A Floresta Atlântica que originalmente formava uma área contínua com mais de 150 milhões de hectares sofre constante degradação. Atualmente somente cerca de 7-8% dessa cobertura vegetal ainda existe, em sua maioria, na forma de fragmentos florestais secundários. A Estação Ecológica de Caetetus possui um dos mais significativos remanescentes da Floresta Estacional Semidecidual que revestia quase todo o interior do estado de São Paulo, parte de Minas Gerais, Mato Grosso do Sul, Paraguai e Argentina. Para compreender as relações entre vegetação nativa e os solos são necessários estudos detalhados que inclui o funcionamento físico-hídrico do solo, assim, as propriedades físicas que possuem grande influência nas relações químicas e biológicas, desempenham papel central nos estudos da dinâmica dos processos do solo. O objetivo desse trabalho foi obter parâmetros quantitativos da estrutura do solo pela análise multifractal e comparar valores de qualidade física de áreas naturais com valores de referência de índices de qualidade física do solo encontrados na literatura, fornecendo dados que podem ser utilizados na avaliação da qualidade do solo em outros tipos de uso. Foi utilizado um banco de dados físico-hídrico e de imagens micromorfológicas de solos sob Floresta Estacional Semidecidual da parcela permanente da Estação Ecológica Caetetus, (Gália - SP, Brasil). Foram analisados três índices, índice S, capacidade de aeração relativa (ACt/Pt) e capacidade de campo relativa (CC/Pt). Os horizontes analisados apresentaram diferentes formas e simetrias pela análise multifractal indicando diferenças na distribuição de poros, com diferença significativa entre os parâmetros de forma f(?)razão, ?razão e ?? (p < 0.05). Os valores de S encontrados foram superiores ao limite proposto de qualidade física do solo (0,035). Os horizontes A e E apresentaram os valores mais altos, pois sua textura arenosa proporciona maiores valores de n. Os horizontes B apresentaram os valores mais baixos, pois seu adensamento natural reflete em valores menores de n. Os valores encontrados para os índices de qualidade do solo ACt/Pt e CC/Pt foram inferiores e superiores aos valores considerados ideais. Os resultados encontrados sugerem a reavaliação dos níveis limites considerados ideias da literatura para a avaliação da qualidade física do solo em regiões tropicais. Por meio da quantificação e integração das propriedades espaciais do sistema poroso do solo, a análise multifractal pode melhorar os sistemas de classificação da estrutura do solo e gerar parâmetros que, incorporados em funções de pedotransferência, agregam o parâmetro estrutura nas predições. / The Atlantic Forest originally covered around 150 million hectares undergoes constant degradation. Nowadays, only 7-8% of the original forest still remains, mostly as secondgrowth forests. The Caetetus Ecological Station has one of the most significant areas of Semideciduous Forest which covered almost all the interior of São Paulo State, part of Minas Gerais, Mato Grosso do Sul, Paraguay and Argentina. To understand the relationship between original vegetation and soil detailed studies are necessary which includes the hydro-physical soil function allowing to characterize the soil behavior. Thus, physical properties have strong influence in the chemical and biological relations and play a central role in studies of soils processes dynamics. The objective of this research was to obtain quantitative parameters of soil structure by multifractal analysis using hydro-physical database and soil micromorphology images of soils under Semi-deciduous Forest in a permanent plot of Caetetus Ecological Station (Gália - SP, Brazil) and compare soil physics quality values with of soil physical quality values founded in the literature, providing data to evaluate soil quality in areas with different soil uses. Three soil quality indexes were used, S index, relative air capacity (ACt/Pt) and relative field capacity (FC/Pt). The soils horizons showed different shapes and symmetries by multifractal analysis indicating differences of pores distribution, the parameters of multifractal shape f(?)ratio, ?ratio and ?? (p < 0.05) showed significant differences. The S values founded were higher and lower than the limit of soil physical quality proposed (0,035). The A and E horizon showed the highest values because its sandy texture allow high n values. The B horizons showed the lowest values, because its natural densificaition decreases the n values. The values founded for ACt/Pt and CC/Pt were higher and lower than the ideal limits. The results founded suggest a reevaluation of the ideal soil physical quality limits for tropical regions. Trough the quantification and integration of soil space properties, the multifractal analysis can improve structure classification systems and create a structure parameter that can be added in pedotransfer functions.

