Ce travail de thèse présente l’étude du diagramme de phase des oxydes lamellaires NaxMoO2dans le cadre de la recherche de nouveaux matériaux. L’identification des transitionsstructurales au cours de l’intercalation et désintercalation électrochimique du sodium dans lesdomaines de composition ½ ≤ x ≤ 1 et ¼ < x ≤ ½ a été faite par électrochimie combinée à ladiffraction des rayons X in situ. Il a été montré que le profil très accidenté de la courbegalvanostatique résulte de multiples réarrangements structuraux au cours du cyclage.Notamment l’existence de nombreuses phases NaxMoO2 particulières a été mise en évidence,pour lesquelles des mises en ordre des ions sodium et des atomes de molybdène sont attendues.Des composés Na~1/2MoO2, Na~2/3MoO2 et NaMoO2 ont été synthétisés ex situ par voieélectrochimique ou chimique et leur caractérisation révèle des arrangements structurauxcomplexes, tel que des chaînes de clusters de molybdène dans les feuillets [MoO2] de NaMoO2. / This work concerns the investigation of the phase diagram of sodium layered oxides NaxMoO2in the search of new materials. Structural transitions upon sodium electrochemical(de)intercalation were studied by electrochemistry combined with in situ X-ray diffraction forcompositions ½ ≤ x ≤ 1 et ¼ < x ≤ ½. It was shown that the very undulating aspect of theelectrochemical curve results from multiple structural rerarrangements upon cycling. Especiallynumerous NaxMoO2 specific phases have been evidenced, for which sodium/vacancy orderingsas well as the formation of Mo-Mo bonds are expected. Na~1/2MoO2, Na~2/3MoO2 et NaMoO2compounds have been (electro)chemically synthesized and their structural characterizationreveals complex structures, such as chains of diamond-like molybdenum clusters in NaMoO2.

The Bayesian nonparametric inference requires the construction of priors on infinite dimensional spaces such as the space of cumulative distribution functions and the space of cumulative hazard functions. Well-known priors on the space of cumulative distribution functions are the Dirichlet process, the two-parameter Poisson-Dirichlet process and the beta-Stacy process. On the other hand, the beta process is a popular prior on the space of cumulative hazard functions. This thesis is divided into three parts. In the first part, we tackle the problem of sampling from the above mentioned processes. Sampling from these processes plays a crucial role in many applications in Bayesian nonparametric inference. However, having exact samples from these processes is impossible. The existing algorithms are either slow or very complex and may be difficult to apply for many users. We derive new approximation techniques for simulating the above processes. These new approximations provide simple, yet efficient, procedures for simulating these important processes. We compare the efficiency of the new approximations to several other well-known approximations and demonstrate a significant improvement. In the second part, we develop explicit expressions for calculating the Kolmogorov, Levy and Cramer-von Mises distances between the Dirichlet process and its base measure. The derived expressions of each distance are used to select the concentration parameter of a Dirichlet process. We also propose a Bayesain goodness of fit test for simple and composite hypotheses for non-censored and censored observations. Illustrative examples and simulation results are included. Finally, we describe the relationship between the frequentist and Bayesian nonparametric statistics. We show that, when the concentration parameter is large, the two-parameter Poisson-Dirichlet process and its corresponding quantile process share many asymptotic pr operties with the frequentist empirical process and the frequentist quantile process. Some of these properties are the functional central limit theorem, the strong law of large numbers and the Glivenko-Cantelli theorem.

