This dissertation mainly studies correlation and then portfolio analysis of financial contagion and capital flight, focusing on currency co-movements around the political uncertainty due to the Brexit referendum on 26 June 2016. The correlation, mean, and covariance computations in the analysis are both time-unconditional and time-conditional, and the generalized autoregressive conditional heteroskedasticity (GARCH) and exponentially weighted moving average (EWMA) methods are applied. The correlation analysis in this dissertation (Chapter 1) extends the previous literature on contagion testing based on a single global factor model, bivariate correlation analysis, and heteroskedasticity bias correction. Chapter 1 proposes an alternatively extended framework, assuming that intensification of financial correlations in a state of distress could coincide with rising global-factor-loading variability, provides simple tests to verify the assumptions of the literature and of the extended framework, and considers capital flight other than merely financial contagion. The outcomes show that, compared to the literature, the extended framework can be deemed more verified to the Brexit case. Empirically, with the UK being the shock-originating economy and the sterling value plummeting on the US dollar, there exist contagions to some other major currencies as well as a flight to quality, particularly to the yen, probably suggesting diversification benefits. When the correlation coefficients are time-conditional, or depend more on more recent data, the evidence shows fewer contagions and flights since the political uncertainty in question disappeared gradually over time. After relevant interest rates were partialled out, some previous statistical contagion and flight occurrences became less significant or even insignificant, possibly due to the significant impacts of the interest rates on the corresponding currency correlations. The portfolio analysis in this dissertation (Chapter 2) examines financial contagion and capital flight implied by portfolio reallocations through mean-variance portfolio analysis, and builds on the correlation analysis in Chapter 1. In the correlation analysis, correlations are bivariate, whereas in the portfolio analysis they are multivariate and the risk-return tradeoff is also vitally involved. Portfolio risk minimization and reward-to-risk maximization are the two analytical cases of portfolio optimality taken into consideration. Robust portfolio optimizations, using shrinkage estimations and newly proposed risk-based weight constraints, are also applied. The evidence demonstrates that the portfolio analysis outcomes regarding currency contagions and flights, implying diversification benefits, vary and are noticeably dissimilar from the correlation analysis outcomes of Chapter 1. Subsequently, it could be inferred that the diversification benefits deduced from the portfolio and correlation analyses differ owing to the dominance, during market uncertainty, of the behaviors of the means and (co)variances of all the shock-originating and shock-receiving returns, over the behaviors of just bivariate correlations between the shock-originating and shock-receiving returns. Moreover, corrections of the heteroskedasticity bias inherent in the shock-originating returns, overall, do not have an effect on currency portfolio rebalancing. Additionally, hedging demands could be implied from detected structural portfolio reallocations, probably as a result of variance-covariance shocks rising from Brexit. / This dissertation mainly studies correlation and then portfolio analysis of financial contagion and capital flight, focusing on currency co-movements around the political uncertainty due to the Brexit referendum on 26 June 2016. The correlation, mean, and covariance computations in the analysis are both time-unconditional and time-conditional, and the generalized autoregressive conditional heteroskedasticity (GARCH) and exponentially weighted moving average (EWMA) methods are applied. The correlation analysis in this dissertation (Chapter 1) extends the previous literature on contagion testing based on a single global factor model, bivariate correlation analysis, and heteroskedasticity bias correction. Chapter 1 proposes an alternatively extended framework, assuming that intensification of financial correlations in a state of distress could coincide with rising global-factor-loading variability, provides simple tests to verify the assumptions of the literature and of the extended framework, and considers capital flight other than merely financial contagion. The outcomes show that, compared to the literature, the extended framework can be deemed more verified to the Brexit case. Empirically, with the UK being the shock-originating economy and the sterling value plummeting on the US dollar, there exist contagions to some other major currencies as well as a flight to