Dans la première partie de cette thèse, on présente des inégalités de concentration convexe pour des intégrales stochastiques. Ces résultats sont obtenus par calcul stochastique e tpar calcul de Malliavin forward/backward. On présente également des inégalités de déviation pour les exponentielles martingales à saut.Dans une deuxième partie on présente des théorèmes limites pour le conditionnement du mouvement brownien. / In the first part of this thesis, we present some convex concentration inequalities for stochastic integrals. These results are obtained by forward/backward stochastic calculus combined with Malliavin calculus. We also present deviation inequalities for exponentialjump-diffusion.In the second part, we present some limit theorems for the conditionning of Brownian motion.

This thesis focuses particularly on the application of chemometrics in the field of analytical chemistry. Chemometrics (or multivariate analysis) consists in finding a relationship between two groups of variables, often called dependent and independent variables. In infrared spectroscopy for instance, chemometrics consists in the prediction of a quantitative variable (the obtention of which is delicate, requiring a chemical analysis and a qualified operator), such as the concentration of a component present in the studied product from spectral data measured on various wavelengths or wavenumbers (several hundreds, even several thousands). In this research we propose a methodology in the field of chemometrics to handle the chemical data (spectrophotometric data) which are often in high dimension. To handle these data, we first propose a new incremental method (step-by-step) for the selection of spectral data using linear and non-linear regression based on the combination of three principles: linear or non-linear regression, incremental procedure for the variable selection, and use of a validation set. This procedure allows on one hand to benefit from the advantages of non-linear methods to predict chemical data (there is often a non-linear relationship between dependent and independent variables), and on the other hand to avoid the overfitting phenomenon, one of the most crucial problems encountered with non-linear models. Secondly, we propose to improve the previous method by a judicious choice of the first selected variable, which has a very important influence on the final performances of the prediction. The idea is to use a measure of the mutual information between the independent and dependent variables to select the first one; then the previous incremental method (step-by-step) is used to select the next variables. The variable selected by mutual information can have a good interpretation from the spectrochemical point of view, and does not depend on the data distribution in the training and validation sets. On the contrary, the traditional chemometric linear methods such as PCR or PLSR produce new variables which do not have any interpretation from the spectrochemical point of view. Four real-life datasets (wine, orange juice, milk powder and apples) are presented in order to show the efficiency and advantages of both proposed procedures compared to the traditional chemometric linear methods often used, such as MLR, PCR and PLSR.

In this thesis, analysis of the forward backward asymmetry of high energy electron pairs at the CMS - LHC with a centre of mass energy of 7 TeV is presented and the possibility of search for a new neutral weak boson Z&rsquo / via measuring the forward backward asymmetry AFB of high energy electron pairs is discussed. The forward backward asymmetry is a natural result of the interference between the neutral current mediators: Photon and Z boson. A new neutral gauge boson would also interfere with these mediators and this new interference would either enhance the forward backward asymmetry at high energies or suppress it. In this analysis, 4.67 fb&minus / 1 data collected at the CMS experiment in 2011 is used

Dans cette thèse nous présentons dans un premier temps une nouvelle notion de différentiabilité généralisée pour les applications multivoques, faisant intervenir des applications positivement homogènes: la H-différentiabilité. Nous étudions la stabilité de cette notion en utilisant la convergence de Fischer, d'abord dédiée aux ensembles mais que nous avons adaptée aux applications multivoques. Nous nous intéressons ensuite à l'étude de la dépendance continue des ensembles de points fixes d'une application multivoque contractante par rapport aux données. Finalement nous analysons la convergence d'une méthode d'approximations successives de type forward-backward splitting, des zéros de la somme de deux opérateurs multivoques non monotones, jouissants notamment de propriétés de pseudo H-différentiabilité / In this thesis we present at first a new concept of generalized differentiation for setvalued mappings, involving positively homogeneous applications: the H-differentiability. We study the stability of this notion by using Fischer convergence,firstly dedicated to sets but which we have adapted to set-valued mappings. We establish the continuous dependence of fixed points sets of set-valued contraction and finally we study the convergence of a forward-backward splitting method for approximating the zeros of the sum of two non-monotone set-valued mappings, notably using properties of pseudo H-differentiability.

