Hurst exponent and variance are two quantities that often characterize real-life, highfrequency observations. We develop the method for simultaneous estimation of a timechanging Hurst exponent H(t) and constant scale (variance) parameter C in a multifractional Brownian motion model in the presence of white noise based on the asymptotic behavior of the local variation of its sample paths. We also discuss the accuracy of the stable and simultaneous estimator compared with a few selected methods and the stability of computations that use adapted wavelet filters. Multifractals have become popular as flexible models in modeling real-life data of high frequency. We developed a method of testing whether the data of high frequency is consistent with monofractality using meaningful descriptors coming from a wavelet-generated multifractal spectrum. We discuss theoretical properties of the descriptors, their computational implementation, the use in data mining, and the effectiveness in the context of simulations, an application in turbulence, and analysis of coding/noncoding regions in DNA sequences. The wavelet thresholding is a simple and effective operation in wavelet domains that selects the subset of wavelet coefficients from a noised signal. We propose the selection of this subset in a semi-supervised fashion, in which a neighbor structure and classification function appropriate for wavelet domains are utilized. The decision to include an unlabeled coefficient in the model depends not only on its magnitude but also on the labeled and unlabeled coefficients from its neighborhood. The theoretical properties of the method are discussed and its performance is demonstrated on simulated examples.

The analysis of Human brain activity in magnetoencephalography (MEG) can be generally conducted in two ways: either by focusing on the average response evoked by a stimulus repeated over time, more commonly known as an ''event-related field'' (ERF), or by decomposing the signal into functionally relevant oscillatory or frequency bands (such as alpha, beta or gamma). However, the major part of brain activity is arrhythmic and these approaches fail in describing its complexity, particularly in resting-state. As an alternative, the analysis of the 1/f-type power spectrum observed in the very low frequencies, a hallmark of scale-free dynamics, can overcome these issues. Yet it remains unclear whether this scale-free property is functionally relevant and whether its fluctuations matter for behavior. To address this question, our first concern was to establish a visual learning paradigm that would entail functional plasticity during an MEG session. In order to optimize the training effects, we developed new audiovisual (AV) stimuli (an acoustic texture paired with a colored visual motion) that induced multisensory integration and indeed improved learning compared to visual training solely (V) or accompanied with acoustic noise (AVn). This led us to investigate the neural correlates of these three types of training using first a classical method such as the ERF analysis. After source reconstruction on each individual cortical surface using MNE-dSPM, the network involved in the task was identified at the group-level. The selective plasticity observed in the human motion area (hMT+) correlated across all individuals with the behavioral improvement and was supported by a larger network in AV comprising multisensory areas. On the basis of these findings, we further explored the links between the behavior and scale-free properties of these same source-reconstructed MEG signals. Although most studies restricted their analysis to the global measure of self-similarity (i.e. long-range fluctuations), we also considered local fluctuations (i.e. multifractality) by using the Wavelet Leader Based Multifractal Formalism (WLBMF). We found intertwined modulations of self-similarity and multifractality in the same cortical regions as those revealed by the ERF analysis. Most astonishing, the degree of multifractality observed in each individual converged during the training towards a single attractor that reflected the asymptotic behavioral performance in hMT+. Finally, these findings and their associated methodological issues are compared with the ones that came out from the ERF analysis.

