Les signaux transitoires, de par leur unicité, sont très difficiles à caractériser. Ils se rencontrent partout et sont généralement le reflet d'un phénomène physique très complexe traduisant de nombreuses informations telles que le signal à l'origine, les effets de la propagation dans le milieu considéré et aussi les effets induits par les capteurs. Ils peuvent aussi bien correspondre à un phénomène de communication entre animaux, qu'être le reflet d'un défaut dans un système électrique ou hydraulique par exemple. Tout ceci rend leur étude très difficile, mais aussi primordiale. De nombreuses techniques en traitement du signal ont été développées ces dernières années pour les étudier: elles reposent souvent sur des approches statistiques, des approches projectives sur différents dictionnaires et des techniques auto-adaptatives. Toutes ces méthodes présentent des avantages et des inconvénients, puisqu'elles permettent souvent de les détecter correctement, néanmoins leur caractérisation à des fins de classification et de discrimination reste compliquée. Cette thèse s'inscrit dans cette optique et propose de nouvelles approches d'étude des transitoires. Après un rapide descriptif des techniques d'étude des signaux transitoires, ce travail s'intéressera dans un premier temps à la représentation des signaux ayant des composantes fréquentielles variant très rapidement. De manière générale l'utilisation des distributions généralisées à temps complexe présente un cadre d'analyse adéquat, mais il est limité aux signaux possédant une bande passante étroite, nous proposons dans une première partie d'étendre cette utilisation à des signaux possédant une bande passante plus large en appliquant un changement d'échelle des signaux. Une deuxième partie s'intéressera davantage à l'extraction de signaux à modulation de phase dans le contexte d'un mélange de bruit non-stationnaire et d'autres signaux cohérents. Ceci sera effectué par des opérateurs de warping couplé à des techniques de débruitage basée sur la compression de données. Le troisième chapitre s'intéressera aux techniques guidées par les données basées sur la représentation des signaux en diagrammes de phase. La contribution principale porte sur la diversité des lags qui permet en effet de mettre en évidence les effets des opérateurs de temps-échelles, mais aussi de modification d'amplitude entre des signaux. Nous développerons donc des méthodes permettant de mettre en évidence ces propriétés. Finalement, les travaux présentés dans les premiers chapitres seront développés dans le cadre de quatre domaines applicatifs qui sont : la segmentation d'ECG, la caractérisation de transitoires électriques, un cas d'acoustique passive et l'étude de signaux acoustiques en milieu immergé. Nous terminerons enfin par une conclusion et quelques perspectives de travail. / For their uniqueness, transient are really difficult to characterize. They are met everywhere and are generally the result of very complex physical phenomena that contain a lot of information such as the transient at its origin, the effect of the propagation through the medium and the effects induced by the transducers. They can correspond to communication between mammals as well as being the reflection of a fault in electrical or hydraulic networks for instance. Hence their study is of great importance even though it is quite complicated. Numerous signal processing methods have been developed in the last decades: they often rely on statistical approaches, linear projections of the signal onto dictionaries and data-driven techniques. All those methods have pros and cons since they often provide good detections, nevertheless their characterization for classification and discrimination purposes remains complicated. In this spirit, this thesis proposes new approaches to study transients. After a brief overview of the existing methods, this work first focuses on the representation of signals having tight-varying time-frequency components. Generally, general complex-time distributions present a proper framework to study them but remain limited to narrow band signals. In a first part, we propose to overcome this limitation in the case of signals with a spread time-frequency variation. This method is based on the compression of the signal's spectrum to a bandwidth that ensures the efficiency of the technique. A second part then focuses on the extraction of nonlinear modulation phase signals in the context of nonstationary noise and other coherent signals. This is performed with warping operators and compressive sensing reconstruction techniques. The third chapter then focuses on data-driven methods based on the representation of the signal in phase space. The main contribution takes advantage of the lag diversity that enables to highlight time scale transformations as well as amplitude modifications between transients. Hence, we develop different techniques enabling to highlight those properties. Finally, works presented in the first chapters are developed in applicative contexts such as: ECG segmentation, electrical transient characterization, a passive acoustic configuration and the study of acoustic signals in an immerse environment. We then end up by some conclusions and perspectives for future works.