A Floresta Atlântica que originalmente formava uma área contínua com mais de 150 milhões de hectares sofre constante degradação. Atualmente somente cerca de 7-8% dessa cobertura vegetal ainda existe, em sua maioria, na forma de fragmentos florestais secundários. A Estação Ecológica de Caetetus possui um dos mais significativos remanescentes da Floresta Estacional Semidecidual que revestia quase todo o interior do estado de São Paulo, parte de Minas Gerais, Mato Grosso do Sul, Paraguai e Argentina. Para compreender as relações entre vegetação nativa e os solos são necessários estudos detalhados que inclui o funcionamento físico-hídrico do solo, assim, as propriedades físicas que possuem grande influência nas relações químicas e biológicas, desempenham papel central nos estudos da dinâmica dos processos do solo. O objetivo desse trabalho foi obter parâmetros quantitativos da estrutura do solo pela análise multifractal e comparar valores de qualidade física de áreas naturais com valores de referência de índices de qualidade física do solo encontrados na literatura, fornecendo dados que podem ser utilizados na avaliação da qualidade do solo em outros tipos de uso. Foi utilizado um banco de dados físico-hídrico e de imagens micromorfológicas de solos sob Floresta Estacional Semidecidual da parcela permanente da Estação Ecológica Caetetus, (Gália - SP, Brasil). Foram analisados três índices, índice S, capacidade de aeração relativa (ACt/Pt) e capacidade de campo relativa (CC/Pt). Os horizontes analisados apresentaram diferentes formas e simetrias pela análise multifractal indicando diferenças na distribuição de poros, com diferença significativa entre os parâmetros de forma f(?)razão, ?razão e ?? (p < 0.05). Os valores de S encontrados foram superiores ao limite proposto de qualidade física do solo (0,035). Os horizontes A e E apresentaram os valores mais altos, pois sua textura arenosa proporciona maiores valores de n. Os horizontes B apresentaram os valores mais baixos, pois seu adensamento natural reflete em valores menores de n. Os valores encontrados para os índices de qualidade do solo ACt/Pt e CC/Pt foram inferiores e superiores aos valores considerados ideais. Os resultados encontrados sugerem a reavaliação dos níveis limites considerados ideias da literatura para a avaliação da qualidade física do solo em regiões tropicais. Por meio da quantificação e integração das propriedades espaciais do sistema poroso do solo, a análise multifractal pode melhorar os sistemas de classificação da estrutura do solo e gerar parâmetros que, incorporados em funções de pedotransferência, agregam o parâmetro estrutura nas predições. / The Atlantic Forest originally covered around 150 million hectares undergoes constant degradation. Nowadays, only 7-8% of the original forest still remains, mostly as secondgrowth forests. The Caetetus Ecological Station has one of the most significant areas of Semideciduous Forest which covered almost all the interior of São Paulo State, part of Minas Gerais, Mato Grosso do Sul, Paraguay and Argentina. To understand the relationship between original vegetation and soil detailed studies are necessary which includes the hydro-physical soil function allowing to characterize the soil behavior. Thus, physical properties have strong influence in the chemical and biological relations and play a central role in studies of soils processes dynamics. The objective of this research was to obtain quantitative parameters of soil structure by multifractal analysis using hydro-physical database and soil micromorphology images of soils under Semi-deciduous Forest in a permanent plot of Caetetus Ecological Station (Gália - SP, Brazil) and compare soil physics quality values with of soil physical quality values founded in the literature, providing data to evaluate soil quality in areas with different soil uses. Three soil quality indexes were used, S index, relative air capacity (ACt/Pt) and relative field capacity (FC/Pt). The soils horizons showed different shapes and symmetries by multifractal analysis indicating differences of pores distribution, the parameters of multifractal shape f(?)ratio, ?ratio and ?? (p < 0.05) showed significant differences. The S values founded were higher and lower than the limit of soil physical quality proposed (0,035). The A and E horizon showed the highest values because its sandy texture allow high n values. The B horizons showed the lowest values, because its natural densificaition decreases the n values. The values founded for ACt/Pt and CC/Pt were higher and lower than the ideal limits. The results founded suggest a reevaluation of the ideal soil physical quality limits for tropical regions. Trough the quantification and integration of soil space properties, the multifractal analysis can improve structure classification systems and create a structure parameter that can be added in pedotransfer functions.

