In a large number of applications arising in various fields of study, time series are approximated using linear MMSE estimates. Such approximations include finite order moving average and autoregressive approximations as well as the causal Wiener filter. In this dissertation, we study two topics related to the estimation of wide sense stationary (WSS) time series using linear MMSE estimates. In the first part of this dissertation, we study the asymptotic behaviour of autoregressive (AR) and moving average (MA) approximations. Our objective is to investigate how faithfully such approximations replicate the original sequence, as the model order as well as the number of samples approach infinity. We consider two aspects: convergence of spectral density of MA and AR approximations when the covariances are known and when they are estimated. Under certain mild conditions on the spectral density and the covariance sequence, it is shown that the spectral densities of both approximations converge in L2 as the order of approximation increases. It is also shown that the spectral density of AR approximations converges at the origin under the same conditions. Under additional regularity assumptions, we show that similar results hold for approximations from empirical covariance estimates. In the second part of this dissertation, we address the problem of detecting interdependence relations within a group of time series. Ideally, in order to infer the complete interdependence structure of a complex system, dynamic behaviour of all the processes involved should be considered simultaneously. However, for large systems, use of such a method may be infeasible and computationally intensive, and pairwise estimation techniques may be used to obtain sub-optimal results. Here, we investigate the problem of determining Granger-causality in an interdependent group of jointly WSS time series by using pairwise causal Wiener filters. Analytical results are presented, along with simulations that compare the performance of a method based on finite impulse response Wiener filters to another using directed information, a tool widely used in literature. The problem is studied in the context of cyclostationary processes as well. Finally, a new technique is proposed that allows the determination of causal connections under certain sparsity conditions.

Purpose: The purpose of this thesis is to study the causal relationship between bank sector development and economic growth in four Nordic countries (Sweden, Finland, Denmark and Norway). Method: Our thesis is based on a quantitative method. The study consists of a compilation and analysis of key financial indicators that represent economic growth and bank sector development. A Granger causality test has been conducted on the time series in order to measure the causal link between economic growth and bank sector development. Theoretical framework: The study is based on the theory of endogenous growth and the causal relationship between bank sector development and economic growth also known as the demand following and supply leading hypothesis.  Results: The results of the four countries are ambiguous. Except for Denmark, that follows the supply leading hypothesis, the remaining countries do not show a unanimous result.

Miscellaneous examples of misleading statistical data or interpretation are presented in a form suitable for students in mathematics or Social Sciences during a first course of statistics. The aim is to promote critical thinking when confronted (mainly by the media or scientific papers) by information that is biased, incomplete, poorly defined, or deliberately oriented towards a preconceived target. Starting with the simple manipulation of Simpson paradox, the emphasis is put on the need for counfounding in the analysis of relationship between variables.

Power distribution networks (PDNs) are conducting structures employed in semiconductor systems with the aim of providing circuits with reliable and constant operating voltage. This network has non-neglible electrical parasitics. Consequently, when digital circuits inside the chip switch, the supply voltage delivered to them does not remain ideal and exhibits spatial and temporal voltage fluctuations. These fluctuations in the supply voltage, known as the power-supply noise (PSN), can affect the functionality and the performance of modern microprocessors. The design of this PDN in the chip is an important part in ensuring power integrity. Modeling and simulation of the PSN in on-chip PDNs is important to reduce the cost of processors. These PDNs have irregular geometries, which affect the PSN. As a result, they have to be modeled. The problem sizes encountered in this simulation are usually large (on the order of millions), necessitating computationally efficient simulation approaches. Existing approaches for this simulation do not guarantee at least one of the following three required properties: computationally efficiency, accuracy, and numerically robustness. Therefore, there is a need to develop accurate, numerically robust, and efficient algorithms for this simulation. For many interconnects (e.g., transmission lines, board connectors, package PDNs), only their frequency responses and SPICE circuits (e.g., nonlinear switching drivers, equivalent circuits of interconnects) terminating them are known. These frequency responses are usually available only up to a certain maximum frequency. Simulating the electrical behavior of these systems is important for the reliable design of microprocessors and for their faster time-to-market. Because terminations can be nonlinear, a transient simulation is required. There is a need for a transient simulation of band-limited frequency-domain data characterizing a multiport passive system with SPICE circuits. The number of ports can be large (greater than or equal to 100 ports). In this simulation, unlike in traditional circuit simulators, normal properties like stability and causality of transient results are not automatically met and have to be ensured. Existing techniques for this simulation do not guarantee at least one of the following three required properties: computationally efficiency for a large number of ports, causality, and accuracy. Therefore, there is a need to develop accurate and efficient time-domain techniques for this simulation that also ensure causality. The objectives of this Ph.D. research are twofold: 1) To develop accurate, numerically robust, and computationally efficient time-domain algorithms to compute PSN in on-chip PDNs with irregular geometries. 2) To develop accurate and computationally efficient time-domain algorithms for the causal cosimulation of band-limited frequency-domain data with SPICE circuits.

