Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are widely-used mathematical models for decomposing multivariate data. They capture spatial relationships between variables, but ignore any temporal relationships that might exist between observations. Probabilistic PCA (PPCA) and Probabilistic CCA (ProbCCA) are versions of these two models that explain the statistical properties of the observed variables as linear mixtures of an alternative, hypothetical set of hidden, or latent, variables and explicitly model noise. Both the noise and the latent variables are assumed to be Gaussian distributed. This thesis introduces two new models, named PPCA-AR and ProbCCA-AR, that augment PPCA and ProbCCA respectively with autoregressive processes over the latent variables to additionally capture temporal relationships between the observations. To make PPCA-AR and ProbCCA-AR robust to outliers and able to model leptokurtic data, the Gaussian assumptions are replaced with infinite scale mixtures of Gaussians, using the Student-t distribution. Bayesian inference calculates posterior probability distributions for each of the parameter variables, from which we obtain a measure of confidence in the inference. It avoids the pitfalls associated with the maximum likelihood method: integrating over all possible values of the parameter variables guards against overfitting. For these new models the integrals required for exact Bayesian inference are intractable; instead a method of approximation, the variational Bayesian approach, is used. This enables the use of automatic relevance determination to estimate the model orders. PPCA-AR and ProbCCA-AR can be viewed as linear dynamical systems, so the forward-backward algorithm, also known as the Baum-Welch algorithm, is used as an efficient method for inferring the posterior distributions of the latent variables. The exact algorithm is tractable because Gaussian assumptions are made regarding the distribution of the latent variables. This thesis introduces a variational Bayesian forward-backward algorithm based on Student-t assumptions. The new models are demonstrated on synthetic datasets and on real remote sensing and EEG data.

Many applications lead to signals with nonnegative function values. Understanding the structure of the spaces of nonnegative signals is therefore of interest in many different areas. Hence, constructing effective representation spaces with suitable metrics and natural transformations is an important research topic. In this thesis, we present our investigations of the structure of spaces of nonnegative signals and illustrate the results with applications in the fields of multispectral color science and content-based image retrieval. The infinite-dimensional Hilbert space of nonnegative signals is conical and convex. These two properties are preserved under linear projections onto lower dimensional spaces. The conical nature of these coordinate vector spaces suggests the use of hyperbolic geometry. The special case of three-dimensional hyperbolic geometry leads to the application of the SU(1,1) or SO 2,1) groups. We introduce a new framework to investigate nonnegative signals. We use PCA-based coordinates and apply group theoretical tools to investigate sequences of signal coordinate vectors. We describe these sequences with oneparameter subgroups of SU(1,1) and show how to compute the one-parameter subgroup of SU(1,1) from a given set of nonnegative signals. In our experiments we investigate the following signal sequences: (i) blackbody radiation spectra; (ii) sequences of daylight/twilight spectra measured in Norrk¨oping, Sweden and in Granada, Spain; (iii) spectra generated by the SMARTS2 simulation program; and (iv) sequences of image histograms. The results show that important properties of these sequences can be modeled in this framework. We illustrate the usefulness with examples where we derive illumination invariants and introduce an efficient visualization implementation. Content-Based Image Retrieval (CBIR) is another topic of the thesis. In such retrieval systems, images are first characterized by descriptor vectors. Retrieval is then based on these content-based descriptors. Selection of contentbased descriptors and defining suitable metrics are the core of any CBIR system. We introduce new descriptors derived by using group theoretical tools. We exploit the symmetry structure of the space of image patches and use the group theoretical methods to derive low-level image filters in a very general framework. The derived filters are simple and can be used for multispectral images and images defined on different sampling grids. These group theoretical filters are then used to derive content-based descriptors, which will be used in a real implementation of a CBIR.