La caractérisation de texture est centrale dans de nombreuses applications liées au traitement d’images. L’analyse de textures peut être envisagée dans le cadre mathématique de l’analyse multifractale qui permet d’étudier les fluctuations de la régularité ponctuelle de l’amplitude d’une image et fournit les outils pratiques pour leur évaluation grâce aux coefficients d’ondelettes ou aux coefficients dominants. Bien que mise à profit dans de nombreuses applications, l’analyse multifractale souffre à présent de deux limitations majeures. Premièrement, l’estimation des paramètres multifractaux reste délicate, notamment pour les images de petites tailles. Deuxièmement, l’analyse multifractale a été jusqu’à présent uniquement considérée pour l’analyse univariée d’images, alors que les données à étudier sont de plus en plus multivariées. L’objectif principal de cette thèse est la mise au point de contributions pratiques permettant de pallier ces limitations. La première limitation est abordée en introduisant un modèle statistique générique pour le logarithme des coefficients dominants, paramétrisé par les paramètres multifractaux d’intérêt. Ce modèle statistique permet de contrebalancer la variabilité résultant de l’analyse d’images de petite taille et de formuler l’estimation dans un cadre bayésien. Cette approche aboutit à des procédures d’estimation robustes et efficaces, que ce soit pour des images de petites ou grandes tailles. Ensuite, l’analyse multifractale d’images multivariées est traitée en généralisant ce cadre bayésien à des modèles hiérarchiques capables de prendre en compte l’hypothèse d’une évolution lente des propriétés multifractales d’images multi-temporelles ou multi-bandes. Ceci est réalisé en définissant des lois a priori reliant les propriétés dynamiques des paramètres multifractaux des différents éléments composant le jeu de données. Différents types de lois a priori sont étudiés dans cette thèse au travers de simulations numériques conduites sur des images multifractales multivariées synthétiques. Ce travail est complété par une étude du potentiel apport de l’analyse multifractale et de la méthodologie bayésienne proposée pour la télédétection à travers l’exemple de l’imagerie hyperspectrale. / Texture characterization is a central element in many image processing applications. Texture analysis can be embedded in the mathematical framework of multifractal analysis, enabling the study of the fluctuations in regularity of image intensity and providing practical tools for their assessment, the coefficients or wavelet leaders. Although successfully applied in various contexts, multi fractal analysis suffers at present from two major limitations. First, the accurate estimation of multifractal parameters for image texture remains a challenge, notably for small sample sizes. Second, multifractal analysis has so far been limited to the analysis of a single image, while the data available in applications are increasingly multivariate. The main goal of this thesis is to develop practical contributions to overcome these limitations. The first limitation is tackled by introducing a generic statistical model for the logarithm of wavelet leaders, parametrized by multifractal parameters of interest. This statistical model enables us to counterbalance the variability induced by small sample sizes and to embed the estimation in a Bayesian framework. This yields robust and accurate estimation procedures, effective both for small and large images. The multifractal analysis of multivariate images is then addressed by generalizing this Bayesian framework to hierarchical models able to account for the assumption that multifractal properties evolve smoothly in the dataset. This is achieved via the design of suitable priors relating the dynamical properties of the multifractal parameters of the different components composing the dataset. Different priors are investigated and compared in this thesis by means of numerical simulations conducted on synthetic multivariate multifractal images. This work is further completed by the investigation of the potential benefit of multifractal analysis and the proposed Bayesian methodology for remote sensing via the example of hyperspectral imaging.

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.

Dans cette thèse, on étudie principalement l’équation de Boltzmann homogène 3D pour les potentiels durs et les potentiels modérément mous et l’équivalence entre une EDS à sauts et l’EDP correspondante. En particulier, on calcule le spectre multifractal de certains processus stochastiques, on étudie le caractère bien-posé et la propagation du chaos pour l’équation de Boltzmann. Dans le premier chapitre, on étudie les propriétés trajectorielle pathologiques du processus stochastique (Vt)t_0 représentant l’évolution de la vitesse d’une particule typique dans un gaz modélisé par l’équation de Boltzmann pour les potentiels durs ou modérément mous. Nous montrons que ce processus est multifractal et qu’il a un spectre déterministe. Pour les potentiels durs, nous donnons aussi le spectre multifractal du processus $X_t =\int_0^t V_s ds$, représentant l’évolution de la position de la particule typique. Dans le deuxième chapitre, nous étudions l’unicité de la solution faible à l’équation de Boltzmann dans la classe de toutes les solutions mesures, pour les potentiels modérément mous. Ceci nous permet aussi d’obtenir un taux quantitatif de propagation du chaos pour le système de particules de Nanbu. / This thesis mainly studies the 3D homogeneous Boltzmann equation for hard potentials and moderately soft potentials and the equivalence between some jumping SDE and the corresponding PDE. In particular, we compute the multifractal spectrum of some stochastic processes, study the well-posedness and the propagation of chaos for the Boltzmann equation. The purpose of the first chapter is to study the pathwise properties of the stochastic process $(V_t)_{t\geq0}, representing the time-evolution of the velocity of a typical particle in a gas modeled by the Boltzmann equation for hard or moderately potentials. We show that this process is multifractal and has a deterministic spectrum. For hard potentials, we also give the multifractal spectrum of the process $X_t =\int_0^t V_s ds$, representing the time-evolution of the position of the typical particle. The second chapter is devoted to study the uniqueness of the weak solution to the Boltzmann equation in the class of all measure solutions, in the case of moderately soft potentials. This allows us to obtain a quantitive rate of propagation of chaos for Nanbu particle system for this singular interaction. Finally in the third chapter, we extend Figalli’s work [19] to study the relation between some jumping SDE and the corresponding Fokker-Planck equation. We prove that for any weak solution $(ft)_{t\in[0,T]}$ of the PDE, there exists a weak solution to the SDE of which the time-marginals are given by the family $(f_t)_{t\in[0,T]$