Cette thèse est consacrée à l’étude statistique des systèmes complexes à travers l’analyse de signaux expérimentaux, de signaux synthétiques et de signaux générés à partir de modèles théoriques. On a choisi la turbulence comme paradigme d’ ́etude en raison de ses propriétés: dynamique non linéaire, comportement multi-échelle, cascade d’énergie, intermittence ... Afin de faire une caractérisation statistique d’un système complexe on s’intéresse à l’étude de la distribution (fonction de densité de probabilité), des corrélations et dépendances, et des relations de causalité de Wiener, des signaux qui décrivent le système. La théorie de l’information apparaît comme un cadre idéal pour developer ce type d’analyse. Dans le cadre de la théorie de l’information on a développé deux méthodologies, différentes mais reliées, pour analyser les propriétés d’auto similarité d’un système complexe, et plus précisément de la turbulence. La première méthodologie est basée sur l’analyse des incréments du processus étudié, avec l’entropie de Shannon et la divergence de Kullback-Leibler. La deuxième méthode, qui permet d’analyser des processus non stationnaires, est basée sur l’analyse du processus avec le taux d’entropie de Shannon. On a étudié la relation entre les deux méthodologies, lesquelles caractérisent la distribution d’information du système et la déformation de la distribution des incréments, à travers les échelles. / Most of the time when studying a system, scientists face processes whose properties are a priori unknown. Characterising these processes is a major task to describe the studied system. During this thesis, which combines signal processing and physics, we were mainly motivated by the study of complex systems and turbulence, and consequently, we were interested in the study of regularity and self-similarity properties, long range dependence structures and multi-scale behavior. In order to perform this kind of study, we use information theory quantities, which are functions of the probability density function of the analysed process, and so depend on any order statistics of its PDF. We developed different, but related, data analysis methodologies, based on information theory, to analyse a process across scales τ. These scales are usually identified with the sampling parameter of Takens embedding procedure, but also with the size of the increments of the process. The methodologies developed during this thesis, can be used to characterize stationnary and non-stationnary processes by analysing time windows of length T of the studied signal.

Submitted by (ana.araujo@ufrpe.br) on 2016-05-25T14:39:16Z No. of bitstreams: 1 Barbara Camboim Lopes de Figueiredo.pdf: 2032958 bytes, checksum: d463c6ab534a96f1ce5aac33c2dde210 (MD5) / Made available in DSpace on 2016-05-25T14:39:16Z (GMT). No. of bitstreams: 1 Barbara Camboim Lopes de Figueiredo.pdf: 2032958 bytes, checksum: d463c6ab534a96f1ce5aac33c2dde210 (MD5) Previous issue date: 2014-02-24 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The study of climate has great importance, given that a variation of climatic elements affect the economy of a certain region and life of the inhabitants. Climate variables temperature, humidity, atmospheric pressure, solar radiation, precipitation and wind can be affected by geophysical and environmental factors such as latitude, altitude, air mass, proximity to sea, sea currents and vegetation. Wind is the most complex climate element representing the natural phenomenon of turbulence, it is characterized by high temporal and spatial variability. Wind is generated by atmospheric air mass movement, and has influence on various environmental phenomena such as soil erosion, pollutant dispersal and transport of pollen and seeds. Knowing wind speed temporal and spatial distribution is crucial to evaluate the potential for generation of eolic energy. In this work we study long-term correlations in wind speed temporal series registered at twelve meteorological stations in the state of Pernambuco, Brazil. To this end we apply Multifractal Detrended Fluctuation Analysis (MF-DFA) on hourly wind speed data for the period 2008-2011. All the analyzed series exhibit multifractal properties with generalized Hurst exponents above 0.5 indicating persistent temporal dynamics for both, small and large fluctuations. We also calculate other multifractal measures Rényi exponent and singularity spectrum, and complexity parameters, position of maximum, width and asymmetry of multifractral spectrum. No correlation was detected between complexity parameters and the geographic parameters longitude, latitude and altitude of the station, except for asymmetry of multifractal spectrum: negative correlation with longitude for maximum wind speed and negative correlation with latitude for average wind speed. However