La théorie des matrices aléatoires a des applications dans des domaines variés : mathématiques, physique, finance, ... En physique, le concept de matrices aléatoires a été utilisé pour l'étude du transport électronique dans des structures mésoscopiques, de systèmes désordonnés, de l'intrication quantique, de modèles d'interfaces 1D fluctuantes en physique statistique, des atomes froids, ... Dans cette thèse, on s'intéresse au transport AC cohérent dans un point quantique, à des propriétés d'interfaces fluctuantes 1D sur un substrat et aux propriétés topologiques de fils quantiques multicanaux. La première partie commence par une introduction générale a la théorie des matrices aléatoires ainsi qu'a la principale méthode utilisée dans cette thèse : le gaz de Coulomb. Cette technique permet entre autres d'étudier la distribution d'observables qui prennent la forme de statistiques linéaires des valeurs propres, qui représentent beaucoup de quantités physiques pertinentes. Cette méthode est ensuite appliquée à des exemples concrets pour étudier le transport cohérent et les problèmes d'interfaces fluctuantes en physique statistique. La seconde partie se concentre sur un modèle de fil désordonné : l'équation de Dirac multicanale avec masse aléatoire. Nous étendons le puissant formalisme utilisé pour l'étude de systèmes unidimensionnels au cas quasi-1D, et établissons une connexion avec un modèle de matrices aléatoires. Nous utilisons ce résultat pour obtenir la densité d'états et les propriétés de localisation. Nous montrons également que ce système présente une série de transitions de phases topologiques (changement d'un nombre quantique de nature topologique, sans changement de symétrie), contrôlées par le désordre. / Random matrix theory has applications in various fields: mathematics, physics, finance, ... In physics, the concept of random matrices has been used to study the electronic transport in mesoscopic structures, disordered systems, quantum entanglement, interface models in statistical physics, cold atoms, ... In this thesis, we study coherent AC transport in a quantum dot, properties of fluctuating 1D interfaces on a substrate and topological properties of multichannel quantum wires. The first part gives a general introduction to random matrices and to the main method used in this thesis: the Coulomb gas. This technique allows to study the distribution of observables which take the form of linear statistics of the eigenvalues. These linear statistics represent many relevant physical observables, in different contexts. This method is then applied to study concrete examples in coherent transport and fluctuating interfaces in statistical physics. The second part focuses on a model of disordered wires: the multichannel Dirac equation with a random mass. We present an extension of the powerful methods used for one dimensional system to this quasi-1D situation, and establish a link with a random matrix model. From this result, we extract the density of states and the localization properties of the system. Finally, we show that this system exhibits a series of topological phase transitions (change of a quantum number of topological nature, without changing the symmetries), driven by the disorder.

[pt] Na primeira parte dessa tese, estudamos o desvio no número de triângulos com respeito à média em ambos os modelos de grafos aleatórios G(n,m) e G(n, p). Focamos no caso em que o grafo aleatório é esparso, no qual a densidade de arestas vai para zero quando o número de vértices cresce para o infinito. Nosso foco também reside no caso de desvios moderados, i.e., aqueles cuja ordem está entre o desvio padrão e a média. Além disso, também derivamos o mesmo tipo de resultado para cerejas (caminhos de comprimento dois). Na segunda parte dessa tese, estudamos a desigualdade de Freedman. Essa desigualdade fornece limitantes para a probabilidade de desvio de um martingal limitado usando sua variância condicional. No nosso trabalho, obtemos uma versão mais forte da desigualdade de Freedman, impondo condições adicionais de simetria nos incrementos do processo martingal. / [en] In the first part of this thesis, we study the deviation of the number of triangles with respect to its mean in both the random graph models G(n,m) and G(n, p). We focus on the case where the random graph is sparse, in which the edge density goes to zero as the number of vertices increases to infinity. Also, our focus is in the case of moderate deviations, i.e., those of order in between the standard deviation and the mean. In addition, we derive the same kind of results for cherries (paths of length two). In the second part of this thesis, we study Freedman s inequality. This inequality gives bounds on the probability of the deviation of a bounded martingale using its conditional variance. In our work, we obtain a strengthening of Freedman s inequality, under additional symmetry conditions on the increments of the martingale process.