Dans cette thèse, on étudie diverses propriétés dimensionnelles de la régularité de processus de difusions à sauts, solution d’une classe d’équations différentielles stochastiques à sauts. En particulier, on décrit la fluctuation de la régularité höldérienne de ces processus et celle de la dimension locale pour la mesure d’occupation qui leur est associée en calculant leur spectre multifractal. La dimension de Hausdorff de l’image et du graphe de ces processus ont aussi étudiées.Dans le dernier chapitre, on applique une nouvelle notion de dimension de grande échelle pour décrire l’asymptote à l’infini du temps de séjour d’un mouvement brownien en dimension 1 sous des frontières glissantes / In this dissertation, we study various dimension properties of the regularity of jump di usion processes, solution of a class of stochastic di erential equations with jumps. In particular, we de- scribe the uctuation of the Hölder regularity of these processes and that of the local dimensions of the associated occupation measure by computing their multifractal spepctra. e Hausdor dimension of the range and the graph of these processes are also calculated.In the last chapter, we use a new notion of “large scale” dimension in order to describe the asymptotics of the sojourn set of a Brownian motion under moving boundaries

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

Dans cette thèse, nous étudions la minimalité et la propriété chaotique de systèmes dynamiques p-adiques. Nous étudions aussi des propriétés multifractales des séries de Davenport avec translation de phases. Dans la première partie, nous commençons par l'étude des systèmes dynamiques affines sur Zp. Nous trouvons une condition nécessaire et suffisante pour qu'un tel système soit minimal. En outre, nous exhibons toutes ses composantes strictement ergodiques si le système n'est pas minimal. De plus, nous étudions aussi les systèmes monômes sur le groupe 1+pZp. Ensuite nous étudions les polynômes localement dilatants et transitifs. Pour un tel polynôme, limité sur son ensemble de Julia, nous prouvons qu'il est conjugué à un sous-shift de type fini. Dans la deuxième partie, nous étudions les séries de Davenport avec translation de phases. Après avoir calculé le saut d'une telle série à chaque point, nous trouvons l'ensemble des points discontinus et obtenons une condition nécessaire et suffisante pour qu'une série de Davenport avec translation de phases soit continue sur R. La convergence ponctuelle de la série est aussi étudiée. Ensuite, nous estimons la borne inférieure de l'exposant hölderien de la série de Davenport avec de phase rationnelle et la borne supérieure du spectre de la singularité / In this thesis, we study the minimality and the chaotic property of p-adic dynamical systems and some multifractal properties of phase translated Davenport series. In the first part, we begin with the study of affine dynamical systems on Zp. We find a necessary and sufficient condition for such a system to be minimal. Furthermore, all its strictly ergodic components are exhibited when it is not minimal. In addition, we study monomial systems on the group 1 + pZp. Then transitive locally expanding polynomial systems are studied. It is proved that such a polynomial system, restricted to its Julia set, is conjugate to a subshift of finite type. In the second part, we study phase translated Davenport series. After having calculated the jump of the series at each point, we characterize the set of discontinuous points and get a sufficient and necessary condition for the series to be continuous on R. Furthermore, the pointwise convergence of the series is studied. Then we estimate the lower bound of the Hölder-exponent of rational translated Davenport series and get an upper bound estimation on the spectrum of singularity. The lower bound of the Hölder-exponent are also discussed for some irrational translated series