quality, particularly to the yen, probably suggesting diversification benefits. When the correlation coefficients are time-conditional, or depend more on more recent data, the evidence shows fewer contagions and flights since the political uncertainty in question disappeared gradually over time. After relevant interest rates were partialled out, some previous statistical contagion and flight occurrences became less significant or even insignificant, possibly due to the significant impacts of the interest rates on the corresponding currency correlations. The portfolio analysis in this dissertation (Chapter 2) examines financial contagion and capital flight implied by portfolio reallocations through mean-variance portfolio analysis, and builds on the correlation analysis in Chapter 1. In the correlation analysis, correlations are bivariate, whereas in the portfolio analysis they are multivariate and the risk-return tradeoff is also vitally involved. Portfolio risk minimization and reward-to-risk maximization are the two analytical cases of portfolio optimality taken into consideration. Robust portfolio optimizations, using shrinkage estimations and newly proposed risk-based weight constraints, are also applied. The evidence demonstrates that the portfolio analysis outcomes regarding currency contagions and flights, implying diversification benefits, vary and are noticeably dissimilar from the correlation analysis outcomes of Chapter 1. Subsequently, it could be inferred that the diversification benefits deduced from the portfolio and correlation analyses differ owing to the dominance, during market uncertainty, of the behaviors of the means and (co)variances of all the shock-originating and shock-receiving returns, over the behaviors of just bivariate correlations between the shock-originating and shock-receiving returns. Moreover, corrections of the heteroskedasticity bias inherent in the shock-originating returns, overall, do not have an effect on currency portfolio rebalancing. Additionally, hedging demands could be implied from detected structural portfolio reallocations, probably as a result of variance-covariance shocks rising from Brexit.

Particle Image Velocimetry (PIV) is an optical fluid measurement technique used to obtain velocity measurements. Two PIV systems were used to capture data simultaneously and measurement error for the MS PIV system is calculated. An investigation of error distribution is performed to determine when uncertainty estimations fail for the CS PIV-UQ method. Investigation of when results from multi pass PIV processing are achieve were performed so that reliable uncertainty estimations are produced with the CS method. An investigation was also performed which determined that error distributions in PIV systems are correlated with flow shear and particle seeding density. Correlation of random errors in space was also performed at the jet core and shear regions of the flow. It was found that in flow regions with large shear that error distributions were non-Gaussian. It was also found in regions of large shear that CS uncertainty results did not match the error. For multi-pass PIV processing with 50% and 75% IW overlap it was found that 4 and 6 passes should be used, respectively, in order for CS uncertainty estimations to be reliable. It was also found that the correlation of random errors in space is much larger in shear regions of the jet flow than in the jet core.

A study was made in order to deduce whether certain chemical species, namely water (H2O) and carbon monoxide (CO), are present in the atmosphere of the exoplanet WASP-107 b, which lies about 200 light-years away from Earth in the constellation Virgo. The project was carried out at Uppsala University at the Department of Physics and Astronomy. This was done through the use of transmission spectroscopy and executed using a cross-correlation technique, one of the leading methods available today to extract exoplanetary atmospheric information. The data used was collected during a transit which occured in March 2022, originally gathered by the spectrograph CRIRES+ stationed at Very Large Telescope (VLT) in Paranal. WASP-107 b is a warm Jupiter-type planet, and since the aforementioned chemical species exhibit spectral lines mainly in the infrared (0.95-5.3 μm), it makes CRIRES+ a desirable instrument due to its specialization for working in the infrared. The data analysis was performed using several scripts built in Python with subsequent data-reduction methods. The data-reduction methods used for this purpose was the standard ESO CRIRES+ data reduction pipeline which includes removal of systemic sources of noise such as dead pixels and cosmic rays, and SysRem, which is an algorithm used to remove any trends with time and any constant features in time for each pixel time series. SysRem is currently one of the most efficient way available for doing so, and is commonly used in these types