Obstructive Sleep Apnea-Hypopnea Syndrome (OSAHS) is a serious sleep disordered affecting up to 24% of men and 9% of woman in the middle aged population. The current standard for the OSAHS diagnosis is Polysomnography (PSG), which refers to the continuous monitoring of multiple physiological variables over the course of a night. The main outcomes of the PSG test are the OSAHS severity measures, such as the Respiratory Disturbance Index (RDI), Arousal Index, Latencies and other information to determine the macro sleep architecture (MSA), which is defined by Wake, Rapid-eye-movement (REM) and non-REM states of sleep. The MSA results are essential for computing the diagnostic measures reported in a PSG. The existing methods of the MSA analysis require the recording of 5-7 electrophysiological signals, including the Electroencephalogram (EEG), Electroculogram (EOG), and the Electromyogram (EMG). Sleep clinicians have to depend on the manual scoring of the overnight data records using the criteria given by Rechtschaffen and Kales (R&K, 1968). The manual analysis of MSA is tedious, subjective and suffers from inter- and intra-scorer variability. Additionally, the RDI and the Apnea-Hypopnea Index (AHI) parameters although used as the primary measures of the OSAHS severity, suffers from subjectivity, low reproducibility and a poor correlation with the symptoms of OSAHS. Sleep is essentially a neuropsychological phenomenon, and the EEG remains the best technique for the functional imaging of the brain during sleep. The EEG is the direct result of the neuronal activity of the brain. However, despite the potential, the wealth of information available in the EEG signal remains virtually untapped in current OSAHS diagnosis. Although the EEG is extensively used in traditional sleep analysis, its usage is mainly limited to staging sleep, based on the four-decade old R&K criteria. This thesis addresses these issues plaguing the PSG. We develop a novel, fully-automated algorithm (Higher-order Estimated Sleep States, HESS-algorithm) for the MSA analysis, which requires only one channel of the EEG data. We also develop an objective MSA analysis technique that uses a single, one-dimensional slice of the Bispectrum of the EEG, representing a nonlinear transformation of a system function that can be considered as the EEG generator. The agreement between the human and the proposed technology was found to be in the range of 70%-87%, which are similar to those, possible between expert human scorers. The ability of the HESS algorithm to compute the MSA parameters reliably and objectively will make a dramatic impact on the diagnosis and treatment of OSAHS and other sleep diseases, such as insomnia. The proposed technology uses low-computation-load Bispectrum techniques independent of R&K Criteria (1968) making real-time automated analysis a reality. In the thesis we also propose a new index (the IHSI) to characterise the severity of sleep apnea. The new index is based on the hemispherical asymmetry of the brain and is computed from the EEG coherence analysis. We achieved a significant (p=0.0001) accuracy of up to 91% in classifying patients into apneic and non-apneic group. Our statistical analysis results show that the IHSI carries potential for providing us with a reproducible measure to assist in diagnosing of OSAHS. With the proposed methods in this thesis it may be possible to develop the technology that will not only attempt to screen the OSAHS patients but will be able to provide OSAHS diagnosis with detailed sleep architecture via home based test. These technologies will simplify the instrumentation dramatically and will make possible to extend EEG/MSA analysis to portable systems as well.