We analyse the Swedish central bank, the Riksbank’s, interest setting policy in a Taylor rule framework. In particular, we examine whether or not the Riksbank has reacted to fluctuations in asset prices during the period 1995:Q1 to 2016:Q2. This is done by estimating a forward-looking Taylor rule with interest rate smoothing, augmented with stock prices, house prices and the real exchange rate, using IV GMM. In general, we find that the Riksbank’s interest setting policy is well described by a forward-looking Taylor rule with interest rate smoothing and that the use of factors as instruments, derived from a PCA, serves to alleviate the weak-identification problem that tend to plague GMM. Moreover, apart from finding evidence that the Riksbank exhibit a substantial degree of policy rate inertia and has acted so as to stabilize inflation and the real economy, we also find evidence that the Riksbank has been reacting to fluctuations in stock prices, house prices, and the real exchange rate.

Bayesian learning methods are the basis of many powerful analysis techniques in neuroimaging, permitting probabilistic inference on hierarchical, generative models of data. This thesis primarily develops Bayesian analysis techniques for magnetic resonance imaging (MRI), which is a noninvasive neuroimaging tool for probing function, perfusion, and structure in the human brain. The first part of this work fits nonlinear biophysical models to multimodal functional MRI data within a variational Bayes framework. Simultaneously-acquired multimodal data contains mixtures of different signals and therefore may have common noise sources, and a method for automatically modelling this correlation is developed. A Gaussian process prior is also used to allow spatial regularization while simultaneously applying informative priors on model parameters, restricting biophysically-interpretable parameters to reasonable values. The second part introduces a novel data fusion framework for multivariate data analysis which finds a joint decomposition of data across several modalities using a shared loading matrix. Each modality has its own generative model, including separate spatial maps, noise models and sparsity priors. This flexible approach can perform supervised learning by using target variables as a modality. By inferring the data decomposition and multivariate decoding simultaneously, the decoding targets indirectly influence the component shapes and help to preserve useful components. The same framework is used for unsupervised learning by placing independent component analysis (ICA) priors on the spatial maps. Linked ICA is a novel approach developed to jointly decompose multimodal data, and is applied to combined structural and diffusion images across groups of subjects. This allows some of the benefits of tensor ICA and spatially-concatenated ICA to be combined, and allows model comparison between different configurations. This joint decomposition framework is particularly flexible because of its separate generative models for each modality and could potentially improve modelling of functional MRI, magnetoencephalography, and other functional neuroimaging modalities.

The purpose of this work is to present the development and validation of a novel method for reconstructing time-dependent, or 4D, cone-beam CT (4DCBCT) images. 4DCBCT can have a variety of applications in the radiotherapy of moving targets, such as lung tumors, including treatment planning, dose verification, and real time treatment adaptation. However, in its current incarnation it suffers from poor reconstruction quality and limited temporal resolution that may restrict its efficacy. Our algorithm remedies these issues by deforming a previously acquired high quality reference fan-beam CT (FBCT) to match the projection data in the 4DCBCT data-set, essentially creating a 3D animation of the moving patient anatomy. This approach combines the high image quality of the FBCT with the fine temporal resolution of the raw 4DCBCT projection data-set. Deformation of the reference CT is accomplished via a patient specific motion model. The motion model is constrained spatially using eigenvectors generated by a principal component analysis (PCA) of patient motion data, and is regularized in time using parametric functions of a patient breathing surrogate recorded simultaneously with 4DCBCT acquisition. The parametric motion model is constrained using forward iterative projection matching (FIPM), a scheme which iteratively alters model parameters until digitally reconstructed radiographs (DRRs) cast through the deforming CT optimally match the projections in the raw 4DCBCT data-set. We term our method FIPM-PCA 4DCBCT. In developing our algorithm we proceed through three stages of development. In the first, we establish the mathematical groundwork for the algorithm and perform proof of concept testing on simulated data. In the second, we tune the algorithm for real world use; specifically we improve our DRR algorithm to achieve maximal realism by incorporating physical principles of image formation combined with empirical measurements of system properties. In the third stage we test our algorithm on actual patient data and evaluate its performance against gold standard and ground truth data-sets. In this phase we use our method to track the motion of an implanted fiducial marker and observe agreement with our gold standard data that is typically within a millimeter.