Functional magnetic resonance imaging (fMRI) has emerged as the method of choice to non-invasively investigate brain function in humans. Though brain is known to act as a nonlinear system, here has not been much effort to explore the applicability of nonlinear analysis techniques to fMRI data. Also, recent trends have suggested that functional localization as a model of brain function is incomplete and efforts are being made to develop models based on networks of regions to understand brain function. Therefore this thesis attempts to introduce the twin concepts of nonlinear dynamics and network analysis into a broad spectrum of fMRI data analysis techniques. First, we characterized the nonlinear univariate dynamics of fMRI noise using the concept of embedding to explain the origin of tissue-specific differences of baseline activity in the brain. The embedding concept was extended to the multivariate case to study nonlinear functional connectivity in the distributed motor network during resting state and continuous motor task. The results showed that the nonlinear method may be more sensitive to the desired gray matter signal. Subsequently, the scope of connectivity was extended to include directional interactions using Granger causality. An integrated approach was developed to alleviate the confounding effect of the spatial variability of the hemodynamic response and graph theory was employed to characterize the network topology. This methodology proved effective in characterizing the dynamics of cortical networks during motor fatigue. The nonlinear extension of Granger causality showed that it was more robust in the presence of confounds such as baseline drifts. Finally, we utilized the integration of the spatial correlation function to study connectivity in local brain networks. We showed that our method is robust and can reveal interesting information including the default mode network during resting state. Application of this technique to anesthesia data showed dose dependent suppression of local connectivity in the default mode network, particularly in the frontal areas. Given the body of evidence emerging from our studies, nonlinear and network characterization of fMRI data seems to provide novel insights into brain function.

We study two methods of data analysis which are common tools for the analysis of neuronal data. In particular, we examine how causal interactions between brain regions can be investigated using time series reflecting the neural activity in these regions. Furthermore, we analyze a method used to study the neural code that evaluates the discrimination of the responses of single neurons elicited by different stimuli. This discrimination analysis is based on the quantification of the similarity of the spike trains with time scale parametric spike train distances. In each case we describe the methods used for the analysis of the neuronal data and we characterize their specificity using simulated or exemplary experimental data. Taking into account our results, we comment the previous studies in which the methods have been applied. In particular, we focus on the interpretation of the statistical measures in terms of underlying neuronal causal connectivity and properties of the neural code, respectively. / Estudiem dos mètodes d'anàlisi de dades que són eines habituals per a l'anàlisi de dades neuronals. Concretament, examinem la manera en què les interaccions causals entre regions del cervell poden ser investigades a partir de sèries temporals que reflecteixen l'activitat neuronal d'aquestes regions. A més a més, analitzem un mètode emprat per estudiar el codi neuronal que avalua la discriminació de les respostes de neurones individuals provocades per diferents estímuls. Aquesta anàlisi de la discriminació es basa en la quantificació de la similitud de les seqüències de potencials d'acció amb distàncies amb un paràmetre d'escala temporal. Tenint en compte els nostres resultats, comentem els estudis previs en els quals aquests mètodes han estat aplicats. Concretament, ens centrem en la interpretació de les mesures estadístiques en termes de connectivitat causal neuronal subjacent i propietats del codi neuronal, respectivament.