La Décomposition Modale Empirique (Empirical Mode Decomposition - EMD) ou la Transformation de Hilbert-Huang (HHT) est une nouvelle méthode d'analyse temps-fréquence qui est particulièrement adaptée pour des séries temporelles nonlinéaires et non stationnaires. Cette méthode a été proposée par NE. HUANG. il y a plus de dix ans. Pendant les dix dernières années, plus de 1000 articles ont appliqué cette méthode dans le cadre de diverses applications ou domaines de recherche. Dans cette thèse, nous appliquons cette méthode à des séries temporelles de turbulence, pour la première fois, et à des séries temporelles environnementales. Nous avons obtenu comme résultat le fait que la méthode EMD correspond à un banc de filtre dyadique (ou quasi-dyadique) pour la turbulence pleinement développée. Pour caractériser les propriétés intermittentes d'une série temporelle invariante d'échelle, nous avons généralisé l'analyse spectrale de Hilbert-Huang classique à des moments d'ordre arbitraire $q$, pour effectuer ce que nous avons appelé ``analyse spectrale de Hilbert d'ordre arbitraire''. Ceci fournit un nouveau cadre pour analyser l'invariance d'échelle directement dans un espace amplitude-fréquence, en estimant une intégrale marginale d'une pdf jointe $p(\omega,\mathcal{A})$ de la fréquence instantanée $\omega$ et de l'amplitude $\mathcal{A}$. Nous validons tout d'abord la méthode en analysant des séries temporelles de mouvement Brownien fractionnaire, et en analysant des séries temporelles multifractales synthétiques, en tant que modèle respectivement de processus monofractals et multifractals. Nous comparons les résultats obtenus avec la nouvelle méthode, à l'analyse classique utilisant les fonctions de structure: nous trouvons numériquement que la méthodologie utilisant l'approche de Hilbert fournit un estimateur plus précis pour le paramètre d'intermittence. Avec une hypothèse de stationarité, nous proposons un modèle analytique pour la fonction d'autocorrélation des incréments de séries temporelles de vitesse $\Delta u_{\ell}(t)$, où $\Delta u_{\ell}(t)=u(t+\ell)-u(t)$, et $\ell$ est l'incrément temporel. Dans le cadre de ce modèle, nous prouvons analytiquement que, si une loi de puissance est valide pour la série d'origine, la position minimisant la fonction d'autocorrélation de la variable d'origine est égale exactement au temps de séparation $\ell$ lorsque $\ell$ appartient à la zone invariante d'échelle. Ce modèle prédit une loi de puissance pour la valeur minimum, comportement vérifié par une simulation de mouvement Brownien fractionnaire et à partir de données expérimentales de turbulence. En introduisant une fonction cumulative pour la fonction d'autocorrélation, la contribution en échelle est alors caractérisée dans l'espace de fréquence de Fourier. Nous observons que la contribution principale à la fonction d'autocorrélation provient des grandes échelles. La même idée est appliquée à la fonction de structure d'ordre 2. Nous obtenons que celle-ci est également fortement influencée par les grandes échelles, ce qui montre que ceci n'est pas une bonne approche pour extraire les exposants invariants d'échelle d'une série temporelle lorsque les données sont caractérisées par des grandes échelles énergétiques. Nous appliquons ensuite cette méthodologie Hilbert-Huang à une base de données de turbulence homogène et presque isotrope, pour caractériser les propriétés multifractales invariantes d'échelle des série temporelles de vitesse en turbulence pleinement développée. Nous obtenons un comportement invariant d'échelle pour la pdf jointe $p(\omega,\mathcal{A})$ avec un exposant proche de la valeur de Kolmogorov. Nous estimons les exposants $\zeta(q)$ dans un espace amplitude-fréquence, pour la première fois. L'hypothèse d'isotropie est testée échelle par échelle dans l'espace amplitude-fréquence. Nous obtenons que le rapport d'isotropie généralisé décroit linéairement avec le moment $q$. Nous effectuons également l'analyse d'une série temporelle de température (scalaire passif) possédant un effet de rampe marqué (ramp-cliff). Pour ces données, l'approche traditionnelle utilisant les fonctions de structure ne fonctionne pas. Mais la nouvelle méthode développée dans cette thèse fournit un net régime invariant d'échelle jusqu'au moment $q=8$. Les exposants $\xi_{\theta}(q)-1$ sont très proches des exposants $\zeta(q)$ obtenus par l'approche des fonctions de structure pour la vitesse longitudinale. Nous nous intéressons ensuite à l'auto-similarité étendue (Extended Self Similarity - ESS) dans le cadre Hilbert-Huang. En ce qui concerne la méthode ESS, qui est devenue classique en turbulence, nous adaptons l'approche pour le cas Hilbert-Huang dans un espace de fréquence, et nous constatons que le modèle lognormal, avec un coefficient adéquat, fournit une très bonne estimation des exposants invariants d'échelle. Finalement nous appliquons la nouvelle méthodologie à des données environnementales: des débits de rivières, et des données de turbulence marine dans la zone de surf. Dans ce dernier cas, la méthode ESS permet de séparer les ondes de vent de la turbulence à petite échelle.