for all stations the strength of multifractality (indicated by width of multifractal spectrum) is greater for maximum wind speed then for average wind speed. These results contribute to a better understanding of the nature of stochastic processes governing wind dynamics which is necessary for development of more accurate predictive models for wind speed temporal variability and diverse phenomena influenced by wind. / O estudo do clima tem grande importância visto que a variação em elementos climáticos afeta a economia de uma região e a vida das pessoas que ali habitam. As variáveis climáticas temperatura, umidade, pressão atmosférica, radiação solar, precipitação e vento podem ser influenciadas por diversos fatores, geofísicos e ambientais, tais como latitude, altitude, massas de ar, continentalidade e maritmidade, relevo e vegetação. Um dos mais complexos elementos do clima é o vento, pelo fato de representar um fenômeno natural de turbulência, caracterizado por uma grande variabilidade temporal e espacial. O vento é gerado pelo movimento das massas de ar e pode influenciar vários fenômenos ambientais como erosão do solo, dispersão de poluentes e transporte de pólen e sementes. O conhecimento da distribuição temporal e espacial da velocidade do vento é crucial para avaliação do potencial eólico de uma região. Neste trabalho estudaram-se correlações de longo alcance das séries temporais de velocidade do vento registradas em 12 estações meteorológicas durante o período de 2008 a 2011 no estado de Pernambuco aplicando-se o método Multifractal Detrended Fluctuation Analysis (MF-DFA) nas séries temporais horárias. Todas as séries analisadas mostram as propriedades multifractais com valores de expoente generalizado de Hurst acima de 0,5 indicando uma dinâmica persistente para pequenas e grande flutuações. Foram calculadas também as outras medidas multifractais, o expoente Rényi e o espectro multifractal bem como os parâmetros de complexidade: posição do máximo, largura e assimetria do espectro multifractal. Não foram encontradas correlação entre os parâmetros de complexidade e as coordenadas geográficas: longitude, latitude e altitude, exceto a medida de assimetria do espectro multifractal: correlação negativa entre a rajada e longitude e entre velocidade e latitude. Para todas estações as larguras do espectro multifractal foram maiores para a rajada que para a velocidade, indicando uma multifractalidade mais forte. Estes resultados contribuem para uma melhor compreensão da natureza dos processos estocásticos geradores da dinâmica do vento, necessária para o desenvolvimento de modelos confiáveis para predição da variabilidade temporal do vento e dos diversos fenômenos influenciados pelo mesmo.

Il existe deux façons d'analyser l'activité cérébrale acquise en magnétoencéphalographie (MEG) : soit en moyennant les réponses suscitées par la répétition d'un stimulus afin d'observer le « champ évoqué »; soit en décomposant le signal en bandes oscillatoires (tel que l'alpha, le bêta ou le gamma), chacune étant associée à différents rôles fonctionnels. Ces méthodes ne prennent cependant pas compte de la complexité de l'activité cérébrale dont l'essentiel est arythmique, notamment au repos. Pour pallier à cela, une autre approche consiste à analyser le spectre de puissance en 1/f observable dans les très basses fréquences, une caractéristique des systèmes dont la dynamique est invariante d'échelle. Pour savoir si cette propriété joue un quelconque rôle dans le fonctionnement cérébral et si elle a des conséquences sur le comportement, nous avons établit un paradigme d'apprentissage visuel permettant d'observer de la plasticité fonctionnelle au cours d'une session MEG. Pour avoir un entraînement optimal, nous avons développé de nouveaux stimuli audiovisuels (AV) (une texture acoustique associée à un nuage de points colorés en mouvement) permettant une intégration multisensorielle et de ce fait un meilleur apprentissage que celui apporté par un entraînement visuel seul (V) ou accompagné d'un bruit acoustique (AVn). Nous avons ensuite étudié les corrélats neuronaux de ces trois types d'apprentissage par l'analyse classique des champs évoqués. Une fois l'activité reconstruite sur la surface corticale de chaque individu à l'aide de MNE-dSPM, nous avons identifié le réseau impliqué dans la tâche au sein de chaque groupe. En particulier, la plasticité sélective observée dans l'aire hMT+ associée au traitement du mouvement visuel corrélait avec les progressions comportementales des individus et était soutenue en AV par un plus vaste réseau comprenant notamment des aires multisensorielles. Parallèlement, nous avons exploré les liens reliant le comportement et les propriétés d'invariance d'échelle de ces mêmes signaux MEG reconstruits sur le cortex. Tandis que la plupart des