Research Doctorate - Doctor of Philosophy (PhD) / This thesis presents results on optimal coding and decoding of discrete-time stochastic signals, in the sense of minimizing a distortion metric subject to a constraint on the bit-rate and on the signal transfer function from source to reconstruction. The first (preliminary) contribution of this thesis is the introduction of new distortion metric that extends the mean squared error (MSE) criterion. We give this extension the name Weighted-Correlation MSE (WCMSE), and use it as the distortion metric throughout the thesis. The WCMSE is a weighted sum of two components of the MSE: the variance of the error component uncorrelated to the source, on the one hand, and the remainder of the MSE, on the other. The WCMSE can take account of signal transfer function constraints by assigning a larger weight to deviations from a target signal transfer function than to source-uncorrelated distortion. Within this framework, the second contribution is the solution of a family of feedback quantizer design problems for wide sense stationary sources using an additive noise model for quantization errors. These associated problems consist of finding the frequency response of the filters deployed around a scalar quantizer that minimize the WCMSE for a fixed quantizer signal-to-(granular)-noise ratio (SNR). This general structure, which incorporates pre-, post-, and feedback filters, includes as special cases well known source coding schemes such as pulse coded modulation (PCM), Differential Pulse-Coded Modulation (DPCM), Sigma Delta converters, and noise-shaping coders. The optimal frequency response of each of the filters in this architecture is found for each possible subset of the remaining filters being given and fixed. These results are then applied to oversampled feedback quantization. In particular, it is shown that, within the linear model used, and for a fixed quantizer SNR, the MSE decays exponentially with oversampling ratio, provided optimal filters are used at each oversampling ratio. If a subtractively dithered quantizer is utilized, then the noise model is exact, and the SNR constraint can be directly related to the bit-rate if entropy coding is used, regardless of the number of quantization levels. On the other hand, in the case of fixed-rate quantization, the SNR is related to the number of quantization levels, and hence to the bit-rate, when overload errors are negligible. It is shown that, for sources with unbounded support, the latter condition is violated for sufficiently large oversampling ratios. By deriving an upper bound on the contribution of overload errors to the total WCMSE, a lower bound for the decay rate of the WCMSE as a function of the oversampling ratio is found for fixed-rate quantization of sources with finite or infinite support. The third main contribution of the thesis is the introduction of the rate-distortion function (RDF) when WCMSE is the distortion metric, denoted by WCMSE-RDF. We provide a complete characterization for Gaussian sources. The resulting WCMSE-RDF yields, as special cases, Shannon's RDF, as well as the recently introduced RDF for source-uncorrelated distortions (RDF-SUD). For cases where only source-uncorrelated distortion is allowed, the RDF-SUD is extended to include the possibility of linear-time invariant feedback between reconstructed signal and coder input. It is also shown that feedback quantization schemes can achieve a bit-rate only 0.254 bits/sample above this RDF by using the same filters that minimize the reconstruction MSE for a quantizer-SNR constraint. The fourth main contribution of this thesis is to provide a set of conditions under which knowledge of a realization of the RDF can be used directly to solve encoder-decoder design optimization problems. This result has direct implications in the design of subband coders with feedback, as well as in the design of encoder-decoder pairs for applications such as networked control. As the fifth main contribution of this thesis, the RDF-SUD is utilized to show that, for Gaussian sta-tionary sources with memory and MSE distortion criterion, an upper bound on the information-theoretic causal RDF can be obtained by means of an iterative numerical procedure, at all rates. This bound is tighter than 0:5 bits/sample. Moreover, if there exists a realization of the causal RDF in which the re-construction error is jointly stationary with the source, then the bound obtained coincides with the causal RDF. The iterative procedure proposed here to obtain Ritc(D) also yields a characterization of the filters in a scalar feedback quantizer having an operational rate that exceeds the bound by less than 0:254 bits/sample. This constitutes an upper bound on the optimal performance theoretically attainable by any causal source coder for stationary Gaussian sources under the MSE distortion criterion.