Réduire la vulnérabilité et accroître la résilience des sociétés d'aujourd'hui aux fortes précipitations et inondations exige de mieux caractériser leur très forte variabilité spatio-temporelle observable sur une grande gamme d'échelle. Nous mettons donc en valeur tout au long de cette thèse l'intérêt méthodologique d'une approche multifractale comme étant la plus appropriée pour analyser et simuler cette variabilité. Cette thèse aborde tout d'abord le problème de la qualité des données, qui dépend étroitement de la résolution temporelle effective de la mesure, et son influence sur l'analyse multifractale et la détermination de lois d'échelle des processus de précipitations. Nous en soulignons les conséquences pour l'hydrologie opérationnelle. Nous présentons la procédure SERQUAL qui permet de quantifier cette qualité et de sélectionner les périodes correspondant aux critères de qualité requise. Un résultat surprenant est que les longues chronologies de pluie ont souvent une résolution effective horaire et rarement de 5 minutes comme annoncée. Ensuite, cette thèse se penche sur les données sélectionnées pour caractériser la structure temporelle et le comportement extrême de la pluie. Nous analysons les sources d'incertitudes dans les méthodes multifractales « classiques » d'estimation des paramètres et nous en déduisons des améliorations pour tenir compte, par exemple, de la taille finie des échantillons et des limites de la dynamique des capteurs. Ces améliorations sont utilisées pour obtenir les caractéristiques multifractales de la pluie à haute résolution de 5 minutes pour plusieurs départements de la France (à savoir, les départements 38, 78, 83 et 94) et pour aborder la question de l'évolution des précipitations durant les dernières décennies dans le cadre du changement climatique. Cette étude est confortée par l'analyse de mosaïques radars concernant trois événements majeurs en région parisienne. Enfin, cette thèse met en évidence une autre application des méthodes développées, à savoir l'hydrologie karstique. Nous discutons des caractéristiques multifractales des processus de précipitation et de débit à différentes résolutions dans deux bassins versant karstiques au sud de la France. Nous analysons, en utilisant les mesures journalière, 30 minutes et 3 minutes, la relation pluie-débit dans le cadre multifractal. Ceci est une étape majeure dans la direction d'une définition d'un modèle multi-échelle pluie-débit du fonctionnement des bassins versants karstiques / To reduce vulnerability and to increase resilience of nowadays societies to heavy precipitations and floods require better understanding of their very strong spatio-temporal variability observable over a wide range of scales. Therefore, throughout this thesis we highlight the methodological interest of a multifractal approach as being most appropriate to analyze and to simulate such the variability. This thesis first discusses the problem of data quality, which strongly depends on the effective temporal resolution of the measurements, and its influence on multifractal analysis determining the scaling laws of precipitation processes. We emphasize the consequences for operational hydrology. We present the SERQUAL procedure that allows to quantify the data quality and to select periods corresponding to the required quality criteria. A surprising result is that long chronological series of rainfall often have an effective hourly data, rather than the pretended 5-minute rainfall data. Then, this thesis focuses on the selected data to characterize the temporal structure and extreme behaviour of rainfall. We analyze the sources of uncertainties of already "classical" multifractal methods for the parameter estimates, and we therefore developed their improvements considering e.g., the finite size of data samples and the limitation of sensor dynamics. These improvements are used to obtain proper multifractal characteristics of 5-minute high-resolution rainfall for several French departments (i.e., 38, 78, 83 and 94), and hence to raise the question of preicipitation evolution during the last decades in the context of climate change. This study is reinforced by the analysis of radar mosaics for three major events in the Paris region. Finally, this thesis highlights another application of the developed methods, i.e. for the karst hydrology. We discuss the multifractal characteristics of rainfall and runoff processes observed at the different resolutions in two karst watersheds on the south of France. Using daily, 30-minute and 3-minute measurements we analyse the rainfall-runoff relationships within the multifractal framework. This is a major step towards defining a rainfall-runoff multi-scale model of the karst watershed functioning

Osteoarthritis is a large problem affecting many patients globally, and diagnosis of osteoarthritis is often done using evidence from arthroscopic surgeries. Making a correct diagnosis is hard, and takes years of experience and training on thousands of images. Therefore, developing an automatic solution to perform the diagnosis would be extremely helpful to the medical field. Since machine learning has been proven to be useful and effective at classifying and segmenting medical images, this thesis aimed at solving the problem using machine learning methods. Multifractal analysis has also been used extensively for medical imaging segmentation. This study proposes two methods of automatic segmentation using neural networks and multifractal analysis. The thesis was performed using real arthroscopic images from surgeries. MultiResUnet architecture is shown to be well suited for pixel perfect segmentation. Classification of multifractal features using neural networks is also shown to perform well when compared to related studies.