6 quotes of prices of high frequency assets - minute by minute - in a period of one year, making approximately 110,000 observations for each asset. One of them is the Ibovespa index and the other 5 are highly tradable shares in the market, representing approximately 32% of the index itself, which is the main theoretical portfolio of shares in the Brazilian market. One of the differentials of this method is that the forecast is performed for a time horizon - called a posterior window - here tested for 1 day, 5 days or 10 days. We sought to verify whether the asset price will rise at any or in some moments - equal to or more than a defined percentage - in relation to the last point of an adjacent interval, called the previous window. This percentage was given the name of threshold. Quality meters generally used in finance, such as MAPE, MASE and RMSE, are not adequate to measure the quality of this type of forecast, as they verify the dispersion of the predicted relative to the realized, observing only one point. The quality measure used here is the Positive Predictive Value, widely diffused in the health area in diagnostic validation tables and demonstrates the degree of accuracy of what is expected to happen in a given time horizon. The criterion for decision making was based on the values of the parameters in the first half of the series, here called the training series, and the tests were done in the second half of the series, here called the test series. The results show 7 parameters that are good predictor markers: Hq (9), Hq (10), Hq (11), tq (11), hq (7), hq (8) and Dq (7), according to the nomenclature adopted here. A previous window size - used for the calculation of the parameters - very efficient is 540 points, and these windows are better to predict a time horizon of 10 days (a reasonable size also found for the posterior window). The main goal of the research was to study the feasibility of using these parameters as markers of the state of the system and to verify if they were able to indicate future behavior with some efficiency. The result was that the FGAMP model is quite feasible, reaching up to 97.54% accuracy when it affirms that the price of the asset will rise equal to or greater than 1%, up to 91.94% of the time for a rise Of 2% or more and up to 88.70% of the time when it affirms an increase of 3% or more. It was defined as efficiency comparator the percentage of correctness when it is stated that the price of the asset will rise more or equal to the threshold in one or some points for all the windows tested (which would be a trivial solution). That percentage was denominated, here, real percentage. It is noticed that the greater the percentage that is predicted (here tested 1%, 2% and 3%) the greater the efficiency of the FGAMP model in relation to the real percentage: the new method reaches more efficiency (till 128.65% more efficient). This demonstrates the feasibility of the method and the results evidence that it can be useful to investors and market analysts, at least as a new tool in Technical Analysis

La description multifractale des signaux a été initiée au cours des vingt dernières années, notamment dans le domaine de la turbulence pleinement développée. Les propriétés de régularité ponctuelle des signaux étudiés sont caractérisées à l'aide d'un spectre de singularités. L'analyse multifractale de ces signaux consiste à mesurer ce spectre de singularités, à l'aide de formalismes multifractals. L'apparition des transformées en ondelette, à la même époque, a permis d'affiner la pratique de l'analyse multifractale, sans pour autant toujours reposer sur des bases mathématiques solides. S. Jaffard a récemment introduit les coefficients dominants, qui permettent de construire un formalisme multifractal mathématiquement bien fondé, et au cadre d'application large : il rend possible la mesure de l'ensemble du spectre de singularités, et reste valide lorsque les signaux analysés contiennent des singularités oscillantes. Ce nouvel outil est pour la première fois mis en oeuvre, numériquement caractérisé et appliqué à des signaux de vitesse turbulente. La question du bon usage pratique des formalismes multifractals, qui reposent sur la mesure d'exposants de fonctions de structure, est essentielle. Le travail présenté se propose d'y apporter des éléments de réponse. Une étude numérique, sur un large panel de processus multifractals synthétiques, a permis d'illustrer et de caractériser un aspect essentiel de l'analyse multifractale pratique, l'existence d'un ordre critique. Un estimateur de cet ordre critique est construit et numériquement caractérisé. Une relecture des résultats obtenus en turbulence est alors effectuée. Enfin, la question de l'universalité des exposants des fonctions de structure en turbulence pleinement développée est abordée. Une modélisation de l'exposant de la fonction de structure d'ordre trois est proposée et comparée à des résultats expérimentaux, mettant en évidence le caractère non universel de sa valeur.