Cette thèse est consacrée à la recherche des zéros d'un opérateur maximal monotone structuré, à l'aide de systèmes dynamiques dissipatifs continus et discrets. Les solutions sont obtenues comme limites des trajectoires lorsque le temps t tend vers l'infini. On s'intéressera principalement aux dynamiques obtenues par régularisation de type Levenberg-Marquardt de la méthode de Newton. On décrira aussi les approches basées sur des dynamiques voisines.Dans un cadre Hilbertien, on s'intéresse à la recherche des zéros de l'opérateur maximal monotone structuré M = A + B, où A est un opérateur maximal monotone général et B est un opérateur monotone Lipschitzien. Nous introduisons des dynamiques continues et discrètes de type Newton régularisé faisant intervenir d'une façon séparée les résolvantes de l'opérateur A (implicites), et des évaluations de B (explicites). A l'aide de la représentation de Minty de l'opérateur A comme une variété Lipschitzienne, nous reformulons ces dynamiques sous une forme relevant du théorème de Cauchy-Lipschitz. Nous nous intéressons au cas particulier où A est le sous différentiel d'une fonction convexe, semi-continue inférieurement, et propre, et B est le gradient d'une fonction convexe, différentiable. Nous étudions le comportement asymptotique des trajectoires. Lorsque le terme de régularisation ne tend pas trop vite vers zéro, et en s'appuyant sur une analyse asymptotique de type Lyapunov, nous montrons la convergence des trajectoires. Par ailleurs, nous montrons la dépendance Lipschitzienne des trajectoires par rapport au terme de régularisation.Puis nous élargissons notre étude en considérant différentes classes de systèmes dynamiques visant à résoudre les inclusions monotones gouvernées par un opérateur maximal monotone structuré M = $partialPhi$+ B, où $partialPhi$ désigne le sous différentiel d'une fonction convexe, semicontinue inférieurement, et propre, et B est un opérateur monotone cocoercif. En s'appuyant sur une analyse asymptotique de type Lyapunov, nous étudions le comportement asymptotique des trajectoires de ces systèmes. La discrétisation temporelle de ces dynamiques fournit desalgorithmes forward-backward (certains nouveaux ).Finalement, nous nous intéressons à l'étude du comportement asymptotique des trajectoires de systèmes dynamiques de type Newton régularisé, dans lesquels on introduit un terme supplémentaire de viscosité évanescente de type Tikhonov. On obtient ainsi la sélection asymptotique d'une solution de norme minimale. / This thesis is devoted to finding zeroes of structured maximal monotone operators, by using discrete and continuous dissipative dynamical systems. The solutions are obtained as the limits of trajectories when the time t tends towards infinity.We pay special attention to the dynamics that are obtained by Levenberg-Marquardt regularization of Newton's method. We also revisit the approaches based on some related dynamical systems.In a Hilbert framework, we are interested in finding zeroes of a structured maximal monotone operator M = A + B, where A is a general maximal monotone operator, and B is monotone and locally Lipschitz continuous. We introduce discrete and continuous dynamical systems which are linked to Newton's method. They involve separately B and the resolvents of A, and are designed to splitting methods. Based on the Minty representation of A as a Lipschitz manifold, we show that these dynamics can be formulated as differential systems, which are relevant to the Cauchy-Lipschitz theorem. We focus on the particular case where A is the subdifferential of a convex lower semicontinuous proper function, and B is the gradient of a convex, continuously differentiable function. We study the asymptotic behavior of trajectories. When the regularization parameter does not tend to zero too rapidly, and by using Lyapunov asymptotic analysis, we show the convergence of trajectories. Besides, we show the Lipschitz continuous dependence of the solution with respect to the regularization term.Then we extend our study by considering various classes of dynamical systems which aim at solving inclusions governed by structured monotone operators M = $partialPhi$+ B, where $partialPhi$ is the subdifferential of a convex lower semicontinuous function, and B is a monotone cocoercive operator. By a Lyapunov analysis, we show the convergence properties of the orbits of these systems. The time discretization of these dynamics gives various forward-backward splittingmethods (some new).Finally, we focus on the study of the asymptotic behavior of trajectories of the regularized Newton dynamics, in which we introduce an additional vanishing Tikhonov-like viscosity term.We thus obtain the asymptotic selection of the solution of minimal norm.