of studies. Several detection maps were then generated and studied in order to deduce whether a detection had been made or not. For this project, one exoplanet was examined and its atmosphere was probed for H2O and CO. The cross-correlation templates utilized were a combination of both species as well as one corresponding to only CO. The detection maps generated from the cross-correlation analysis initially suggested non-detections for all combinations of SysRem iterations and templates, except for two which presented features that might imply a detection but without any strong certainty. Those results indicate the possible existence of CO in the atmosphere of WASP-107 b, but further investigation is needed in order to determine their validity. / Denna rapport beskriver en studie som utförts för att undersöka ifall vissa kemiska arter, nämligen vatten (H2O) och kolmonoxid (CO), existerar i atmosfären kring exoplaneten WASP-107 b. Exoplaneten ligger cirka 200 ljusår bort från jorden i konstellationen Jungfrun. Arbetet utfördes på Uppsala universitet på institutionen för fysik och astronomi, eller Department of Physics and Astronomy. Detta gjordes huvudsakligen med hjälp av transmissionsspektroskopi och cross-correlation - en av de ledande metoderna idag för att analysera exoplanetära atmosfärer. Datan som använts för denna studie samlades in under en transit som skedde i mars 2022 med hjälp av spektrografen CRIRES+, stationerad vid Very Large Telescope (VLT) i Paranal. WASP-107 b klassas som en varm Jupiter, och eftersom de undersökta kemiska arterna huvudsakligen uppvisar spektrallinjer i det infraröda området (0.95-5.3 μm), är CRIRES+ ett sunt val då spektrografen är specialiserad på att undersöka infrarött ljus. Dataanalysen utfördes genom användningen av flertal script, byggda i Python med påföljande datareduktion. De datareduktionsmetoder som användes i detta syfte var ESO CRIRES+ standard data reduction pipeline, vilken inkluderar avlägsnandet av systematiska källor till brus såsom döda pixlar och den kosmiska bakgrundsstrålningen, och SysRem, vilket är en algoritm som används för att ta bort trender samt konstanta drag beroende på tid utmed varje pixelserie. I nuläget är SysRem en av de mer effektiva sätten att göra detta på, och är en vanlig metod i studier som denna. I detta projekt blev en exoplanet undersökt och dess atmosfär granskad för att se ifall H2O och CO förekommer i den. De cross-correlation templates som användes bestod av en som använde en kombination av båda kemiska arter, tillika en som endast detekterade CO. De detection maps som genererats från cross-correlation analysen föreslog först en ickedetektion för alla kombinationer av SysRem iterationer och templates, förutom två, vilka uppvisade signalement som möjligtvis indikerade en detektion, men utan särskild stark säkerhet. Dessa resultat föreslog en möjlig detektion av CO i atmosfären, men för att säkerställa detta krävs vidare undersökning.

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摘要 皮爾森相關係數通常作為描述區間尺度變數間相關性的參考指標，然而在社會科學領域中，由於資料多數以順序尺度的形式呈現，因此藉由傳統的皮爾森相關係數來描述順序尺度資料間的相關性通常會導致某種程度的誤差。儘管如此，以往的文獻多數傾向支持以等距離分數來取代順序尺度資料，並直接計算皮爾森相關係數。藉由模擬實驗的結果，我們發現這樣的作法並非在所有情況下都合理。 此外本研究中也對多序類相關係數進行探討。就表示順序變數間相關性的準確程度而言，多序類相關係數明顯優於利用等距離分數來計算皮爾森相關係數的方法；但若以操作上的便利程度而言，後者仍具有其優勢。 關鍵字：順序尺度、皮爾森相關係數、多序類相關係數。 / Abstract Pearson correlation coefficient is typically used to describe the correlation between two interval-scaled variables. In social science, however, most of the data are represented in ordinal-scale, and hence describing the correlation between two ordinal-scaled variables in terms of Pearson correlation coefficient would inevitably result in certain errors. Though the practice is deemed acceptable and generally supported in literatures, we found, through intensive simulations, that it should be executed with care. Polychoric correlation coefficient was also investigated. In order to describe the correlation between two ordinal-scaled variables, we found, in terms of the degree of accuracy, that Polychoric correlation coefficient is definitely better than Pearson correlation coefficient with equal-distance scores. Pearson correlation coefficient, on the other hands, is much easier to calculate, and should not be totally ignored. Key words：Ordinal-scale、Pearson correlation coefficient、Polychoric correlation coefficient。

This thesis concerns the relations between correlation matrix, difference propagation matrix and other matrices used in the block cipher cryptanalysis. We show that some relations between these matrices can be seen just as a change of basis provided by the discrete Fourier transform. This can be used for an easier proof of a well-known theorem. We also study properties of difference propagation matrix, describe a class of vectorial Boolean functions which have the same difference propagation matrix and state a numerically justified hypothesis that this class contains all such functions.