The automotive safety company Veoneer are producers of high end driver visual assistance systems, but the knowledge about the absolute accuracy of their dynamic calibration algorithms that estimate the vehicle’s orientation is limited. In this thesis, a novel measurement system is proposed to be used in gathering reference data of a vehicle’s orientation as it is in motion, more specifically the pitch and roll angle of the vehicle. Focus has been to estimate how the uncertainty of the measurement system is affected by errors introduced during its construction, and to evaluate its potential in being a viable tool in gathering reference data for algorithm performance evaluation. The system consisted of three laser distance sensors mounted on the body of the vehicle, and a range of data acquisition sequences with different perturbations were performed by driving along a stretch of road in Linköping with weights loaded in the vehicle. The reference data were compared to camera system data where the bias of the calculated angles were estimated, along with the dynamic behaviour of the camera system algorithms. The experimental results showed that the accuracy of the system exceeded 0.1 degrees for both pitch and roll, but no conclusions about the bias of the algorithms could be drawn as there were systematic errors present in the measurements. / Bilsäkerhetsföretaget Veoneer är utvecklare av avancerade kamerasystem inom förarassistans, men kunskapen om den absoluta noggrannheten i deras dynamiska kalibreringsalgoritmer som skattar fordonets orientering är begränsad. I denna avhandling utvecklas och testas ett nytt mätsystem för att samla in referensdata av ett fordons orientering när det är i rörelse, mer specifikt dess pitchvinkel och rollvinkel. Fokus har legat på att skatta hur osäkerheten i mätsystemet påverkas av fel som introducerats vid dess konstruktion, samt att utreda dess potential när det kommer till att vara ett gångbart alternativ för att samla in referensdata för evaluering av prestandan hos algoritmerna. Systemet bestod av tre laseravståndssensorer monterade på fordonets kaross. En rad mätförsök utfördes med olika störningar introducerade genom att köra längs en vägsträcka i Linköping med vikter lastade i fordonet. Det insamlade referensdatat jämfördes med data från kamerasystemet där bias hos de framräknade vinklarna skattades, samt att de dynamiska egenskaperna kamerasystemets algoritmer utvärderades. Resultaten från mätförsöken visade på att noggrannheten i mätsystemet översteg 0.1 grader för både pitchvinklarna och rollvinklarna, men några slutsatser kring eventuell bias hos algoritmerna kunde ej dras då systematiska fel uppstått i mätresultaten.

The Bayesian nonparametric inference requires the construction of priors on infinite dimensional spaces such as the space of cumulative distribution functions and the space of cumulative hazard functions. Well-known priors on the space of cumulative distribution functions are the Dirichlet process, the two-parameter Poisson-Dirichlet process and the beta-Stacy process. On the other hand, the beta process is a popular prior on the space of cumulative hazard functions. This thesis is divided into three parts. In the first part, we tackle the problem of sampling from the above mentioned processes. Sampling from these processes plays a crucial role in many applications in Bayesian nonparametric inference. However, having exact samples from these processes is impossible. The existing algorithms are either slow or very complex and may be difficult to apply for many users. We derive new approximation techniques for simulating the above processes. These new approximations provide simple, yet efficient, procedures for simulating these important processes. We compare the efficiency of the new approximations to several other well-known approximations and demonstrate a significant improvement. In the second part, we develop explicit expressions for calculating the Kolmogorov, Levy and Cramer-von Mises distances between the Dirichlet process and its base measure. The derived expressions of each distance are used to select the concentration parameter of a Dirichlet process. We also propose a Bayesain goodness of fit test for simple and composite hypotheses for non-censored and censored observations. Illustrative examples and simulation results are included. Finally, we describe the relationship between the frequentist and Bayesian nonparametric statistics. We show that, when the concentration parameter is large, the two-parameter Poisson-Dirichlet process and its corresponding quantile process share many asymptotic pr operties with the frequentist empirical process and the frequentist quantile process. Some of these properties are the functional central limit theorem, the strong law of large numbers and the Glivenko-Cantelli theorem.

Performance of static analysis of the London Eye structure is the subject of this diploma thesis. First chapters of the thesis analyses overview of realized structures of the Ferris wheel. The main part of the thesis analyses the London Eye structure itself. Specifically are described response analyses, sensitivity analyses, analyses of ultimate limit state and serviceability, stress analyses, analyses of fatigue stress and lifetime analyses. The thesis describes among static analysis also a design of dynamic vibration absorbers. The results of each analysis are evaluated in the final chapters.