The increased demand of energy storage systems and electric vehicles on the market result in high demand of lithium-ion batteries. As a lithium-ion battery manufacturer, Northvolt runs quality tests on the products to assess their performance, life and safety. Batteries that are tested are most often behaving as expected, but sometimes deviations occur. Anomaly detection is today most often performed by plotting and comparing produced data to other test-data to find which parameters that are deviating. The purpose of this thesis is to automatize anomaly detection and a proposed solution is to use state-of-the-art machine learning methods. These include using supervised and unsupervised machine learning. Before applying machine learning, the feature engineering is presented. It describes what parameters are extracted from the experiment data sets. Then the supervised machine learning framework is described. For the unsupervised machine learning, a principal component analysis is presented to locate deviations. This thesis also presents a differential capacity analysis, as this could be incorporated with the features in the future. The results shows that the subset of labeled data for supervised learning is too small to produce a model that predicts future deviations. The extracted features are also used in the principal component analysis, where the results show deviations (outliers) and aid targeting the anomalies. These can then be used to determine the root-cause of particular anomalies and mitigate future deviations.

Актуальность диссертационной работы заключается в необходимости изучения взаимосвязи между технологиями управления отношением к здоровому образу жизни и девиантным поведением молодёжи. Рассмотрены теоретические аспекты сущности понятий «молодёжь», «девиантное поведение», «здоровый образ жизни», а также опыт применения и распространения технологий управления отношением к здоровому образу жизни молодёжи. Во второй главе диссертационной работы представлены результаты эмпирического социологического исследования технологий управления отношением к ЗОЖ как профилактики девиации молодёжи на примере Екатеринбургского института физической культуры (филиал) ФГБОУ ВО "УралГУФК". По итогам эмпирического исследования и анализа отечественного, зарубежного опыта применения технологий управления ЗОЖ был разработан и реализован проект «Студенты-центр здорового образа жизни», а также определена его эффективность. / The relevance of the dissertation work lies in the need to study the relationship between technologies for managing attitudes towards a healthy lifestyle and deviant behavior of young people. The theoretical aspects of the essence of the concepts of "youth", "deviant behavior", "healthy lifestyle", as well as the experience of applying and disseminating technologies for managing attitudes towards a healthy lifestyle of young people are considered. The second chapter of the dissertation presents the results of an empirical sociological study of technologies for managing attitudes towards a healthy lifestyle as a prevention of youth deviation on the example of the Yekaterinburg Institute of Physical Culture (branch) of the Federal State Budgetary Educational Institution of Higher Education "UralGUPC". Based on the results of empirical research and analysis of domestic and foreign experience in the application of healthy lifestyle management technologies, the project "Students-Healthy Lifestyle Center" was developed and implemented, and its effectiveness was determined.