Självskattningsformulär utgör ett viktigt kliniskt redskap för både utredning och intervention av röstproblem men i nuläget är tillgången till olika formulär i Sverige begränsad då antalet validerade svenska översättningar är få. Syfte med studien var att översätta och preliminärt validera The Voice Symptom Scale (VoiSS) som består av 30 frågor tilldelade komponenterna Nedsättning, Emotionellt och Fysiskt. Den svenska versionen av VoiSS framtogs genom ”Forward-backward Translation” med en efterföljande pilotstudie. Sammanlagt deltog 203 vuxna individer som rekryterades via webb- och pappersenkät. Av dessa uppgav 86 deltagare att de upplevde röstbesvär. Resultaten visade på tydliga gruppskillnader där gruppen Med upplevda röstproblem genererade högre genomsnittliga svarspoäng än gruppen Utan upplevda röstproblem. Inga överlappningar kunde konstateras. En principalkomponentanalys (PCA) var i stort sett förenlig med en trekomponentstruktur som tillsammans med gruppseparationen visade på hög konstruktvaliditet. Vidare noterades samstämmighet mellan den svenska versionen och VoiSS-originalet. Sensitivitets- och specificitetsvärden bekräftade en hög diagnostisk validitet. Slutsatsen drogs att formuläret med god validitet förmår att diagnosticera upplevelse av röstproblem. Den preliminära valideringen visade således att den svenska versionen av VoiSS kan användas som ett instrument vid utredning av röstproblem men att ytterligare forskning behövs för att säkerställa formulärets användbarhet i klinisk verksamhet. / Self-assessment questionnaires are important clinical instruments for both investigation and intervention of voice problems but at date access to various questionnaires in Sweden is limited due to few validated translations. The objective of this study was to translate and preliminary validate the Voice Symptom Scale (VoiSS) consisting of 30 questions assigned Impairment, Emotional and Physical. The Swedish version of VoiSS was developed through ”Forward-backward Translation” followed by a pilot study. The questionnaire was completed by a total of 203 adults who were recruited by web and paper survey. Out of these, 86 participants experienced voice problems. Obvious group differences were observed in that the group With experienced voice problems generated higher mean scores than the group Without experienced voice problems. No overlaps were observed. A principal component analysis (PCA) was largely consistent with a three component structure that, combined with the group separation, affirmed high construct validity. Moreover, concurrence between the Swedish version and the VoiSS-original was found. Calculated values of sensitivity and specificity confirmed a high diagnostic validity. The conclusion was made that the self-assessment questionnaire with good validity was able to diagnose experience of voice problems. In conclusion, preliminary validation showed that the Swedish version of VoiSS can be used as a diagnostic tool in assessing voice problems. However, more research needs to be done to ensure the questionnaires adaptation to clinical context.