L'objectif de cette thèse est le développement d'outils technologiques et logiciels permettant un monitoring de la qualité de l'air intérieur. Cela comprend la conception de capteurs miniaturisés permettant la détection simultanée d'un grand nombre de polluants, ainsi que le développement de modèles numériques inverses utilisant les données issues de ces capteurs et permettant la reconstruction de sources de polluants. Ces travaux ont mené à l'élaboration d'un prototype fonctionnel de micro-chromatographe en phase gazeuse, système d'analyse chimique miniaturisé permettant la détection de multiples polluants. La colonne de séparation fabriquée en technologie MEMS a permis la séparation de divers composés organiques volatils en quelques dizaines de secondes. Le micro-détecteur TCD, fondé sur une mesure 4-pointes couplée à un circuit d'asservissement en température original, a permis la détection des composés séparés dans la colonne. Afin d'améliorer et de tirer au mieux parti des micro-chromatographes, des méthodes d'injections stochastiques ont été développées. Il a été démontré que ces méthodes ont plusieurs intérêts. D'une part, elles permettent facilement un gain de rapport signal/bruit de l'ordre de la décade, ce qui permet la détection de polluants plus faiblement concentrés. Il a été observé d'autre part qu'il est possible de suivre en temps réel l'évolution moyenne de la concentration des polluants alors que cela n'est pas possible lorsque le chromatographe est utilisé de manière standard. Enfin, une méthode d'injection et de traitement du signal permettant l'analyse simultanée de plusieurs échantillons avec un unique capteur a été développée. Enfin, ces travaux ont été complétés par le développement de modèles inverses 2D permettant, à partir de données issues de micro-chromatographes placés dans l'espace, la reconstruction de sources de polluants et de champs de vitesses par méthode des gaz traceur. Ces modèles sont fondés sur une approche de contrôle optimal et utilisent une résolution des équations de Navier-Stokes et de diffusion-advection par la méthode éléments finis. L'utilisation de bases orthonormées obtenues par POD a permis de régulariser ces modèles inverses / The goal of this thesis is the development of technological and numerical tools for the monitoring of indoor air quality. That comprises the design of miniaturized sensors capable of detecting a large number of pollutants, and the development of inverse models allowing the reconstruction of pollutant sources from concentration measurements. In this work we present the realization of a micro-gas chromatograph, miniaturized chemical-analysis system fabricated with silicon-based MEMS technology. The separation column can separate multiple volatile organic compounds in less than a minute. The integrated thermal conductivity detector, based on a 4-points measurement technique coupled with an original temperature control circuit, can detect compounds separated in the column. In order to improve the performances of such micro-chromatographs, stochastic injection techniques have been developped. We have shown that these techniques easily allow to reduce the detection noise by an order of magnitude so that low-concentrated pollutants can be detected. We also observed that it is possible to follow in real time the mean evolution of the concentration with such techniques. We finally developped an original multiplexing technique that allows to monitor multiple sample streams simultaneoulsy with a single sensor. Finally, this work is completed by the development of 2D inverse models that allow, from data measured by micro-chromatographs placed in a room, to reconstruct pollutant sources, concentration fields or airflow patterns. Those models are based on an optimal control approach and use the resolution of Navier-Stokes and diffusion-advection equations with the finite element method. POD orthonormal basis are used for the regularization of the problem

Ziel dieser Arbeit ist es eine Toolbox zur Charakterisierung der anomalen Diffusion von Tracerpartikeln in dicht gepackten Systemen mit Fluoreszenz-Korrelationsspektroskopie (FCS) zur Verfügung zu stellen. Es wird gezeigt, dass die robusten Informationen über die Wahrscheinlichkeitsdichtefunktion (PDF) der Verschiebung des Tracers im asymptotischen Verhalten der FCS-Kurven auf langen, sowie auf kurzen Zeitskalen enthalten sind. So liefert die Analyse des Kurzzeitverhaltens zuverlässige Aussagen über die Werte des Exponenten der anomalen Diffusion, des Diffusionskoeffizienten und der niedrigeren Momente der PDF. Dies erlaubt es eine Gaußverteilung zu bestätigen oder zu widerlegen. Der Test auf Gaußverteilung könnte als Index verwendet werden, um die richtige Form der PDF aus einer Reihe von konkurrierenden