études se limitent à analyser l'auto-similarité (une caractéristique globale synonyme de longue mémoire), nous avons aussi considéré les fluctuations locales (c-à-d la multifractalité) au moyen de l'analyse WLBMF. Nous avons trouvé des modulations couplées de l'auto-similarité et de la multifractalité dans des régions similaires à celles révélées par l'analyse des champs évoqués. Plus surprenant, Le degré de multifractalité relevé dans chaque individu convergeait durant l'entraînement vers un même attracteur reflétant la performance comportementale asymptotique. / The analysis of Human brain activity in magnetoencephalography (MEG) can be generally conducted in two ways: either by focusing on the average response evoked by a stimulus repeated over time, more commonly known as an ``event-related field'' (ERF), or by decomposing the signal into functionally relevant oscillatory or frequency bands (such as alpha, beta or gamma). However, the major part of brain activity is arrhythmic and these approaches fail in describing its complexity, particularly in resting-state. As an alternative, the analysis of the 1/f-type power spectrum observed in the very low frequencies, a hallmark of scale-free dynamics, can overcome these issues. Yet it remains unclear whether this scale-free property is functionally relevant and whether its fluctuations matter for behavior. To address this question, our first concern was to establish a visual learning paradigm that would entail functional plasticity during an MEG session. In order to optimize the training effects, we developed new audiovisual (AV) stimuli (an acoustic texture paired with a colored visual motion) that induced multisensory integration and indeed improved learning compared to visual training solely (V) or accompanied with acoustic noise (AVn). This led us to investigate the neural correlates of these three types of training using first a classical method such as the ERF analysis. After source reconstruction on each individual cortical surface using MNE-dSPM, the network involved in the task was identified at the group-level. The selective plasticity observed in the human motion area (hMT+) correlated across all individuals with the behavioral improvement and was supported by a larger network in AV comprising multisensory areas. On the basis of these findings, we further explored the links between the behavior and scale-free properties of these same source-reconstructed MEG signals. Although most studies restricted their analysis to the global measure of self-similarity (i.e. long-range fluctuations), we also considered local fluctuations (i.e. multifractality) by using the Wavelet Leader Based Multifractal Formalism (WLBMF). We found intertwined modulations of self-similarity and multifractality in the same cortical regions as those revealed by the ERF analysis. Most astonishing, the degree of multifractality observed in each individual converged during the training towards a single attractor that reflected the asymptotic behavioral performance in hMT+. Finally, these findings and their associated methodological issues are compared with the ones that came out from the ERF analysis.

Séries temporais financeiras, como índices de mercado e preços de ativos, são produzidas por interações complexas dos agentes que participam do mercado. As propriedades fractais e multifractais destas séries fornecem evidências para detectar com antecedência a ocorrência de movimentos bruscos de mercado (crashes). Tais evidências são obtidas ao aplicar o conceito de Calor Específico Análogo C(q), proveniente da equivalência entre a Multifractalidade e Termodinâmica. Na proximidade de um crash, C(q) apresenta um ombro anômalo à direita de sua curva, enquanto que na ausência de um crash, possui o formato parecido com uma distribuição gaussiana. Com base neste comportamento, o presente trabalho propõe um novo indicador temporal IA(i), definido como a taxa de variação da área sob a curva de C(q). O indicador foi construído por intermédio de uma janela temporal de tamanho s que se movimenta ao longo da série, simulando a entrada de dados na série ao longo do tempo. A análise de IA(i) permite detectar com antecedência a ocorrência de grandes movimentos, como os famosos crashes de 1929 e 1987 para os índices Dow Jones, S&P500 e Nasdaq. Além disso, a análise simultânea de medidas como a Energia Livre, a Dimensão Multifractal e o Espectro Multifractal, sugerem que um crash de mercado se assemelha a uma transição de fase. A robustez do método para diferentes ativos e diferentes períodos de tempo, demonstra a importância dos resultados. Além disso, modelos estatísticos não lineares para a volatilidade foram empregados no trabalho para estudar grandes flutuações causadas por crashes e crises financeiras ao longo do tempo. / Financial time series such