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The aim of this project was to analyze howthe voltage magnitudes of an electrical grid is affectedwhen wind power production varies in an area aroundthe river of Ångermanälven. The goal of the project wasto keep the voltage deviation within 10 % from the setbase value. A secondary goal was to make a profitabilityassessment between power losses and costs related tothe power grid.A transmission grid model was built around Ångermanälven and simulations were made in MATLAB,with the open-source tool package called MATPOWER,to simulate the properties of the grid. Thesesimulations included real hourly historical data fordemand and power generation. Voltage deviation andlosses in the transmission grid for the system was thendetermined with power flow analysis.For the base case, the voltage deviation was keptwithin the limit of a maximum deviation of 10 %. Thebase case was thereafter upgraded to improve transmissionefficiency and resiliency. Increasing the basevoltage resulted in lower losses and voltage deviationsbelow 5 %. To make the grid more resilient and fulfillthe N-1 and N-2 criteria, additional transmission lineswere added. However, these were deemed necessary fora reliable grid, even though the upgrades increased thetotal cost of the system. / Strävan med detta projekt varatt analysera hur spänningsnivån för ett elnätpåverkas av varierande vindkraftsproduktion för ettområde kring Ångermanälven. Målet med projektetvar hålla spänningen inom 10 % från den sattabasspänningen. Ett sekundärt mål var att göra enlönsamhetsbedömning mellan effektförluster och kostnaderrelaterade till elnätet.En model av transmission nätet byggdes kring Ångermanälven och simuleringar utfördes i MATLAB,med hjälp av ett open-source verktyg kallat MATPOWER,för att simulera nätets egenskaper. Simuleringarnainkluderade verklig historisk timvis data förbehov och kraftproduktion. Spänningsavvikelser ochförluster i transmissionsnätet fastställdes med belastningsfördelning.För basfallet hölls spänningsavvikelserna inom denmaximala gränsen på 10 %. Basfallet uppgraderasdärefter för att förbättra transmissionseffektivitet ochtillförlitlighet. Ökning av basspänningen resulterade ilägre andel förluster och spänningsavvikelser på under5 %. För ett mer tillförlitligt nät och för att kunnauppfylla N-1 och N-2 kriterierna, installerades extraledningar. Dessa ledningar ansågs nödvändiga för attuppnå ett tillförlitligt elnät, även om det innebar ettkrav på ökade investeringskostnader för systemet. / Kandidatexjobb i elektroteknik 2021, KTH, Stockholm

The preludes as a whole do not conform to any specific formal mold, but offer a variety of form: binary, ternary, one-part, and five-part. As such, no new formal structures have been introduced by this "first" of the nineteenth century and twentieth century "disconnected" preludes. On the other hand, they are a heterogenous collection of styles, moods, and forms--a precedent that was followed by Debussy, Rachmoninoff, and various others. To determine the degree to which Chopin was harmonically advanced would require comparative analyses of works by his contemporaries and later nineteenth-century composers. Suffice it to say that one would be hard put to locate a collection of compositions of similar length and scope, written in the 1820's, that contains the wealth of harmonic innovations found within Opus 28.

Quand le mouvement de particules sous l'action d'un forçage extérieur est restreint par des mécanismes d'exclusion ou de blocage, des corrélations spatio-temporelles non triviales peuvent être observées, dans une dynamique caractérisé par des hétérogénéités spatiales et grandes fluctuations dans le temps.Dans cette thèse, nous étudions deux exemples d'un tel type de mouvement, en prenant en considération deux processus d'exclusion sur des réseaux discrètes en 2d et en 1d.Le premier modèle est inspiré par les mécanismes de relaxation lents observés dans le cisaillement ou le forçage de systèmes colloïdaux ou granulaires: pour des densités élevées, en augmentant le forçage la viscosité peut croitre énormément. Nous expliquons le mécanisme de blocage à grandes densités comme conséquence de l'existence simultanée de régions bloquées et mobiles dans le système, et nous déterminons la signature d'une telle dynamique par le moyen de la thermodynamique des histoires. Nous mesurons aussi l'extension spatiale des structures hétérogènes et fournissons un modèle phénoménologique reliant les propriétés microscopiques de la dynamique au comportement macroscopique de l'écoulement.Le deuxième modèle consiste en un processus d'exclusion en une dimension, incluant les effets dus à la présence structurelle d'un défaut dynamique localisé. Inspirés par la complexité et la richesse du processus de translation du ARN messager, nous proposons un nouveau modèle pour la dynamique de particules dont le mouvement est affecté par des modification stochastiques et structurelles de leur conditions de transport. Nous fournissons une description complète du modèle, avec la caractérisation de tous les régimes dynamiques possibles et une explication quantitative des profils macroscopiques du courant. / When the motion of particles driven by external forces is restricted by exclusion mechanisms or bottlenecks, non-trivial space-time correlations in their motion may be observed, giving rise to a dynamics which involves spatial heterogeneities and large fluctuations in time.Here we study two examples of such kind of motion, considering two exclusion processes on discrete lattices in 2d and 1d.The first model is inspired by the slow relaxation occurring when stirring or shearing colloidal or granular materials: at high densities (or packing fractions) increasing the external forcing may lead to a strong increase in the viscosity. We explain the blockage dynamics at high density as the coexistence of blocked and mobile regions and we determine the signature of such dynamics with the use of the thermodynamics of histories. We also quantify the spatial extension of such structures and provide a phenomenological model relating the microscopic properties of the dynamics to the macroscopic flow behavior.The second model consists in a one-dimensional exclusion process incorporating a structural, localized, dynamical defect. Inspired by the complexity and richness of mRNA translation, we propose a new model for the dynamics arising when the particles flow is regulated by structural or conformational changes in the transport medium. We provide a complete description of the model, characterizing all the possible dynamical regimes and addressing a quantitative explanation of the macroscopic current profiles.

