Stochastic analysis provides a rationale for the treatment of uncertainties, founded on the principles of probability theory and statistics, and is concerned with a quantifiable measure of the confidence or the reliability associated with any design process. In this thesis, a stochastic approach is employed in the design of flexible pavement structures, to facilitate the development of safe and reliable pavement structures. The important aspects that have been explored in sufficient detail include the system reliability and global sensitivity analysis, and the spatial and temporal uncertainties that pervade the life of pavements. Chapter 1 of the thesis provides an introduction to the stochastic modelling of flexible pavements and its significance in the present day. Highlighting the need for this study, this chapter also enumerates its objectives and presents an overview of the organization of the thesis. Chapter 2 provides a review of the existing literature of the design of flexible pavements and the approaches adopted to deal with the various sources of uncertainties in a probabilistic setting. The estimation of the uncertainties in fundamental pavement design inputs and their integration into the general performance prediction procedures has become a required component of the modern Mechanistic-Empirical pavement design methodology, which has been described in detail. This chapter also provides the scope of the thesis by identifying the areas of stochastic analysis that have received little attention in the flexible pavement design, which include the effect of spatial variability on the pavement structural responses and the techniques of global sensitivity analysis. Chapter 3 provides a detailed overview of the various methodologies adopted in this thesis to carry out the stochastic modelling of flexible pavements. The fundamental technique adopted for the analysis of reliability is the Monte Carlo Simulation (MCS), which relies upon a numerical/analytical model of the physical system, i.e. the pavement model and a probabilistic description of the design parameters represented by random variables or random fields. The high computational expense associated with the MCS, particularly in the case of random fields, is tackled by the use of meta-models based on the stochastic response surface methodology. The chapter outlines the steps followed to develop the meta-models in the form of Polynomial Chaos Equations (PCEs) and its extension to the Sparse PCE that can conveniently represent the spatial variability of the pavement fields. Chapter 4 deals with the probabilistic modelling of flexible pavements, where the design parameter and model uncertainties are quantified based on the available literature studies. The global sensitivity analysis, which aims to study the impact of the input uncertainty on the variation of a model output (critical pavement responses) through uncertainty propagation, is achieved by the construction of the Polynomial Chaos Equations (PCEs). To implement the global sensitivity analysis in a system reliability framework, a generalized approach based on Bayes’ theorem and the concept of entropy as a sensitivity measure, has been proposed in this chapter. Chapter 5 deals with the characterization of the spatial variability inherent in the pavement layer by employing random fields and analyzing the effect on the pavement responses. The discretization of the random field into a vector of random variables is achieved through the simple Midpoint Discretization and the efficient Expansion Optimal Linear Estimation method. Since the computational effort in stochastic problems is proportional to the number of random variables involved, it is desirable to use a small number of random variables to represent the random field. To achieve this, the principle of transformation of the original random variables into a set of uncorrelated random variables through an eigenvalue orthogonalization procedure is adopted. To further increase the computational efficiency of generating random fields for Monte Carlo Simulation, the variance reduction technique of Latin Hypercube Sampling and the meta-modelling technique using Sparse Polynomial Chaos Equations (SPCEs) are implemented. The primary focus of this chapter is to analyze the influence of the spatial variability of the pavement layer moduli, including its anisotropic characteristics on the pavement structural responses. Chapter 6 focuses on the time-dependent reliability of the pavement structures as they age in service, with due consideration given to degradation of strength with traffic loading. The study is concerned with the fatigue reliability and thereby only the decrease in the asphalt modulus with time is considered as a function of the accumulated damage due to repeated loading, whose uncertainty is determined by the uncertainties of material parameters and the traffic loading. The time-dependent model adopted in this chapter can be quite effortlessly embedded in the Mechanistic-Empirical design framework, and provides a tool to effectively schedule the maintenance of the pavement structure and ensure that the reliability level remains at the desired level for the entire design life of the structure. Chapter 7 summarizes the various studies reported in this thesis and highlights the important conclusions.