Cette thèse de doctorat concerne deux problèmes mathématiques issus de la mécanique quantique. On considère une particule quantique, non relativiste et sans spin, astreinte à se mouvoir sur une surface bidimensionnelle $\cal S$, plongée dans un champ magnétique homogène qui lui est perpendiculaire. Dans un premier problème, $(\cal S)=\R\times \mathbb(S)_L^1$, qui est un cylindre infini de circonférence $L$, ce qui correspond à des conditions aux bords periodiques. Dans le deuxième cas, $(\cal S)=\R^2$. En fonction du problème étudié, on ajoute un potentiel convenable. On est ainsi amené à étudier deux opérateurs de Schrödinger. Le premier opérateur analysé génère la dynamique d'une particule soumise à un potentiel aléatoire de type Anderson ainsi qu'un potentiel non aléatoire dont le but est de confiner la particule le long de l'axe du cylindre, sur une longueur $L$. Dans ce cas, on localise le spectre et on le classifie par le courant quantique porté par les fonctions propres correspondantes. On montre qu'il y a des régions spectrales où n'existent que des valeurs propres avec courant d'ordre un par rapport à $L$, et des régions spectrales où sont mélangées valeurs propres avec courant d'ordre un et valeurs propres avec courant infinitésimal par rapport à $L$. Ces resultats on un intétet physique dans le cadre de l'effect Hall entier. Le deuxième opérateur de Schrödinger étudié, correspond à la situation physique où le potentiel est donné par la somme d'un potentiel ``local'' et d'un potentiel dû à un petit champ électrique $F$ constant. Dans ce cas on montre que les états résonants induits par le champ électrique décroissent exponentiellement avec un taux donné par la partie imaginaire des valeurs propres d'un certain opérateur non auto-adjoint. On montre de plus que cette partie imaginaire possède une borne supérieure de l'ordre de $\exp(-1/F^2)$, pour $F$ tendant vers zéro. Ainsi, le temps de vie de l'état résonant en question est au moins de l'ordre de $\exp(1/F^2)$.

<p>This thesis focuses on responses in raised bogs to changes in the effective humidity during the Holocene. Raised bogs are terrestrial deposits that can provide contiguous records of past climate changes. Information on and knowledge about past changes in climate is crucial for our understanding of natural climate variability. Analyses on different spatial and temporal scales have been conducted on a number of raised bogs in south-central Sweden in order to gain more knowledge about Holocene climate variability.</p><p>Peatlands are useful as palaeoenvironmental archives because they develop over the course of millennia and provide a multi-faceted contiguous outlook on the past. Peat humification, a proxy for bog surface wetness, has been used to reconstruct palaeoclimate. In addition measurements of carbon and nitrogen on sub-recent peat from two bogs have been performed. The chronologies have been constrained by AMS radiocarbon dates and tephrochronology and by SCPs for the sub-recent peat.</p><p>A comparison between a peat humification record from Värmland, south-central Sweden, and a dendrochronological record from Jämtland, north-central Sweden, indicates several synchronous changes between drier and wetter climate. This implies that changes in hydrology operate on a regional scale.</p><p>In a high resolution study of two bogs in Uppland, south-central Sweden, C, N and peat humification have been compared to bog water tables inferred from testate amoebae and with meteorological data covering the last 150 years. The results indicate that peat can be subjected to secondary decomposition, resulting in an apparent lead in peat humification and C/N compared to biological proxies and meteorological data.</p><p>Several periods of wetter conditions are indicated from the analysis of five peat sequences from three bogs in Värmland. Wetter conditions around especially c. 4500, 3500, 2800 and 1700-1000 cal yr BP can be correlated to several other climate records across the North Atlantic region and Scandinavia, indicating wetter and/or cooler climatic conditions at these times. Frequency analyses of two bogs indicate periodicities between 200 and 400 years that may be caused by cycles in solar activity.</p>