as market index and asset prices, are produced by complex interactions of agents that trade in the market. The fractal and multifractal properties of these series provides evidence for early detection of the occurrence of sudden market movements (crashes). This evidence is obtained by applying the concept of Analog Specific Heat C(q), from the equivalence between the Multifractal Analysis and Thermodynamics. In the vicinity of a crash, C(q) exhibits a shoulder at the right side of its curve, while in the absence of a crash, C(q) presents a form similar to a Gaussian distribution curve. Based on this behavior, it is proposed in this work a new temporal indicator IA(i) defined here as the area variation rate over the Specific Heat function. We have constructed the mentioned indicator from a window of data with the first points (size s), that moves throughout the series, simulating the actual input of data over time. The indicator IA(i) allows one detecting in advance the occurrence of large financial market movements, such as those occurred in 1929 and 1987 for the marked indexes Dow Jones, Nasdaq and S&P500. Moreover, the simultaneous analysis of measures such as the Free Energy, Multifractal Dimension and Multifractal Spectrum suggest that a market crash resembles a phase transition. The robustness of the method for others assets and different periods of time demonstrates the importance of the results. Moreover, nonlinear statistical models for volatility have been employed in the work to study large fluctuations caused by crashes and financial crises over time.

Séries temporais financeiras, como índices de mercado e preços de ativos, são produzidas por interações complexas dos agentes que participam do mercado. As propriedades fractais e multifractais destas séries fornecem evidências para detectar com antecedência a ocorrência de movimentos bruscos de mercado (crashes). Tais evidências são obtidas ao aplicar o conceito de Calor Específico Análogo C(q), proveniente da equivalência entre a Multifractalidade e Termodinâmica. Na proximidade de um crash, C(q) apresenta um ombro anômalo à direita de sua curva, enquanto que na ausência de um crash, possui o formato parecido com uma distribuição gaussiana. Com base neste comportamento, o presente trabalho propõe um novo indicador temporal IA(i), definido como a taxa de variação da área sob a curva de C(q). O indicador foi construído por intermédio de uma janela temporal de tamanho s que se movimenta ao longo da série, simulando a entrada de dados na série ao longo do tempo. A análise de IA(i) permite detectar com antecedência a ocorrência de grandes movimentos, como os famosos crashes de 1929 e 1987 para os índices Dow Jones, S&P500 e Nasdaq. Além disso, a análise simultânea de medidas como a Energia Livre, a Dimensão Multifractal e o Espectro Multifractal, sugerem que um crash de mercado se assemelha a uma transição de fase. A robustez do método para diferentes ativos e diferentes períodos de tempo, demonstra a importância dos resultados. Além disso, modelos estatísticos não lineares para a volatilidade foram empregados no trabalho para estudar grandes flutuações causadas por crashes e crises financeiras ao longo do tempo. / Financial time series such as market index and asset prices, are produced by complex interactions of agents that trade in the market. The fractal and multifractal properties of these series provides evidence for early detection of the occurrence of sudden market movements (crashes). This evidence is obtained by applying the concept of Analog Specific Heat C(q), from the equivalence between the Multifractal Analysis and Thermodynamics. In the vicinity of a crash, C(q) exhibits a shoulder at the right side of its curve, while in the absence of a crash, C(q) presents a form similar to a Gaussian distribution curve. Based on this behavior, it is proposed in this work a new temporal indicator IA(i) defined here as the area variation rate over the Specific Heat function. We have constructed the mentioned indicator from a window of data with the first points (size s), that moves throughout the series, simulating the actual input of data over time. The indicator IA(i) allows one detecting in advance the occurrence of large financial market movements, such as those occurred in 1929 and 1987 for the marked indexes Dow Jones, Nasdaq and S&P500. Moreover, the simultaneous analysis of measures such as the Free Energy, Multifractal Dimension and Multifractal Spectrum suggest that a market crash resembles a phase transition. The robustness of the method for others assets and different periods of time demonstrates the importance of the results. Moreover, nonlinear statistical models for volatility have been employed in the work to study large fluctuations caused by crashes and financial crises over time.