The Swedish Moderate Party had for a long time varied widely in election results. This essay emerges that the theory of dealignment and realignment explains the variation. Dealignment meaning that contemporary voters in western democracies don’t establish relations with political parties in a wide form as traditional. This essay show that the traditional ways of political identity and later voting acts are not important in the same way as before. The Moderate party has in the public eye been a party that people tend to have strong feelings about. The established explanation, the right left scale and class, were found to be less likely to explain why people like or don ́t like the Moderate Party. It is part of a major social change that has been established in most Western democracies. Essentially, this is about new post material value based parties. This study shows that it also affects a large established party like the Moderate Party and a part of a realignment in Swedish politics where new patterns are established. Also that it is an ongoing development were social background and political scale of the traditional values are becoming more and more ineffective in the cause of contemporary voters' behavior.

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Cette thèse développe une réflexion épistémologique autour de la notion de biomarqueurs dans le cas de la maladie d’Alzheimer. Elle est centrée sur le transfert des connaissances du domaine de la biologie à celui de la pratique médicale et clinique, avec une attention particulière aux techniques de diagnostic précoce et aux Big Data. La maladie d’Alzheimer présente une temporalité particulière, son apparition étant insidieuse et sa phase asymptomatique longue. Elle se différencie des cancers en ne se prêtant pas à l’analyse génomique de cellules spécifiques, et permet ainsi d’aborder différemment le statut épistémique des biomarqueurs. Le biomarqueur (que ce soit une molécule, un réseau d’interactions, voire un algorithme), est porteur d’information sans pour autant établir un lien de causalité directe avec la maladie. C’est essentiellement un indice et non la représentation de la condition réelle d’un sujet ; c’est ensuite un objet entouré d’incertitude ; c’est enfin un objet dont la maîtrise n’est pas totale, un objet qui n’est jamais complètement donné. Enfin, les relations entre le biomarqueur et le milieu extérieur font partie intégrante de son fonctionnement. Les biomarqueurs sont essentiels dans la transformation des pratiques médicales vers l’anticipation et le suivi de l’évolution de la condition d’un sujet. En mettant en évidence des éléments transformant des facteurs de risque en une pathologie, les biomarqueurs invitent chacun à se surveiller et permettent un accompagnement des personnes dans une situation où elles n’ont encore aucun signe clinique d’une maladie évolutive. / This dissertation develops epistemological reflections on the notion of biomarkers in the case of Alzheimer’s disease. It focuses on the challenge posed by the transfer of knowledge from the field of biology to medical and clinical practices, with a special attention to the techniques of early diagnosis and especially the role of Big Data. Alzheimer's disease presents a particular temporality, its appearance being insidious with a long asymptomatic phase. It differs from cancer by not being amenable to genomic analysis of specific cells, and thus allows a different approach to the epistemic status of biomarkers. The biomarker whether it be a molecule, network of interactions, or even an algorithm, sheds light on the disease in the absence of any direct causal links between the biomarker and the disease. It is primarily an indicator rather than the representation of a body condition. As a consequence, it is always surrounded by uncertainty and never fully mastered, nor fully given. The biomarker is an object whose relations with the environment are an integral part of its functioning. Biomarkers are essential in transforming medical practices towards anticipating and monitoring the evolution of a subject's health condition. By highlighting elements that transform risk factors into a pathology, biomarkers invite everyone to monitor themselves and make it possible to support people well ahead of the appearance of clinical signs of an evolving disease.