L'objectif de l'analyse multifractale (introduite dans le cadre de la turbulence pleinement developpee) est de déterminer la dimension des ensembles de points où une fonction a une régularité hölderienne fixée. Cette information ne peut être calculée directement sur les signaux réels et une formule appelée formalisme multifractal a été introduite pour calculer ces dimensions à partir de quantités obtenues directement par traitement du signal. Elle n'est pas vraie en toute généralité et nous étudions dans cette thèse différentes situations dans lesquelles le formalisme multifractal n'est pas valide.<br />Des résultats de type " Baire " démontrent que le formalisme multifractal est vrai quasi-sûrement pour de petites valeurs de l'exposant de Hölder et faux pour les autres valeurs. Nous montrons que cela est dû à la présence de singularités oscillantes.<br />D'autre part le formalisme multifractal ne s'applique qu'aux fonctions continues. Nous montrons qu'il est possible de généraliser la formule, en passant d'un critère de régularité ponctuelle hölderienne à un critère plus faible, à des fonctions qui peuvent ne plus être continues.<br />Enfin nous étudions un cas particulier de phénomène oscillant en dimension 2 qui n'est pas caractérisé par les critères de régularité ponctuelle précédents. Nous proposons une méthode d'analyse de ce comportement à base d'un algorithme de traitement de l'image.

Il est fondamental, dans beaucoup de domaines (étude de la<br />turbulence , traitement du signal), mais également d'un point de vue théorique, de pouvoir détecter et caractériser les singularités d'une fonction ou d'une distribution. Pour mesurer la régularité autour d'un point $x_0$ d'une fonction $f$, on utilise souvent l'exposant ponctuel de \ho de $f$ en $x_0$, noté $\alp(x_0)$. Mais cet exposant n'est pas suffisant pour décrire entièrement les comportements locaux.<br /><br />L'exposant de \ho local, noté $\all(x_0)$, permet de compléter les<br />informations procurées par $\alp(x_0)$. Les relations entre les<br />fonctions $x\ra \all(x)$ et $x\ra\alp(x)$ sont complètement mises a<br />jour.<br /><br />Les espaces 2-microlocaux, notés $\css'$, permettent de généraliser la notion d'exposant de régularité. Une caractérisation temporelle des espaces $\css'$ pour les fonctions $C^\ep$ ($\ep>0$) est démontrée. Cela s'avère utile en traitement du signal, car accessible numériquement (FRACLAB).<br /><br />Les espaces $\css'$ permettent d'associer à un point non plus un ou<br />plusieurs exposants, mais une courbe dans $\R^2$ appelée frontière<br />2-microlocale. Cette dernière englobe les exposants cités plus<br />haut, et donne une description géométrique de la régularité<br />locale. On montre que la frontière 2-microlocale d'une distribution $f$ en $x_0$ est la transformée de Legendre d'une fonction $\chi_(x_0)$ appelée (\em spectre 2-microlocal): on parle du formalisme 2-microlocal. $\chi_(x_0)$ est lié au comportement des coefficients d'ondelettes de $f$ autour de $x_0$. L'étude de<br />$\chi_(x_0)$ et du formalisme 2-microlocal s'avère fructueuse: les<br />liens avec les exposants sont explicités, des propriétés<br />nouvelles de la régularité sont mises en évidence. Le calcul de<br />$\chi_(x_0)$ est effectué pour plusieurs fonctions classiques ou<br />originales.<br /><br />Deux applications du spectre 2-microlocal à l'analyse multifractale<br />sont présentées. Nous proposons la construction de fonctions et<br />processus multifractals. étant donnée une mesure de Borel positive<br />$\mu$ et deux réels positifs $s_0$ et $p_0$ vérifiant<br />$s_0-1/p_0>0$, on étudiera la fonction $F_\mu$ <br />$$F_\mu(x)=\sum_(j\geq 0) \sum_(k\in \mathbb(Z)) \pm<br />2^(-j(s_0-\frac(1)(p_0))) |\mu\big ([k2^(-j),(k+1)2^(-j))\big<br />)|^(\frac(1)(p_0)) \psijk(x).$$ Si $\mu$ satisfait un certain<br />formalisme multifractal (proche du formalisme usuel) pour les mesures, alors la fonction $F_\mu$ satisfait au formalisme multifractal pour les fonctions. Ce résultat s'applique aux grandes classes de mesures multifractales: quasi-Bernoulli, cascades de Mandelbrot, ... En particulier, on résout ainsi la conjecture de Arnéodo, Bacry, Muzy sur la valeur du spectre de leurs cascades aléatoires d'ondelettes, qui servaient de modèle à un fluide turbulent.<br /><br />Enfin la relation entre présence d'oscillations et validité du<br />formalisme multifractal est étudiée. Ce travail a une conséquence<br />inattendue: on montre qu'un seuillage effectué sur les coefficients<br />d'ondelettes peut créer des singularités oscillantes et faire<br />échouer le formalisme.