In this thesis, we present some new results in distribution theory for both discrete and continuous random variables, together with their motivating applications. We start with some results about the Multivariate Gaussian Distribution and its characterization as a maximizer of the Strichartz Estimates. Then, we present some characterizations of discrete and continuous distributions through ideas coming from optimal transportation. After this, we pass to the Simpson's Paradox and see that it is ubiquitous and it appears in Quantum Mechanics as well. We conclude with a group of results about discrete and continuous distributions invariant under symmetries, in particular invariant under the groups $A_1$, an elliptical version of $O(n)$ and $\mathbb{T}^n$. As mentioned, all the results proved in this thesis are motivated by their applications in different research areas. The applications will be thoroughly discussed. We have tried to keep each chapter self-contained and recalled results from other chapters when needed. The following is a more precise summary of the results discussed in each chapter. In chapter \ref{chapter 2}, we discuss a variational characterization of the Multivariate Normal distribution (MVN) as a maximizer of the Strichartz Estimates. Strichartz Estimates appear as a fundamental tool in the proof of wellposedness results for dispersive PDEs. With respect to the characterization of the MVN distribution as a maximizer of the entropy functional, the characterization as a maximizer of the Strichartz Estimate does not require the constraint of fixed variance. In this chapter, we compute the precise optimal constant for the whole range of Strichartz admissible exponents, discuss the connection of this problem to Restriction Theorems in Fourier analysis and give some statistical properties of the family of Gaussian Distributions which maximize the Strichartz estimates, such as Fisher Information, Index of Dispersion and Stochastic Ordering. We conclude this chapter presenting an optimization algorithm to compute numerically the maximizers. Chapter \ref{chapter 3} is devoted to the characterization of distributions by means of techniques from Optimal Transportation and the Monge-Amp\`{e}re equation. We give emphasis to methods to do statistical inference for distributions that do not possess good regularity, decay or integrability properties. For example, distributions which do not admit a finite expected value, such as the Cauchy distribution. The main tool used here is a modified version of the characteristic function (a particular case of the Fourier Transform). An important motivation to develop these tools come from Big Data analysis and in particular the Consensus Monte Carlo Algorithm. In chapter \ref{chapter 4}, we study the \emph{Simpson's Paradox}. The \emph{Simpson's Paradox} is the phenomenon that appears in some datasets, where subgroups with a common trend (say, all negative trend) show the reverse trend when they are aggregated (say, positive trend). Even if this issue has an elementary mathematical explanation, the statistical implications are deep. Basic examples appear in arithmetic, geometry, linear algebra, statistics, game theory, sociology (e.g. gender bias in the graduate school admission process) and so on and so forth. In our new results, we prove the occurrence of the \emph{Simpson's Paradox} in Quantum Mechanics. In particular, we prove that the \emph{Simpson's Paradox} occurs for solutions of the \emph{Quantum Harmonic Oscillator} both in the stationary case and in the non-stationary case. We prove that the phenomenon is not isolated and that it appears (asymptotically) in the context of the \emph{Nonlinear Schr\"{o}dinger Equation} as well. The likelihood of the \emph{Simpson's Paradox} in Quantum Mechanics and the physical implications are also discussed. Chapter \ref{chapter 5} contains some new results about distributions with symmetries. We first discuss a result on symmetric order statistics. We prove that the symmetry of any of the order statistics is equivalent to the symmetry of the underlying distribution. Then, we characterize elliptical distributions through group invariance and give some properties. Finally, we study geometric probability distributions on the torus with applications to molecular biology. In particular, we introduce a new family of distributions generated through stereographic projection, give several properties of them and compare them with the Von-Mises distribution and its multivariate extensions. / Thesis / Doctor of Philosophy (PhD)