Ergebnissen zu erraten. Darüber hinaus untersuchen wir die Konsequenz der nicht skalierenden PDF auf Ergebnis der FCS-Kurven. Wir berechnen die FCS für ein Continuous Time Random Walk Modell mit Wartezeiten gemäß einer Lévy-stabilen Verteilung mit exponentiellem cut-off. Die Ergebnisse zeigen, dass obwohl die Abweichungen vom Gauß’schen Verhalten bei der asymptotischen Analyse erkannt werden können, ihre Körper immer an Formen für die normale Diffusion perfekt angepasst werden können. Schließlich schlagen wir einen alternativen Ansatz für die Durchführung von Spot Variation FCS mit dem gewöhnlichen FCS-Setup vor. Wir führen eine nicht-lineare Transformation ein, die auf das mit Binning oder Kernel smoothing method geglättete Intensitätsprofil der detektierten Fluoreszenzphotonen angewendet wird. Ihre Autokorrelation imitiert die FCS-Kurven für die Größen des Laserspots, die im Experiment effektiv kleiner als die anfängliche Größe sind. Die erhaltenen FCS-Kurven werden verwendet, um künstliche dicht gepackte Systeme sowie lebende Zellen auf Nano-Domänen oder Barrieren hin zu untersuchen. / The objective of this thesis is to provide a toolbox for characterization of anomalous diffusion of tracer particle in crowded systems using fluorescence correlation spectroscopy (FCS). We discuss that the robust information about the probability density function (PDF) of the particle’s displacement is contained in the asymptotic behaviour of the FCS curves at long and short times. Thus, analysis of the short-time behaviour provides reliable values of exponent of anomalous, diffusion coefficient and lower moments of the PDF. This allows one to to confirm or reject its Gaussian nature. The Gaussianity test could be then used to guess the correct form of the PDF from a set of competing models. We show the applicability of the proposed analysis protocol in artificially crowded systems and in living cell experiments. Furthermore, we investigate the consequence of non-scaling PDF on the possible results of the FCS data. As an example of such processes, we calculate the FCS curve for a continues time random walk model with waiting times delivered from Lévy-stable distribution with an exponential cut-off in equilibrium. The results indicate that, although the deviations from Gaussian behaviour may be detected when analyzing the short- and long-time asymptotic of the corresponding curves, their bodies are still perfectly fitted by the fit form used for normal diffusion. Finally, we propose an alternative approach for performing spot variation FCS using an ordinary FCS set-up. We introduce a non-linear transformation which applies on the smoothed intensity profile of the detected fluorescence photons with binning or smoothing kernel method. Autocorrelation of the generated intensity profiles mimic the FCS curves for the sizes of laser spots which are effectively smaller than the initial one in the experiment. The obtained FCS curves are used to investigate the presence of nano-domains or barriers in artificially crowded systems and in living cells.

Les mesures optiques dimensionnelles sont des techniques en plein essor dont la maîtrise et l'exploitation soulèvent encore de nombreuses questions. Pour une meilleure compréhension d'un système de mesure par stéréo-corrélation d'images, des études de caractérisation et d'évaluation de l'erreur de mesure en corrélation à partir d'images synthétiques et en stéréovision à partir d'images réelles ont été réalisées. Les résultats mettent en avant l'influence de plusieurs paramètres : fenêtre de corrélation, déformation et gradient de déformation. La dernière partie de l'étude est consacrée à l'identification de comportements constitutifs à partir des mesures de champs. Deux méthodes sont mises en œuvre : la méthode des champs virtuel pour l'identification des paramètres élastiques d'un matériau et l'identification paramétrique par recalage éléments finis pour le cas des comportements élasto-plastiques. / The optical dimensional measurements are emergent techniques whose control and exploitation still address many questions. For a better understanding of the stereo-correlation measurement systems, studies are made to characterize and assess the digital image correlation measurement error by the way of synthetic images. The stereovision characterization is made using real images. The results highlight the influence of several parameters : subset size, strain and strain gradient. The last part of this study is devoted to the identification of constitutive behaviour law using full-field measurements. Two identification methods are used : the virtual fields method to determine the elastic parameters of a material and the finite element model updating method to identify the elasto-plastic behaviour law.