Les fonctions aléatoires stationnaires ont été utilisées avec succès dans les applications géostatistiques depuis plusieurs décennies. La structure de dépendance spatiale sous-jacente de la fonction aléatoire est alors représentée par un variogramme ou une covariance stationnaire. Cependant, dans certaines situations, il y a très peu de raisons de s'attendre à une structure de dépendance spatiale stationnaire sur l'ensemble du domaine d'intérêt. Dans cette thèse, deux approches de modélisation non-stationnaire de fonctions aléatoires sont considérées: déformation d'espace et convolution stochastique. Pour chacune d'elle, nous développons une méthodologie statistique d'estimation de la structure de dépendance spatiale non-stationnaire, dans le contexte d'une réalisation unique. Par ailleurs, nous montrons également comment dans ce cadre non-stationnaire, les prédictions spatiales et les simulations conditionnelles peuvent être menées. Les méthodes d'inférence développées permettent de capturer des structures de dépendance variables tout en garantissant la cohérence globale du modèle final. L'évaluation de leur performance selon plusieurs critères, sur des données synthétiques et réelles montre qu'elles donnent de meilleurs résultats de prédiction qu'une méthode stationnaire. Au delà de la prédiction, elles peuvent également servir comme outil pour une analyse exploratoire de la non-stationnarité. / Stationary Random Functions have been sucessfully applied in geostatistical applications for decades. The underlying spatial dependence structure of the Random Function is represented by a stationary variogram or covariance. However, in some instances, there is little reason to expect the spatial dependence structure to be stationary over the whole region of interest. In this manuscript, two non-stationary modelling approaches for Random Functions are considered: space deformation and stochastic convolution. For each of them, we develop a statistical methodology for estimating the non-stationary spatial dependence structure, in the context of a single realization. Moreover, we also show how spatial predictions and conditional simulations can be carried out in this non-stationary framework. The developed inference methods allow to capture varying spatial structures while guaranteeing the global consistency of the final model. The assessment of their performance on both synthetic and real datasets show that they outperform stationary method, according to several criteria. Beyond the prediction, they can also serve as a tool for exploratory analysis of the non-stationarity.

Le problème des bandits manchots est un cadre théorique permettant d'étudier le compromis entre exploration et exploitation lorsque l'information observée est partielle. Dans celui-ci, un joueur dispose d'un ensemble de K bras (ou actions), chacun associé à une distribution de récompenses D(µk) de moyenne µk Є [0, 1] et de support [0, 1]. A chaque tour t Є [1, T], il choisit un bras kt et observe la récompense y kt tirée depuis D (µkt). La difficulté du problème vient du fait que le joueur observe uniquement la récompense associée au bras joué; il ne connaît pas celle qui aurait pu être obtenue en jouant un autre bras. À chaque choix, il est ainsi confronté au dilemme entre l'exploration et l'exploitation; explorer lui permet d'affiner sa connaissance des distributions associées aux bras explorés tandis qu'exploiter lui permet d'accumuler davantage de récompenses en jouant le meilleur bras empirique (sous réserve que le meilleur bras empirique soit effectivement le meilleur bras). Dans la première partie de la thèse nous aborderons le problème des bandits manchots lorsque les distributions générant les récompenses sont non-stationnaires. Nous étudierons dans un premier temps le cas où même si les distributions varient au cours du temps, le meilleur bras ne change pas. Nous étudierons ensuite le cas où le meilleur bras peut aussi changer au cours du temps. La seconde partie est consacrée aux algorithmes de bandits contextuels où les récompenses dépendent de l'état de l'environnement. Nous étudierons l'utilisation des réseaux de neurones et des forêts d'arbres dans le cas des bandits contextuels puis les différentes approches à base de méta-bandits permettant de sélectionner en ligne l'expert le plus performant durant son apprentissage. / The multi-armed bandit is a framework allowing the study of the trade-off between exploration and exploitation under partial feedback. At each turn t Є [1,T] of the game, a player has to choose an arm kt in a set of K and receives a reward ykt drawn from a reward distribution D(µkt) of mean µkt and support [0,1]. This is a challeging problem as the player only knows the reward associated with the played arm and does not know what would be the reward if she had played another arm. Before each play, she is confronted to the dilemma between exploration and exploitation; exploring allows to increase the confidence of the reward estimators and exploiting allows to increase the cumulative reward by playing the empirical best arm (under the assumption that the empirical best arm is indeed the actual best arm).In the first part of the thesis, we will tackle the multi-armed bandit problem when reward distributions are non-stationary. Firstly, we will study the case where, even if reward distributions change during the game, the best arm stays the same. Secondly, we will study the case where the best arm changes during the game. The second part of the thesis tacles the contextual bandit problem where means of reward distributions are now dependent of the environment's current state. We will study the use of neural networks and random forests in the case of contextual bandits. We will then propose meta-bandit based approach for selecting online the most performant expert during its learning.