Les îles tropicales sont soumises à un ennuagement hétérogène et changeant rapidement. Par ailleurs, elles ont une ressource solaire importante mais significativement variable d’un jour à l’autre. Dans le sud-ouest de l’océan indien (SWIO), La Réunion fait partie de ces îles tropicales ayant un potentiel solaire colossal mais fortement intermittent. Dans cette étude, nous proposons une nouvelle approche de prévision déterministe des cartes journalières rayonnement solaire (SSR), basée sur quatre modèles de régression linéaire : une régression linéaire multiple (MLR), une régression en composantes principales (PCR), une régression des moindres carrés (PLSR) et une régression pas à pas (stepwise--SR). Ces quatre régressions sont appliquées sur les données satellites SARAH-E (CM SAF) à 5km de résolution entre 2007 et 2016, en vue d’en effectuer la prévision. Pour obtenir de meilleures performances, nous proposons d'inclure les paramètres multi-fractale (H,C_1 et α) comme nouveaux paramètres prédictifs. Ceux-ci sont obtenus à partir de l'analyse de l'intermittence du SSR basée sur la méthode d’analyse d’ordre spectral arbitraire de Hilbert. Cette analyse qui est une extension de la transformation d’Hilbert Huang (HHT) est utilisée afin d’estimer l’exposant d’échelle ξ(q). On effectue la combinaison d’une décomposition en mode empirique et de l’analyse spectrale de Hilbert (EMD + HSA). Dans une première étape, l’analyse multi-fractale est appliquée sur une mesure du SSR d'une seconde échelle à partir d'un pyranomètre SPN1 à Moufia en 2016. La moyenne infra journalière, journalière et saisonnière de la structure multi-fractale a été dérivée, et la loi d’échelle d’exposants ξ(q) a été analysée. Dans une seconde partie, l’analyse de l’intermittence est effectuée sur les mesures du SSR, d'une période d’une minute, à partir le réseau de SPN1 contenant 11 stations en 2014. Les modèles spatiaux pour toutes les stations avec les paramètres multi-fractales H,C_1 et α sont mis en évidence. La variabilité de la largeur du spectre de singularité est considérée pour étudier l'intermittence spatiale et la multi-fractalité dans l'échelle quotidienne et l'échelle saisonnière. Sur la base de ces analyses d'intermittence faites sur les mesures de plusieurs stations, les paramètres multi-fractaux universels (H,C_1 et α) pourraient être choisis comme de nouveaux prédicteurs afin d’indiquer les propriétés multi-fractales du SSR. / Due to the heterogeneous and rapidly-changing cloudiness, tropical islands, such as Reunion Island in the South-west Indian Ocean (SWIO), have significant solar resource that is highly variable from day-to-day. In this study, we propose a new approach for deterministic prediction of daily surface solar radiation (SSR) maps based on four linear regression models: multiple linear regression (MLR), principal component regression (PCR), partial least squares regression (PLSR), and stepwise regression (SR), that we have applied on the SARAH-E@5km satellite data (CM SAF) for the period during 2007-2016. To improve the accuracy of prediction, the multifractal parameters (H,C_1 and α) are proposed to include as new predictors in the predictive model. These parameters are obtained from the analysis of SSR intermittency based on arbitrary order Hilbert spectral analysis. This analysis is the extension of Hilbert Huang Transform (HHT) and it is used to estimate the generalized scaling exponent ξ(q). It is the combination of the Empirical Mode Decomposition and Hilbert spectral analysis (EMD+HSA). In a first step, the multifractal analysis is applied onto one-second SSR measurements form a SPN1 pyranometer in Moufia in 2016. The mean sub-daily, daily and seasonal daily multifractal patterns are derived, and the scaling exponent ξ(q) is analyzed. In a second step, the intermittency study is conducted on one-minute SSR measurements from a SPN1 network with 11 stations in 2014. The spatial patterns for all the stations with the multifractal parameters H,C_1 and α are shown. The variability of singularity spectrum width is considered to study the spatial intermittency at the daily and seasonal scale. Based on this intermittency analysis from measurements at several stations, the universal multifractal parameters (H,C_1 and α) could be taken as new predictors for indicating the multifractal properties of SSR.