In spectral analysis of high dimensional multivariate time series, it is crucial to obtain an estimate of the spectrum that is both numerically well conditioned and precise. The conventional approach is to construct a nonparametric estimator by smoothing locally over the periodogram matrices at neighboring Fourier frequencies. Despite being consistent and asymptotically unbiased, these estimators are often ill-conditioned. This is because a kernel smoothed periodogram is a weighted sum over the local neighborhood of periodogram matrices, which are each of rank one. When treating high dimensional time series, the result is a bad ratio between the smoothing span, which is the effective local sample size of the estimator, and dimension. In classification, clustering and discrimination, and in the analysis of non-stationary time series, this is a severe problem, because inverting an estimate of the spectrum is unavoidable in these contexts. Areas of application like neuropsychology, seismology and econometrics are affected by this theoretical problem. We propose a new class of nonparametric estimators that have the appealing properties of simultaneously having smaller L2-risk than the smoothed periodogram and being numerically more stable due to a smaller condition number. These estimators are obtained as convex combinations of the averaged periodogram and a shrinkage target. The choice of shrinkage target depends on the availability of prior knowledge on the cross dimensional structure of the data. In the absence of any information, we show that a multiple of the identity matrix is the best choice. By shrinking towards identity, we trade the asymptotic unbiasedness of the averaged periodogram for a smaller mean-squared error. Moreover, the eigenvalues of this shrinkage estimator are closer to the eigenvalues of the real spectrum, rendering it numerically more stable and thus more appropriate for use in classification. These results are derived under a rigorous general asymptotic framework that allows for the dimension p to grow with the length of the time series T. Under this framework, the averaged periodogram even ceases to be consistent and has asymptotically almost surely higher L2-risk than our shrinkage estimator. Moreover, we show that it is possible to incorporate background knowledge on the cross dimensional structure of the data in the shrinkage targets. We derive an exemplary instance of a custom-tailored shrinkage target in the form of a one factor model. This offers a new answer to problems of model choice: instead of relying on information criteria such as AIC or BIC for choosing the order of a model, the minimum order model can be used as a shrinkage target and combined with a non-parametric estimator of the spectrum, in our case the averaged periodogram. Comprehensive Monte Carlo studies we perform show the overwhelming gain in terms of L2-risk of our shrinkage estimators, even for very small sample size. We also give an overview of regularization techniques that have been designed for iid data, such as ridge regression or sparse pca, and show the interconnections between them.

This thesis addresses the challenges encountered when dealing with signal decomposition problems with an unknown number of components in a Bayesian framework. Particularly, we focus on the issue of summarizing the variable-dimensional posterior distributions that typically arise in such problems. Such posterior distributions are defined over union of subspaces of differing dimensionality, and can be sampled from using modern Monte Carlo techniques, for instance the increasingly popular Reversible-Jump MCMC (RJ-MCMC) sampler. No generic approach is available, however, to summarize the resulting variable-dimensional samples and extract from them component-specific parameters. One of the main challenges that needs to be addressed to this end is the label-switching issue, which is caused by the invariance of the posterior distribution to the permutation of the components. We propose a novel approach to this problem, which consists in approximating the complex posterior of interest by a "simple"--but still variable-dimensional parametric distribution. We develop stochastic EM-type algorithms, driven by the RJ-MCMC sampler, to estimate the parameters of the model through the minimization of a divergence measure between the two distributions. Two signal decomposition problems are considered, to show the capability of the proposed approach both for relabeling and for summarizing variable dimensional posterior distributions: the classical problem of detecting and estimating sinusoids in white Gaussian noise on the one hand, and a particle counting problem motivated by the Pierre Auger project in astrophysics on the other hand.

This thesis focuses on responses in raised bogs to changes in the effective humidity during the Holocene. Raised bogs are terrestrial deposits that can provide contiguous records of past climate changes. Information on and knowledge about past changes in climate is crucial for our understanding of natural climate variability. Analyses on different spatial and temporal scales have been conducted on a number of raised bogs in south-central Sweden in order to gain more knowledge about Holocene climate variability. Peatlands are useful as palaeoenvironmental archives because they develop over the course of millennia and provide a multi-faceted contiguous outlook on the past. Peat humification, a proxy for bog surface wetness, has been used to reconstruct palaeoclimate. In addition measurements of carbon and nitrogen on sub-recent peat from two bogs have been performed. The chronologies have been constrained by AMS radiocarbon dates and tephrochronology and by SCPs for the sub-recent peat. A comparison between a peat humification record from Värmland, south-central Sweden, and a dendrochronological record from Jämtland, north-central Sweden, indicates several synchronous changes between drier and wetter climate. This implies that changes in hydrology operate on a regional scale. In a high resolution study of two bogs in Uppland, south-central Sweden, C, N and peat humification have been compared to bog water tables inferred from testate amoebae and with meteorological data covering the last 150 years. The results indicate that peat can be subjected to secondary decomposition, resulting in an apparent lead in peat humification and C/N compared to biological proxies and meteorological data. Several periods of wetter conditions are indicated from the analysis of five peat sequences from three bogs in Värmland. Wetter conditions around especially c. 4500, 3500, 2800 and 1700-1000 cal yr BP can be correlated to several other climate records across the North Atlantic region and Scandinavia, indicating wetter and/or cooler climatic conditions at these times. Frequency analyses of two bogs indicate periodicities between 200 and 400 years that may be caused by cycles in solar activity.