The goal in this thesis is to develop a novel statistical approach to identity functional interactions between regions in a brain network. Wavelets are effective for capturing time varying properties of non-stationary signals because they have compact support that can be compressed or stretched according to the dynamic properties of the signal. Wavelets provide a multi-scale decomposition of signals and thus can be few for exploring potential cross-scale interactions between signals. To achieve this, we propose the scale-specific sub-processes of a multivariate locally stationary wavelet stochastic process. Under this proposed framework, a novel cross-scale dependence measurement is developed, which provides a measure for dependence structure of components at different scales of multivariate time series. Extensive simulation experiments are conducted to demonstrate that the theoretical properties hold in practice. The developed cross-scale analysis is performed on the electroencephalogram (EEG) data to study alterations in the functional connectivity structure in children diagnosed with attention deficit hyperactivity disorder (ADHD). Our approach identified novel interesting cross-scale interactions between channels in the brain network. The proposed framework can be extended to other signals, which can also capture the statistical association between the stocks at different time scales.

Application of pressure in the form of taping and bracing has been shown to improve proprioception, and inducing localized muscle fatigue at various musculatures has been shown to adversely affect postural control. However, the potential for pressure application to mitigate the effects of localized muscle fatigue on postural control has not yet been determined. This study investigated specifically the effects of circumferential ankle pressure (CAP) and induced ankle fatigue on postural control. Fourteen young participants (seven males and seven females) performed fatiguing sub-maximal isotonic plantar flexion exercises on an isokinetic dynamometer, in the absence and presence of a pressure cuff (60 mm Hg) used to apply CAP. Proprioceptive acuity (PA) was determined using a passive-active joint position sense test, with categorical scores (low or high PA) used as a covariate. Postural sway during quiet standing was assessed using a force platform both pre- and post-fatigue as well as in the absence and presence of CAP. Application of CAP resulted in larger postural sway in individuals with low PA, and reduced postural sway in individuals with high PA. Fatigue effects on postural sway in individuals with low PA were more substantial as compared to individuals with high PA. CAP was found to be ineffective in mitigating the effects of fatigue on postural sway in individuals with lower PA. As a whole, the results suggest a potential for CAP as an ergonomic intervention in controlling fatigue-related fall incidents, though conclusive recommendations for use are not justified. / Master of Science

Increased extreme precipitation has been documented in many regions around the world, in- cluding central and northern Europe. Global warming increases average temperature, which in turn enhances atmospheric water holding capacity. These changes are believed to increase the frequency and/or intensity of extreme precipitation events. In determining the design storm, or a worst probable storm, for infrastructure design and failure risk assessment, experts commonly assume that statistics of extreme precipitation do not change significantly over time. This so- called notion of stationarity assumes that the statistics of future extreme precipitation events will be similar to those of historical observations. This study investigates the consequences of using a stationary assumption as well as the alternative: a non-stationary framework that con- siders temporal changes in statistics of extremes. Here we evaluate stationary and non-stationary return levels for 10-year to 50-year extreme precipitation events for different durations (1-day, 2-day, ..., 7-day precipitation events), based on the observed daily precipitation from Sweden. Non-stationary frequency analysis is only considered for stations with statistically significant trends over the past 50 years at 95% confidence (i.e., 15 to 39 % out of 139 stations, depend- ing on duration, 1-day, 2-day, ..., 7-day). We estimate non-stationary return levels using the General Extreme Value distribution with time-dependent parameters, inferred using a Bayesian approach. The estimated return levels are then compared in terms of duration, recurrence in- terval and location. The results indicate that a stationary assumption might, when a significant trend exists, underestimate extreme precipitation return levels by up to 40 % in Sweden. This report highlights the importance of considering better methods for estimating the recurrence in- terval of extreme events in a changing climate. This is particularly important for infrastructure design and risk reduction. / Ökad extrem nederbörd har dokumenterats globalt, däribland centrala och norra Europa. Den globala uppvärmningen medför en förhöjd medeltemperatur vilket i sin tur ökar avdunstning av vatten från ytor samt atmosfärens förmåga att hålla vatten. Dessa förändringar tros kunna öka och intensifiera nederbörd. Vid bestämning av dimensionerande nederbördsintensiteter för byggnationsprojekt antas idag att frekvensen och storleken av extrem nederbörd inte kommer att förändras i framtiden (stationäritet), vilket i praktiken innebär ingen förändring i klimatet. Den här studien syftar till att undersöka effekten av en icke-stationärt antagande vid skattning av dimensionerande nederbördsintensitet. Icke-stationära och stationära nerderbördsintensiteter föråterkomsttider mellan 10 och 100år bestämdes utifrån daglig och flerdaglig svensk nederbörds- data. Nederbördintensiteterna bestämdes med extremvärdesanalys i mjukvaran NEVA, där den generella extremvärdesfördelningen anpassades till årlig maximum nederbörd på platser i Sverige som påvisade en ökande trend under de senaste 50åren (15% till 39 % utav 139 stationer, beroende på varaktighet). De dimensionerande nederbördsintensiteterna jämfördes sedan med avseende på varaktighet, återkomsttid och plats. Resultaten indikerade på att ett stationärt antagande riskerar att underskatta dimensionerande nederbördsintensiteter för en viss återkomsttid med upp till 40 %. Detta indikerar att antagandet om icke-stationäritet har större betydelse för olika platser i Sverige, vilket skulle kunna ge viktig information vid bestämning av dimensionerande regnintensiteter.

Les objectifs de cette thèse sont: i) de mettre au point de nouvelles techniques adaptées à la période néonatale d'analyse automatique des signaux physiologiques cardiaque (ECG) et respiratoire (RESP) afin d'étudier la variabilité de la fréquence cardiaque (VFC) et respiratoire (VFR), ainsi que les interrelations cardiorespiratoires; ii) de les valider et de les utiliser sur des modèles ovins pour mieux comprendre les altérations du contrôle cardiorespiratoire dans des différentes situations expérimentales. Durant les expérimentations, les agneaux étaient non sédationnés et libres de leurs mouvements, ce qui rend le traitement des signaux ECG et RESP enregistrés durant plusieurs heures difficile, à cause des artefacts. D'abord, une chaîne de traitement semi-automatique des signaux a été proposée. Elle comprend l'élimination automatique des périodes artefactuelles, l'extraction des séries temporelles des segments propres de l'ECG et du signal RESP, l'application d'un test de stationnarité sur ces séries temporelles pour extraire les segments stationnaires et le calcul de différents indices de la VFC et la VFR obtenus en appliquant des analyses linéaires et non linéaires. Ces analyses ont été complétées par la mesure des interrelations cardiorespiratoires. Cette chaîne de traitement a permis d'étudier les effets de trois situations expérimentales sur le contrôle cardiorespiratoire. La première situation cherche à étudier l'exposition d'agneaux nouveau-nés à la fumée de cigarette durant les deux premières semaines de vie. Une importante altération des interrelations cardiorespiratoires a été mise en évidence, surtout au niveau de l'arythmie sinusale respiratoire et du couplage cardioventilatoire. Ce résultat inédit donne un éclairage nouveau sur la physiopathologie des effets de l'exposition à la fumée de cigarette en période néonatale, incluant en particulier le syndrome de la mort subite du nourrisson. La deuxième situation expérimentale examine l'hyperbilirubinémie (HB) des agneaux prématurés. Une HB modérée a été induite durant 17h par injection intraveineuse de bilirubine. Les effets de l'HB modérée sur la VFC, la VFR et les interrelations cardiorespiratoires ont été évalués sur 7 heures d'enregistrement au moment de l'HB (J0) et 72h plus tard (J3), après normalisation de la bilirubinémie. À J0, une augmentation de la variabilité accompagnée d'une augmentation des indices fréquentiels de la VFC a été observée indiquant une coactivation sympathovagale. Tous ces effets ont disparu à J3. Une diminution de la fréquence respiratoire a été retrouvé avec une augmentation de la VFR; ces effets étaient maintenus jusqu'à J3. Une augmentation de l'arythmie sinusale respiratoire, de la synchronisation et du nombre de RR dans une inspiration et une expiration a été observée. Ces deux derniers effets étaient toujours présents au jour 3. La troisième situation expérimentale concerne l'application nasale d'une pression