This thesis explored the possibilities of using a Hidden Markov Model approach for multi-target localisation in an urban environment, with observations generated from Wi-Fi sensors. The area is modelled as a network of nodes and arcs, where the arcs represent sidewalks in the area and constitutes the hidden states in the model. The output of the model is the expected amount of people at each road segment throughout the day. In addition to this, two methods for analyzing the impact of events in the area are proposed. The first method is based on a time series analysis, and the second one is based on the updated transition matrix using the Baum-Welch algorithm. Both methods reveal which road segments are most heavily affected by a surge of traffic in the area, as well as potential bottleneck areas where congestion is likely to have occurred. / I det här examensarbetet har lokalisering av gångtrafikanter med hjälp av Hidden Markov Models utförts. Lokaliseringen är byggd på data från Wi-Fi sensorer i ett område i Stockholm. Området är modellerat som ett graf-baserat nätverk där linjerna mellan noderna representerar möjliga vägar för en person att befinna sig på. Resultatet för varje individ är aggregerat för att visa förväntat antal personer på varje segment över en hel dag. Två metoder för att analysera hur event påverkar området introduceras och beskrivs. Den första är baserad på tidsserieanalys och den andra är en maskinlärningsmetod som bygger på Baum-Welch algoritmen. Båda metoderna visar vilka segment som drabbas mest av en snabb ökning av trafik i området och var trängsel är troligt att förekomma.

Existing low-voltage networks may not accommodate high penetrations of low-carbon technologies. The topic of this thesis is unbalance, which if minimised can delay or avoid the constraining of these technologies or the replacing of still-useful network assets. Most of the discussion on unbalance, as seen in the standards and the literature, centres on the effects of voltage unbalance on consumer equipment. Its effects on the network are not equally reported. This thesis recognises fundamental differences between the consumer and network perspectives. It can inform distribution network operators on the interpretation of measurements taken on low-voltage networks and guide research on unbalance due to high penetrations of low-carbon technologies. Much of the work involved simulations of LV networks. Initially, existing 3 x 3 or 5 x 5 approaches to the forward-backward sweep method were thought suitable. After a review of these approaches however, there were doubts as to how accurately they accounted for the shared neutral-earth return path on which the out-of-balance current flows. This led to the derivation of a new 5 x 5 approach using only Kirchhoff s voltage (KVL) and current laws (KCL). Its results are validated thoroughly in the thesis. In addition to satisfying KVL and KCL, they match Matlab SimPowerSystems exactly and are in close agreement with measurements taken on a very unbalanced rural feeder. This thesis also investigates the mitigation of unbalance using the static balancer. This is a transformer with a single interconnected-star winding. It was used in 1930-1950s to correct unbalance. Contributions are made for its possible re-introduction as a retrofit option. They include a model for use in the forward-backward sweep method, validated by laboratory and field measurements, and the quantification of the static balancer s strengths and weaknesses as this can help identify when it should be used.

In this thesis, first we study the unique classical solution of quasi-linear second order parabolic partial differential equations (PDEs). For this, we study the existence and uniqueness of the $L^2_{\rho}( \mathbb{R}^{d}; \mathbb{R}^{d}) \otimes L^2_{\rho}( \mathbb{R}^{d}; \mathbb{R}^{k})\otimes L^2_{\rho}( \mathbb{R}^{d}; \mathbb{R}^{k\times d})$ valued solution of forward backward stochastic differential equations (FBSDEs) with finite horizon, the regularity property of the solution of FBSDEs and the connection between the solution of FBSDEs and the solution of quasi-linear parabolic PDEs. Then we establish their connection in the Sobolev weak sense, in order to give the weak solution of the quasi-linear parabolic PDEs. Finally, we study the unique weak solution of quasi-linear second order elliptic PDEs through the stationary solution of the FBSDEs with infinite horizon.

Dans la première partie de cette thèse, on présente des inégalités de concentration convexe pour des intégrales stochastiques. Ces résultats sont obtenus par calcul stochastique e tpar calcul de Malliavin forward/backward. On présente également des inégalités de déviation pour les exponentielles martingales à saut.Dans une deuxième partie on présente des théorèmes limites pour le conditionnement du mouvement brownien.