L'objectif de cette étude était de réaliser des revêtements de TiO2 présentant une large variété de morphologies et d'établir des corrélations entre la structure de ces couches et leurs propriétés fonctionnelles, notamment la photocatalyse. Deux voies de synthèse employant le même précurseur, le tétra-isopropropoxide (TTIP) de titane, ont été utilisées, le procédé sol-gel et le dépôt chimique en phase vapeur (MOCVD). L'emploi de ces deux techniques permet de produire TiO2 sous une large gamme de morphologies mais avec des variétés polymorphiques similaires. Les revêtements synthétisés ont été caractérises afin de déterminer leur composition polymorphique, la taille des cristallites, la surface spécifique, la rugosité et l'épaisseur. Puis leur activité photocalytique pour la dégradation du bleu de méthylène a été déterminée. Par voie sol-gel, des dispersions de nano-cristallites de TiO2 dans l'eau, stables sur une longue durée (plus d'un an) en termes de composition polymorphique, taille d'agglomérats et de cristallites ont été synthétisées. Les revêtements ont été réalisés par tape-casting et dip-coating. Pour la synthèse en MOCVD, un plan d'expérience (PeX) a été utilisé, à notre connaissance pour la première fois. Il a permis de déterminer, d'une manière efficace et économique (avec un nombre minimum de tests expérimentaux), les paramètres les plus importants du procédé contrôlant les diverses propriétés quantifiables du revêtement. Il a aussi permis de mettre en évidence les interactions entre les paramètres de synthèse et leur effet sur la structure du revêtement. Les conclusions tirées du PeX sont en accord avec les résultats obtenus lors des études précédentes. L'analyse en composantes principales (ACP) a été réalisée pour avoir une vue globale de la façon dont les diverses propriétés des revêtements sont reliées entre elles / The overall objectives of this study was to find an environmental-friendly and simple procedure to synthesize titanium-dioxide, as well as, to determine the relation between the structural and functional properties of titanium dioxide coatings. Both of these objective have been attained in this study. By the sol-gel technique, titanium dioxide sols were synthesized by the hydrolysis of titanium(IV)isopropoxide. Nanocrystalline dispersions of TiO2 in water were prepared that were suitable for coatings and having long-term stability (more than 1 year) in terms of polymorphic composition, crystallite and agglomerate size. A design of experiments (DoE) was utilised, to our knowledge, for the first time in MOCVD for the synthesis of TiO2 coatings. It was employed to determine, in a timely and economical manner, the most significant process parameters for any quantifiable property of the coating and to highlight the interaction between these operating parameters, as well as, the correlation between the structure of the coating and the process. The conclusions drawn from the DoE were compared to results obtained by previous studies and were found to concur. Therefore, the DoE was successful in screening the most important process parameters, with a minimum number of experimental trials. For most of the properties that were under investigation, the DoE showed that, the deposition temperature and reactor pressure were, often-times, the most significant. Therefore, to change the microstructure and composition of MOCVD coatings, changing these process parameters will ensure the highest impact. It has to be stressed that the conclusions drawn from the DoE are restricted to the experimental range that was under investigation. Principal Component Analysis (PCA) was conducted to have an overall view of how the different properties of the coatings related with one another. The interpretations made from this analysis were that the photocatalytic (PC) activity of the coatings produced did not relate strongly to the polymorphic composition, which is contrary to literature review and is explained to be a result of the different morphologies that lead to different porosities and specific surface area. The PC activity did not depend on the mass over a critical mass. With this analysis it appeared to be clear that the porosity and specific surface area played a larger role than polymorphic composition. This hypothesis has to be verified because we did not succeed in determining the specific surface area of our coatings during this study. However, some preliminary tests have been conducted showing that cyclic voltametry could be used to evaluate the surface area of our films

The term "personality" nowadays occurs more often not only in psychological studies of humans but also in animal studies. Studying of personality help us to define the behavioural characteristics which can vary within the age, sexes, species or enviroments. Behavioral experiments are used to detect these behavioral patterns and they can divide the animals into the different groups. The subject of our research became three populations of house mouse (Mus musculus sensu lato) which we tested in a series of experiments involving free exploration, forced exploration, hole- board test, test of vertical activity and Elevated plus-maze. These experiments should reveal wheter the mice differ in their behaviour through the context of sex, comensalism or subspecies. We found (with in excepcion of one test) that intrapopulation variability differences are very small but interpopulation differences purely increase in the cas of comensalism and effects of subspecies. Keywords: Mus musculus, comensalism, open fieldtest, Elevated plus-maze, Principal Component Analysis (PCA)