positive continue (PPC) de 6 cmH2O à des agneaux nouveau-nés sains pendant 6 heures. Une augmentation de la fréquence cardiaque a été observée avec diminution des indices temporels et fréquentiels de la VFC et augmentation de la complexité des intervalles RR. De plus, un ralentissement de la respiration a été montré avec allongement de la durée de l'expiration et diminution de la VFR indiquant une stabilisation de la respiration. Enfin, la seule altération des interrelations cardiorespiratoires retrouvée était une augmentation du nombre de RR dans le cycle respiratoire attribuable à l'augmentation de la fréquence cardiaque et à la diminution de la fréquence respiratoire. L'interprétation des résultats a été approfondie en utilisant une approche à base de modèles pour représenter le comportement des systèmes cardiovasculaire, respiratoire et du baroréflexe artériel dans les conditions expérimentales. Celle-ci permet d'accéder à des variables physiologiques difficilement observables durant les expérimentations. / The objectives of this thesis are: i) to develop new techniques, adapted to the neonatal period, for the automatic analysis of cardiac (ECG) and respiratory (RESP) signals in order to study heart rate variability (HRV), respiratory rate variability (RRV), as well as cardiorespiratory interrelations; ii) to validate these techniques and use them on neonatal ovine models to better understand alterations in the cardiorespiratory control in experimental situations mimicking exposure to postnatal environmental tobacco smoke, hyperbilirubinemia in the premature infant and continuous positive airway pressure application. In the different experimental situations, the lambs were without sedation and moving freely; this makes the treatment of ECG and RESP signals recorded for several hours difficult because of artifacts. As a first step, a semi-automated signal processing approach has been proposed. It includes the automatic elimination of artefactual periods, the extraction of time series from the clean segments of the ECG and RESP signals, the performance of a stationarity test in order to extract stationary segments, the application of linear (in time and frequency domains) and nonlinear HRV and RRV analysis as well as the calculation of cardiorespiratory interrelations indices. This approach was validated and allowed to study the effects of three different experimental conditions on cardiorespiratory control. The first condition explored the effects of exposing newborn lambs to postnatal environmental tobacco smoke (ETS) for the first two weeks of life. Significant impairment of cardiorespiratory interrelations was demonstrated, particularly for respiratory sinus arrhythmia and cardioventilatory coupling. This novel result sheds new light on the physiopathology of the effects of ETS exposure in the neonatal period, particularly for sudden infant death syndrome. The second experimental situation corresponds to hyperbilirubinemia (HB) of premature lambs. Moderate HB was induced for 17h by intravenous injection of bilirubin. The effects of moderate HB on HRV, RRV and cardiorespiratory interrelationships were assessed over 7 hours of recording during acute HB (D0) and after 72h (D3), following normalization of bilirubinemia. On D0, an increase in HRV accompanied by an increase in frequency indices of HRV was observed, indicating sympathovagal coactivation. These effects were absent on D3. A decreased respiratory rate and an increase in RRV were noted on D0; these effects were maintained until D3. The study of cardiorespiratory interrelations showed an increase in respiratory sinus arrhythmia, phase synchronization and the number of RRs in inspiration and expiration. The latter effects were still observed on day 3. The third experimental situation concerns the nasal application of a continuous positive pressure (CPAP) of 6 cmH2O in healthy neonatal lambs for 6 hours. An increase in heart rate associated with a decrease in temporal and frequency indices of HRV and an increase in RR interval complexity was observed. In addition, we observed a decrease in respiratory rate accompanied by a prolonged expiration and a decreased RRV, indicating a stabilization of breathing. Finally, no alterations of cardiorespiratory interrelations were observed excepted an increase in the number of RRs in the respiratory cycle explained by the increased heart rate and decreased respiratory rate. To further understand these results, a model of cardiorespiratory coupling comprising three compartments mimicking the functioning of the cardiovascular and respiratory systems and the arterial baroreflex, was adapted to the conditions of the experiment. Results obtained with the model allowed to gain access to variables that were not measured during the experiments.