Environ 25% de la population mondiale est atteinte de troubles psychiatriques qui sont typiquement associés à des problèmes comportementaux, fonctionnels et/ou cognitifs et dont les corrélats neurophysiologiques sont encore très mal compris. Non seulement ces dysfonctionnements réduisent la qualité de vie des individus touchés, mais ils peuvent aussi devenir un fardeau pour les proches et peser lourd dans l’économie d’une société. Cibler les mécanismes responsables du fonctionnement atypique du cerveau en identifiant des biomarqueurs plus robustes permettrait le développement de traitements plus efficaces. Ainsi, le premier objectif de cette thèse est de contribuer à une meilleure caractérisation des changements dynamiques cérébraux impliqués dans les troubles mentaux, plus précisément dans la schizophrénie et les troubles d’humeur. Pour ce faire, les premiers chapitres de cette thèse présentent, en intégral, deux revues de littératures systématiques que nous avons menées sur les altérations de connectivité cérébrale, au repos, chez les patients schizophrènes, dépressifs et bipolaires. Ces revues révèlent que, malgré des avancées scientifiques considérables dans l’étude de l’altération de la connectivité cérébrale fonctionnelle, la dimension temporelle des mécanismes cérébraux à l’origine de l’atteinte de l’intégration de l’information dans ces maladies, particulièrement de la schizophrénie, est encore mal comprise. Par conséquent, le deuxième objectif de cette thèse est de caractériser les changements cérébraux associés à la schizophrénie dans le domaine temporel. Nous présentons deux études dans lesquelles nous testons l’hypothèse que la « disconnectivité temporelle » serait un biomarqueur important en schizophrénie. Ces études explorent les déficits d’intégration temporelle en schizophrénie, en quantifiant les changements de la dynamique neuronale dite invariante d’échelle à partir des données magnétoencéphalographiques (MEG) enregistrés au repos chez des patients et des sujets contrôles. En particulier, nous utilisons (1) la LRTCs (long-range temporal correlation, ou corrélation temporelle à longue-distance) calculée à partir des oscillations neuronales et (2) des analyses multifractales pour caractériser des modifications de l’activité cérébrale arythmique. Par ailleurs, nous développons des modèles de classification (en apprentissage-machine supervisé) pour mieux cerner les attributs corticaux et sous-corticaux permettant une distinction robuste entre les patients et les sujets sains. Vu que ces études se basent sur des données MEG spontanées enregistrées au repos soit avec les yeux ouvert, ou les yeux fermées, nous nous sommes par la suite intéressés à la possibilité de trouver un marqueur qui combinerait ces enregistrements. La troisième étude originale explore donc l’utilité des modulations de l’amplitude spectrale entre yeux ouverts et fermées comme prédicteur de schizophrénie. Les résultats de ces études démontrent des changements cérébraux importants chez les patients schizophrènes au niveau de la dynamique d’invariance d’échelle. Elles suggèrent une dégradation du traitement temporel de l’information chez les patients, qui pourrait être liée à leurs symptômes cognitifs et comportementaux. L’approche multimodale de cette thèse, combinant la magétoencéphalographie, analyses non-linéaires et apprentissage machine, permet de mieux caractériser l’organisation spatio-temporelle du signal cérébrale au repos chez les patients atteints de schizophrénie et chez des individus sains. Les résultats fournissent de nouvelles preuves supportant l’hypothèse d’une « disconnectivité temporelle » en schizophrénie, et étendent les recherches antérieures, en explorant la contribution des structures cérébrales profondes et en employant des mesures non-linéaires avancées encore sous-exploitées dans ce domaine. L’ensemble des résultats de cette thèse apporte une contribution significative à la quête de nouveaux biomarqueurs de la schizophrénie et démontre l’importance d’élucider les altérations des propriétés temporelles de l’activité cérébrales intrinsèque en psychiatrie. Les études présentées offrent également un cadre méthodologique pouvant être étendu à d’autres psychopathologie, telles que la dépression. / Psychiatric disorders affect nearly a quarter of the world’s population. These typically bring about debilitating behavioural, functional and/or cognitive problems, for which the underlying neural mechanisms are poorly understood. These symptoms can significantly reduce the quality of life of affected individuals, impact those