Title: Large deviations and their applications in insurance mathematics Author: Lucia Fuchsová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Zbyněk Pawlas, Ph.D. Supervisor's e-mail address: Zbynek.Pawlas@mff.cuni.cz Abstract: In the present work we study large deviations theory. We discuss heavy-tailed distributions, which describe the probability of large claim oc- curence. We are interested in the use of large deviations theory in insurance. We simulate claim sizes and their arrival times for Cramér-Lundberg model and first we analyze the probability that ruin happens in dependence on the parameters of our model for Pareto distributed claim size, next we compare ruin probability for other claim size distributions. For real life data we model the probability of large claim size occurence by generalized Pareto distribu- tion. 1

La réalisation de formes complexes comme les moules ou les prothèses médicales nécessite l’utilisation d’opérations de super finition pour obtenir de faibles défauts géométriques, pouvant aller jusqu’au poli-miroir. Ces opérations de pré-polissage et de polissage sont encore régulièrement réalisées manuellement. En effet, malgré des avantages en termes de répétabilité, de productivité et de qualité géométrique, les méthodes de polissage automatique sont peu utilisées car elles nécessitent une mise au point importante. Les travaux de recherche présentés participent à la maîtrise du procédé de polissage automatique tout en contrôlant la qualité géométrique des pièces. Pour parvenir à cette maîtrise, un outil de simulation de l’enlèvement de matière est mis en place. Cet outil permet de simuler l’enlèvement de matière au cours d’une opération de prépolissage réalisée sur centre d’usinage 5 axes. Il se base sur un modèle du contact obtenu entre l’outil de pré-polissage et la pièce, ainsi que sur un modèle du pouvoir abrasif intégrant l’usure et l’encrassement du disque. Cette simulation permet de vérifier la régularité de l’abrasion sur une surface et d’identifier les zones pouvant faire apparaitre des défauts macro-géométriques importants. Une méthode est également proposée pour compenser les variations du pouvoir abrasif au cours du temps. La compensation s’effectue en optimisant les consignes de vitesse d’avance et/ou de fréquence de broche le long de la trajectoire. Cette méthode de pilotage permet d’obtenir un taux d’enlèvement de matière plus constant et ainsi de réduire les défauts géométriques générés pendant une opération de prépolissage. / Complex shapes such as medical implants or injection molds require the use of super-finishing operations to minimize geometrical defects, down to mirror effect finish. These pre-polishing and polishing operations are still regularly performed manually by skilled workers. In spite of advantages in terms of repeatability, productivity and geometrical quality, automatic polishing methods are not widely used because they require systematic and significant developments. The present work contributes to enhance the automatic polishing process compared to the geometric quality of the parts. To achieve this control, a numerical simulation of material removal is implemented. This software simulates the material removal during a pre-polishing operation performed on 5-axis machining center. It is based on a contact model obtained between the pre-polishing tool and the part, as well as an abrasive model including wear of the disc. This simulation allows to check the uniformity of the material removal on the surface and to identify potential areas where macro-geometric defects appear. A method is also proposed to balance variations of the abrasive efficiency. The correction is performed by optimizing the federate and/or the spindle speed along the tool path. This method provides a constant material removal and reduces the geometrical deviations generated during pre-polishing operations.