The research focus is on the various modeling aspects of flow and sediment transport in water bodies and watersheds. The interaction of flow with a mobile bed involves a complex process in which various turbulent scales characterized by coherent structures cause a chaotic sediment motion. In many rivers and natural waterways secondary flows that are dominating flow struc-tures bring about more complications. In estuaries and open waterbodies thermal stratification and internal mixing control the flow structure besides the flow interaction with the mobile bed. To adequately model these processes 3D coupled flow and transport models are needed. The research is based on use and adaptation of open source codes for 3D hydrodynamic and sediment transport model known as Estuarine Coastal Ocean Model (ECOMSED) and the Soil and Water Assessment Tool (SWAT) model. A bed load transport model was developed and coupled to ECOMSED. The flow and sediment transport characteristics in a curved channel and a river reach were successfully captured by the model. Improvements in ECOMSED were made to study the effect of wind and basin bathymetry on mixing and flow exchange between two estuaries. Using spectral analysis the hydrological component of SWAT model was investigated for its applicability under limited data conditions in three Ethiopian catchments. / QC 20100827

No description available.

The Sun’s corona expands outward, populating the solar system with plasma. This plasma is known as the solar wind. The solar wind carries with it the Sun’s magnetic field, which is also known as the interplanetary magnetic field (IMF). The resulting configuration of the IMF creates a current sheet at solar equatorial latitudes, which the Earth crosses as it orbits the Sun. When the Earth is on one side of the current sheet it is in a sector where the IMF is directed largely away from or toward the Sun. On the other side of the current sheet the IMF is in opposite direction. The crossing of the current sheet is known as a sector boundary crossing (SBC). The solar wind and IMF properties change significantly near the current sheet, and this affects the Earth’s ionosphere. The Super Dual Auroral Radar Network (SuperDARN) high frequency (HF) radar data rates from 2001-2011 were examined using several techniques: a superposed epoch analysis, a fast fourier transform (FFT) analysis, and a cross–correlation analysis. Data from multiple instruments were analyzed in this study. These include the solar wind and IMF data from spacecraft, observations of charged particles precipitating into the Earth’s ionosphere, echoes from ground–based SuperDARN radars, and data from gound–based neutron monitors that detect galactic cosmic rays. Solar wind and IMF properties change significantly across a sector boundary. An increase in the IMF magnitude of about 30% occurs on the day of the SBC, and the IMF returns to pre–crossing values over the next two days. There is a decrease in the solar wind speed of about 15% the day before and the day of the SBC, and the solar wind density doubles at the time of the SBC. The polarity of the SBC does not appear to affect the solar wind and IMF. A peak in the data rate of SuperDARN echoes from both the ionosphere and ground occurs within one day of the SBC, though the variability of these data is quite large. The hemispherical power, which is an estimation of the electron energy flux precipitating into the ionosphere derived from satellite observations, increases following a SBC. Satellite particle data also revealed that the equatorward auroral oval boundary moves equatorward following a SBC. The cosmic ray counts at the Earth’s surface appear to be unaffected by the SBC. The solar wind and ionosphere data sets exhibited strong periodicities, and these were harmonics of the synodic rotational period of the Sun (approximately 27 days). Common periodicities observed were 27 days, 13.5 days, 9 days, 6.75 days and 5.4 days. There was a dominant 9–day periodicity observed in the solar wind and ionospheric data from 2005–2008, but was not observed in the solar 10.7 cm wavelength electromagnetic flux. The 9-day periodicity in the solar wind during this period has been linked to three persistent features on the Sun that produced corotating high–speed streams, or areas of fast solar wind. The parameters whose change did not depend on the polarity of the SBC had periodicities that were half that of the SBCs. From the cross–correlation analysis some relationships between the data sets became evident. For periods of high solar wind speed there were low SuperDARN data rates, and vice versa. The solar wind speed and hemispherical power were found to be well correlated, while the hemispherical power and the SuperDARN scatter occurrence were found to be anticorrelated. The solar wind changes appear to be affecting the state of the ionosphere, likely through particle precipitation. The SuperDARN scatter occurrence has been shown in past studies to be most greatly affected by changes in the electron density profile of the ionosphere, which can be influenced by changes in particle precipitation. These results demonstrate a link between the solar wind and the state of the ionosphere.