[ES] El objetivo de la tesis es proponer una metodología que permita la definición de pasarelas de un único vano a partir de unas condiciones de contorno determinadas, utilizando unos diseños estéticamente atractivos. Se desarrolla el diseño y la formulación geométrica de tres pasarelas paramétricas, denominadas Von Mises, Monocontentio y Bicontentio, cuyo diseño se basa en cinco fundamentos básicos: integración en la geometría del terreno, búsqueda continua de la sencillez, siluetas que emanan del comportamiento estructural, formas unitarias y detalles perdurables. La silueta de la pasarela Von Mises se basa en la gráfica del criterio de comparación de Von Mises de una viga biapoyada, la del prototipo Monocontentio en la ley de momentos de una viga empotrada-apoyada y la de la pasarela Bicontentio en la gráfica de flectores de una viga biempotrada. El trabajo incluye una metodología de formulación, que permite obtener las expresiones matemáticas que gobiernan las principales dimensiones y espesores de las pasarelas, en función de su anchura y su luz. Un análisis comparativo de diferentes tipologías de pasarelas viga permite constatar la eficiencia de los prototipos Von Mises, Monocontentio y Bicontentio. Esta se debe a su canto variable adaptado a los esfuerzos de solicitación y al empotramiento en estribos. Asimismo, se realiza un análisis que liga el enfoque de diseño y el pensamiento ingenieril con la expresión estética de los puentes. La tesis supone la puesta en orden de una particular filosofía de diseño utilizada por el autor en una treintena de puentes proyectados durante los últimos 25 años, para poder ser aplicada de manera sistemática por otros profesionales. / [CA] L'objectiu de la tesi és proposar una metodologia que permeta la definició de passarel·les d'un únic tram a partir d'unes condicions de contorn determinades, utilitzant uns dissenys estèticament atractius. Es desenvolupa el disseny i la formulació geomètrica de tres passarel·les paramètriques, denominades Von Mises, Monocontentio i Bicontentio, el disseny de les quals es basa en cinc fonaments bàsics: integració en la geometria del terreny, cerca contínua de la senzillesa, siluetes que emanen del comportament estructural, formes unitàries i detalls perdurables. La silueta de la passarel·la Von Mises es basa en la gràfica del criteri de comparació de Von Mises d'una biga bi- recolzada, la del prototip Monocontentio en la llei de moments d'una biga encastada-recolzada i la de la passarel·la Bicontentio en la gràfica de flectors d'una biga bi-encastada. El treball inclou una metodologia de formulació, que permet obtindre les expressions matemàtiques que governen les principals dimensions i grossàries de les passarel·les, en funció de la seua amplària i la seua llum. Una anàlisi comparativa de diferents tipologies de passarel·les biga permet constatar l'eficiència dels prototips Von Mises, Monocontentio i Bicontentio. Aquesta es deu al seu cant variable adaptat als esforços de sol·licitació i a l'encast en estreps. Així mateix es realitza una anàlisi que lliga l'enfocament de disseny i el pensament de l'enginyer amb l'expressió estètica dels ponts. / [EN] The purpose of this thesis is to propose a methodology for single-span, pedestrian bridges, based on specific conditions, using an attractive design.This thesis explains the design and geometric formulation of three types of pedestrian bridges, namely Von Mises, Monocontentio and Bicontentio. Their designs are based on five basic principles: (1) integration into the geometry of the environment; (2) permanent search for simplicity; (3) design based on a geometry that emanates from structural behavior; (4) uniform shapes; and (5) enduring details. The silhouette of the Von Mises bridge is inspired by the Von Mises criterion graph, corresponding to a simply- supported beam.The Monocontentio prototype is inspired by the bending moment diagram of a beam fixed at one end and simply supported at the other end. The Bicontentio bridge is inspired by the bending moment diagram of a beam fixed at both ends. This thesis includes a formulation methodology that defines mathematical expressions that govern the main dimensions and thickness of a pedestrian bridge, depending on its respective width and span. A comparative analysis demonstrates the efficiency of these three particular prototypes, due to their variable depth, adapted to the internal forces, and due to fix the structure in abutments. Likewise, this paper analyses and links the design and engineering with the aesthetic expression of the bridges.The author has used this design philosophy in thirty bridge projects over the last 25 years, and such philosophy may be applied in a systematic way by other professionals. / Guisasola Ron, M. (2022). Desarrollo de nuevas formas parametrizadas para pasarelas eficientes y elegantes [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/180776