close to them, and bring on an economic burden on society. Hence, targeting the baseline neurophysiology associated with psychopathologies, by identifying more robust biomarkers, would improve the development of effective treatments. The first goal of this thesis is thus to contribute to a better characterization of neural dynamic alterations in mental health illnesses, specifically in schizophrenia and mood disorders. Accordingly, the first chapter of this thesis presents two systematic literature reviews, which investigate the resting-state changes in brain connectivity in schizophrenia, depression and bipolar disorder patients. Great strides have been made in neuroimaging research in identifying alterations in functional connectivity. However, these two reviews reveal a gap in the knowledge about the temporal basis of the neural mechanisms involved in the disruption of information integration in these pathologies, particularly in schizophrenia. Therefore, the second goal of this thesis is to characterize the baseline temporal neural alterations of schizophrenia. We present two studies for which we hypothesize that the resting temporal dysconnectivity could serve as a key biomarker in schizophrenia. These studies explore temporal integration deficits in schizophrenia by quantifying neural alterations of scale-free dynamics using resting-state magnetoencephalography (MEG) data. Specifically, we use (1) long-range temporal correlation (LRTC) analysis on oscillatory activity and (2) multifractal analysis on arrhythmic brain activity. In addition, we develop classification models (based on supervised machine-learning) to detect the cortical and sub-cortical features that allow for a robust division of patients and healthy controls. Given that these studies are based on MEG spontaneous brain activity, recorded at rest with either eyes-open or eyes-closed, we then explored the possibility of finding a distinctive feature that would combine both types of resting-state recordings. Thus, the third study investigates whether alterations in spectral amplitude between eyes-open and eyes-closed conditions can be used as a possible marker for schizophrenia. Overall, the three studies show changes in the scale-free dynamics of schizophrenia patients at rest that suggest a deterioration of the temporal processing of information in patients, which might relate to their cognitive and behavioural symptoms. The multimodal approach of this thesis, combining MEG, non-linear analyses and machine-learning, improves the characterization of the resting spatiotemporal neural organization of schizophrenia patients and healthy controls. Our findings provide new evidence for the temporal dysconnectivity hypothesis in schizophrenia. The results extend on previous studies by characterizing scale-free properties of deep brain structures and applying advanced non-linear metrics that are underused in the field of psychiatry. The results of this thesis contribute significantly to the identification of novel biomarkers in schizophrenia and show the importance of clarifying the temporal properties of altered intrinsic neural dynamics. Moreover, the presented studies offer a methodological framework that can be extended to other psychopathologies, such as depression.

The aim of this thesis is to examine an empirical relationship between multifrac- tality of financial time series and its returns. We approach the multifractality of a given time series as a measure of its complexity. Multifractal financial time series exhibit repeating self-similar patterns. Multifractality could be a good predictor of stock returns or a factor which can be used in asset pricing. We expected that capturing the complexity of a given time series by a model, a positive or a negative risk premia for investing into "more multifractal assets" could be found. Daily prices of 31 stock indices and daily returns of 10-years US government bonds were downloaded. All the data were recorded between 2012 and 2021. After estimation the multifractal spectra, applying MF-DFA method, of all stock indices, we ordered all stock indices from the lowest to the most multifractal. Then, we constructed a "multifractal portfolio" holding a long position in the 7 most multifractal and holding a short position in the 7 least multifractal stock indices. Fama-MacBeth regression with market risk premia and multifractal variable as independent variables was applied. Multi- fractality in all examined financial time series was found. We also found a very low negative risk premia for holding "a multifractal...