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Cette thèse est une contribution à la connaissance des impacts, quantitatifs et qualitatifs, liés à la déprise minière de la région d’Alès. Le travail a consisté en l’analyse et l’interprétation de données quantitatives et qualitatives des eaux d’émergences des anciennes mines de charbon du bassin alésien afin de connaître la composition chimique des eaux d’émergences et de l’expliquer. Pour cela, nous avons utilisé des Analyses en Composantes Principales (ACP), des diagrammes de Piper et de Schoeller-Berkalov sur l’ensemble des émergences. Dans un deuxième temps, nous avons réalisé une analyse de l’évolution temporelle des concentrations de chaque élément pour les émergences où les données sont disponibles. L’aspect quantitatif est étudié grâce à une synthèse des connaissances disponible sur le réservoir minier de Fontanes (géologie, répartition spatiale, données de pompage et de niveaux piézométriques). Certaines émergences présentent une qualité qui rend impossible leur rejet direct dans l’environnement et il est important dans cette situation de bien définir la masse d’eau concernée. Pour cela, nous avons élaboré un modèle hydrodynamique par automates séquentiels. Il est appliqué aux anciens travaux de Rochebelle-St-Martin, aboutissant à la détermination des paramètres perméabilité et épaisseur du réservoir par reconstitution du niveau piézométrique du réservoir tout en tenant compte d’un pompage encore maintenu dans l’exploitation. Cette modélisation permet de mieux connaître les paramètres définissant l’aquifère minier dans la perspective d’exploiter cette réserve. Ces eaux de mines présentent une qualité médiocre. A partir d’une meilleure connaissance hydrodynamique du système, obtenue par la modélisation, il devient possible de proposer une valorisation de cette eau par utilisation de ses calories en géothermie connaissant la géométrie du réservoir minier. Les anciennes exploitations minières sont à nouveau source d’énergie / This thesis is a contribution to the knowledge of the quantitative and qualitative impacts, linked to the abandonment of the mining works on Alès coal basin. This work consisted in analysis and interpretation of quantitative and qualitative data on the waters outflows of former coal mines in order to determine the chemical composition of groundwaters outflows and the water chemistry. For that, we used principal component analysis, diagrams of Piper and Schoeller-Berkalov on all waters outflows. Secondly, we analyzed the temporal evolution of concentrations of each element for the waters outflows. The quantitative aspect is therefore considered by the synthesis of knowledge available on the mining reservoir of Fontanes (geology, spatial distribution, pumping data and piezometrics levels). Some groundwaters outflows have a quality that makes their direct discharge into the environment impossible and it is important, in this situation, to define the affected body of the water. For that, we have developed a hydrodynamical model by sequential automaton. It is applied to the former works of Rochebelle-St-Martin de Valgalgues leading to the determination of the parameters permeability and thickness of mining aquifer recovery of piezometric level of the reservoir while taking into account a pumping still maintained. This model will lead to a better comprehension of the parameters defining the aquifer in the mining perspective to exploit this reserve. The mine water has a poor quality. After a better knowledge obtained by a hydrodynamical modeling, it becomes realistic to propose a recovery of this water by use of its calories from geothermal and knowing the geometry of the tank mine

Photoconductive antenna (PCA) array based THz near-field imager incorporating Hadamard multiplexing method is developed in this work. By using a 2 × 2 dipole antenna array as the THz transmitter, the system signal-to-noise ratio (SNR) is demonstrated to be improved by a factor of 2 as the theory predicts. Additionally, a 2-D scanning of a metallic structure on a THz-transparent substrate (with a total scanning area of 1 × 1 mm2) is experimentally implemented. Correlation coefficient estimation is made afterwards to quantify the reconstructed image quality.