Human upright posture exhibits an everlasting oscillatory behavior of complex nature, called as human postural sway. Variations in the position of the Center-of-Pressure (CoP) were used to describe the human postural sway. In this study / CoP data, which has experimentally been collected from 28 different subjects (14 males and 14 females with their ages ranging from 6 to 84), who were divided into 4 groups according to their ages has been analyzed. The data collection from each of the subjects was performed in 5 successive trials, each of which has lasted for 180-seconds long. Linear analysis methods such as the variance/standard deviation, Fast Fouri&eacute / r Transformation, and Power Spectral Density estimates were applied to the detrended CoP signal of human postural sway. Also the Run test and Ensemble averages methods were used to search for stationarity and ergodicity of the CoP signal respectively. Furthermore, in order to reveal the nonlinear characteristics of the human postural sway, its dynamics were reconstructed in m-dimensional state space from the CoPx signals. Then, the correlation dimension (D2) estimates from the embedded dynamics were calculated. Additionally, the statistical and dynamical measures computed were checked against any significant changes, which may occur during aging. The results of the study suggested that human postural sway is a stationary process when 180-second long biped quiet stance data is considered. In addition, it exhibits variable dynamical structure complex in nature (112 deterministic chaos versus 28 stochastic time series of human postural sway) for five successive trials of 28 different subjects. Moreover, we found that groups were significantly different in the correlation dimension (D2) measure (p&amp / #8804 / 0.0003). Finally, the behavior of the experimental CoPx signals was checked against two types of linear processes by using surrogate data method. The shuffled CoPx signals (Surrogate I) suggested that temporal order of CoPx is important / however, phase-randomization (Surrogate II) did not change the behavioral characteristics of the CoPx signal.

No description available.

In Geostatistical modelling of the spatial distribution of rock attributes, the multivariate distribution of a Random Function defines the range of possible values and the spatial relationships among them. Under a decision of stationarity, the Random Function distribution and its statistics are inferred from data within a spatial domain deemed statistically homogenous. Assuming stationary multiGaussianity allows spatial prediction techniques to take advantage of this simple parametric distribution model. These techniques compute the local distributions with surrounding data and global spatially invariant statistics. They often fail to reproduce local changes in the mean, variability and, particularly, the spatial continuity, that are required for geologically realistic modelling of rock attributes. The proposed alternative is to build local Random Function models that are deemed stationary only in relation to the locations where they are defined. The corresponding location-dependent distributions and statistics are inferred by weighting the samples inversely proportional to their distance to anchor locations. These distributions are locally Gaussian transformed. The transformation models carry information on the local histogram. The distance weighted experimental measures of spatial correlation are able to adapt to local changes in the spatial continuity and are semi-automatically fitted by locally defined variogram models. The fields of local variogram and transformation parameters are used in locally stationary spatial prediction algorithms. The resulting attribute models are rich in non-stationary spatial features. This process implies a higher computational demand than the traditional techniques, but, if data is abundant enough to allow a reliable inference of the local statistics, the proposed locally stationary techniques outperform their stationary counterparts in terms of accuracy and precision. These improved models have the potential of providing better decision support for engineering design. / Mining Engineering