L'objet de cette thèse est de présenter une étude du comportement thermomécanique des disques de frein automobiles pour la prédiction de leur tenue en fatigue. La stratégie de calcul numérique est repose sur le code de calcul Ansys v.11. Ce dernier qui est basé sur la méthode des éléments finis et qui possède des algorithmes de gestion du contact avec frottement est utilisé pour simuler dans l'application du freinage le comportement du mécanisme malgré son complexité. Dans un premier temps, est présentée une analyse des phénomènes thermiques opérant dans un disque de frein en service (flux de chaleur généré par frottement, gradients thermiques élevés, élévation de température). Cette modélisation est effectuée en tenant compte l'influence d'un certains nombre de paramètre tel que le type de freinage, le mode de refroidissement, les matériaux de conceptions. Ensuite, une étude purement mécanique du contact sec entre le disque et plaquettes est développée avec une bonne prédiction devient un enjeu majeur pour les industriels tout en modélisant le chargement et les conditions aux limites autours du disque. Nous avons utilisé le même code de calcul pour visualiser les déplacements, les déformations globales dans le disque, les contraintes de cisaillement, les contraintes de Von Mises et les outils de contact des plaquettes tout en effectuant une étude paramétrique telle que ( le module de Young des plaquettes, le coefficient de frottement , le type de chargement , la vitesse de rotation du disque ,..) pour voir sa sensibilité sur les résultats de calcul. Ainsi, les analyses faites sur le comportement thermique et mécanique que de ces prototypes montrent que ces types de solutions technologiques représentent de réelles pistes d'amélioration qui répond au besoin de l'ingénieur en charge de la conception des disques de frein.

The dissertation concerns F. A. Hayek’s (1899–1992) critique of legislation. The purpose of the investigation is to clarify and assess that critique. I argue that there is in Hayek’s work a critique of legislation that is distinct from his well-known critique of social planning. Further that the main claim of this critique is what I refer to as Hayek’s legislation tenet, namely that legislation that aims to achieve specific aggregate results in complex orders of society will decrease the welfare level.           The legislation tenet gains support; (i) from the welfare claim – according to which there is a positive correlation between the utilization of knowledge and the welfare level in society; (ii) from the dispersal of knowledge thesis – according to which the total knowledge of society is dispersed and not available to any one agency; and (iii) from the cultural evolution thesis – according to which evolutionary rules are more favorable to the utilization of knowledge in social cooperation than are legislative rules. More specifically, I argue that these form two lines of argument in support of the legislation tenet. One line of argument is based on the conjunction of the welfare claim and the dispersal of knowledge thesis. I argue that this line of argument is true. The other line of argument is based on the conjunction of the welfare claim and the cultural evolution thesis. I argue that this line of argument is false, mainly because the empirical work of political scientist Elinor Ostrom refutes it. Because the two lines of argument support the legislation tenet independently of each other, I argue that Hayek’s critique of legislation is true. In this dissertation, I further develop a legislative policy tool as based on the welfare claim and Hayek’s conception of coercion. I also consider Hayek’s idea that rules and law are instrumental in forging rational individual action and rational social orders, and turn to review this idea in light of the work of experimental economist Vernon Smith and economic historian Avner Greif. I find that Smith and Greif support this idea of Hayek’s, and I conjecture that it contributes to our understanding of Adam Smith’s notion of the invisible hand: It is rules – not an invisible hand – that prompt subjects to align individual and aggregate rationality in social interaction. Finally, I argue that Hayek’s critique is essentially utilitarian, as it is concerned with the negative welfare consequences of certain forms of legislation. And although it may appear that the dispersal of knowledge thesis will undermine the possibility of carrying out the utilitarian calculus, due to the lack of knowledge of the consequences of one’s actions – and therefore undermine the legislation tenet itself – I argue that the distinction between utilitarianism conceived as a method of deliberation and utilitarianism conceived as a criterion of correctness may be used to save Hayek’s critique from this objection.