Histopathological classification and grading of biopsy specimens play an important role in early cancer detection and prognosis. Nottingham Grading System (NGS) is one of the standard grading procedures used in breast cancer assessment, where three parameters, Mitotic Count (MC), Nuclear Pleomorphism (NP), and Tubule Formation (TF) are used for prognostic information. The grading takes into account the deviations in cellular structures and appearance between tumour and normal cells, using measures such as density, size, colour, and regularity. Cell structures in tissue images are also known to exhibit multifractal characteristics. This research focused on the multifractal properties of several graded biopsy specimens and analysed the dependency and variation of the fractal parameters with respect to the scores pre-assigned by pathologists. The effectiveness of using multifractal techniques on breast cancer grading was measured with a set of quantitative evaluations for MC, NP, and TF criteria. The developed method for MC scoring has obtained 82.87% true positive rate on detecting mitotic cells. Furthermore, the overall positive classification rates for NP and TF analysis were 67.38% and 71.82%, respectively, while obtaining 30.26% of false classification rate for NP analysis and 27.17% for TF analysis. The results have shown that multifractal formalism is a feasible and novel method that could be used for automatic grading of biopsy sections.

Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2017-12-01T23:34:01Z No. of bitstreams: 1 SergioRobertoDantas_DISSERT.pdf: 1439747 bytes, checksum: d876ed77a5433b952a46ba0482101886 (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2017-12-05T21:54:18Z (GMT) No. of bitstreams: 1 SergioRobertoDantas_DISSERT.pdf: 1439747 bytes, checksum: d876ed77a5433b952a46ba0482101886 (MD5) / Made available in DSpace on 2017-12-05T21:54:18Z (GMT). No. of bitstreams: 1 SergioRobertoDantas_DISSERT.pdf: 1439747 bytes, checksum: d876ed77a5433b952a46ba0482101886 (MD5) Previous issue date: 2017-09-06 / Frequentemente, as superf?cies seletivas em frequ?ncias t?m recebido grande aten??o por parte de pesquisadores em todo o mundo, devido a suas caracter?sticas de filtragem. Essas estruturas evolu?ram em termos de fabrica??o. Assim, as geometrias utilizadas, inicialmente, eram fios em forma de grade e, posteriormente, diversos tipos de novas geometrias tais como: elementos retangulares, quadrados, circulares, an?is, espiras quadradas etc., foram utilizadas. Recentemente, elementos fractais e, mais recentemente, multifractais foram empregados. O emprego dessas geometrias ? feito com o objetivo de se obter uma resposta em frequ?ncia espec?fica. Par?metros importantes, como largura de banda e frequ?ncia de resson?ncia s?o atendidos a partir do emprego de uma determinada geometria. Neste trabalho ? proposta uma geometria multifractal com dupla similaridade, que tem como caracter?stica principal baixa sensibilidade ? varia??o da periodicidade com rela??o ? frequ?ncia de resson?ncia. Essa especificidade trar? ganho no que diz respeito ? elabora??o do projeto, pois o controle da largura de banda ? feito apenas com a altera??o da periodicidade. Diversas simula??es foram implementadas no Ansoft Designer e para efeito de comprova??o, estruturas tradicionais foram simuladas, visando ? demonstra??o do efeito da periodicidade na frequ?ncia de resson?ncia e, em seguida, dois prot?tipos foram constru?dos e feitas medi??es para validar experimentalmente as simula??es. / Often, frequency selective surfaces have received wide attention from researchers around the world because of their filtering characteristics. These structures evolved in terms of manufacturing. Thus, the geometries used, initially, were yarns in the form of a grid and later, several types of new geometries such as: rectangular, square, circular, rings, square, etc., were used. Recently, fractals and, more recently, multifractal elements have been employed. The use of these geometries is done in order to obtain a specific frequency response. Important parameters such as bandwidth and resonant frequency are met from the use of a given geometry. In this work a multifractal geometry with double similarity is proposed, which has as main characteristic low sensitivity to the variation of the periodicity with respect to the resonance frequency. This specificity will bring gain with regard to the elaboration of the project, because the control of the bandwidth is made only with the change of periodicity. Several simulations were implemented in Ansoft Designer and for the purpose of proving, traditional structures were simulated, aiming at demonstrating the effect of periodicity on the resonance frequency, and then two prototypes were constructed and measurements were taken to experimentally validate the simulations.