Cette thèse traite d’une routine d’algèbre linéaire largement utilisée pour la résolution des systèmes li- néaires, il s’agit de la factorisation LU. Habituellement, pour calculer une telle décomposition, on utilise l’élimination de Gauss avec pivotage partiel (GEPP). La stabilité numérique de l’élimination de Gauss avec pivotage partiel est caractérisée par un facteur de croissance qui est reste assez petit en pratique. Toutefois, la version parallèle de cet algorithme ne permet pas d’atteindre les bornes inférieures qui ca- ractérisent le coût de communication pour un algorithme donné. En effet, la factorisation d’un bloc de colonnes constitue un goulot d’étranglement en termes de communication. Pour remédier à ce problème, Grigori et al [60] ont développé une factorisation LU qui minimise la communication(CALU) au prix de quelques calculs redondants. En théorie la borne supérieure du facteur de croissance de CALU est plus grande que celle de l’élimination de Gauss avec pivotage partiel, cependant CALU est stable en pratique. Pour améliorer la borne supérieure du facteur de croissance, nous étudions une nouvelle stra- tégie de pivotage utilisant la factorisation QR avec forte révélation de rang. Ainsi nous développons un nouvel algorithme pour la factorisation LU par blocs. La borne supérieure du facteur de croissance de cet algorithme est plus petite que celle de l’élimination de Gauss avec pivotage partiel. Cette stratégie de pivotage est ensuite combinée avec le pivotage basé sur un tournoi pour produire une factorisation LU qui minimise la communication et qui est plus stable que CALU. Pour les systèmes hiérarchiques, plusieurs niveaux de parallélisme sont disponibles. Cependant, aucune des méthodes précédemment ci- tées n’exploite pleinement ces ressources. Nous proposons et étudions alors deux algorithmes récursifs qui utilisent les mêmes principes que CALU mais qui sont plus appropriés pour des architectures à plu- sieurs niveaux de parallélisme. Pour analyser d’une façon précise et réaliste / This dissertation focuses on a widely used linear algebra kernel to solve linear systems, that is the LU decomposition. Usually, to perform such a computation one uses the Gaussian elimination with partial pivoting (GEPP). The backward stability of GEPP depends on a quantity which is referred to as the growth factor, it is known that in general GEPP leads to modest element growth in practice. However its parallel version does not attain the communication lower bounds. Indeed the panel factorization rep- resents a bottleneck in terms of communication. To overcome this communication bottleneck, Grigori et al [60] have developed a communication avoiding LU factorization (CALU), which is asymptotically optimal in terms of communication cost at the cost of some redundant computation. In theory, the upper bound of the growth factor is larger than that of Gaussian elimination with partial pivoting, however CALU is stable in practice. To improve the upper bound of the growth factor, we study a new pivoting strategy based on strong rank revealing QR factorization. Thus we develop a new block algorithm for the LU factorization. This algorithm has a smaller growth factor upper bound compared to Gaussian elimination with partial pivoting. The strong rank revealing pivoting is then combined with tournament pivoting strategy to produce a communication avoiding LU factorization that is more stable than CALU. For hierarchical systems, multiple levels of parallelism are available. However, none of the previously cited methods fully exploit these hierarchical systems. We propose and study two recursive algorithms based on the communication avoiding LU algorithm, which are more suitable for architectures with multiple levels of parallelism. For an accurate and realistic cost analysis of these hierarchical algo- rithms, we introduce a hierarchical parallel performance model that takes into account processor and network hierarchies. This analysis enables us to accurately predict the performance of the hierarchical LU factorization on an exascale platform.

The work deals with the diagnostic of the business performance for the period 2005 - 2010, were used traditional and modern indicators for evaluation, composite indices and models of bankruptcy and financial standing. At the conclusion of the work were objective evaluation of overall performance results obtained compared with average values in the diagnostic system using financial indicators INFA objective evaluation.

La plupart des études en gestion sur la performance des entreprises sont centréessur l'explication de la relation entre les facteurs internes ou des caractéristiquesintrinsèques de l'entreprise (niveau d'endettement, diversification des produits, lastratégie concurrentielle, etc.) et son performance. Cette thèse vise à déterminerquels sont les facteurs de risque exogènes qui ont un impact sur la performance desentreprises en République Dominicaine? Ces facteurs, affectent-ils différemment lesmicro, petites et moyennes entreprises en fonction de leur secteur d'activité. Quelest le risque pour chacun des plus représentatifs sous-secteurs des entreprisesDominicaines? Nous avons constaté que les facteurs de risque les plusstatistiquement significatifs sont les dépenses de consommation des ménages, letaux d'intérêt des banques commerciales, l'investissement total, le taux de changede DOP à USD et le déficit de la balance commerciale. La composition etl'importance des facteurs varient considérablement en fonction de la taille desentreprises et le sous-secteur auquel ils appartiennent. Les grandes entreprises sonten moyenne moins risqué que des moyennes, petites et micro entreprises, n’importequel que soit le sous-secteur auquel ils appartiennent. / Many of the management studies on the performance of the company are focusedon explaining the relationship between the internal factors or intrinsic characteristicsof the firm (debt level, diversification of products, competitive strategy, etc.) and itsperformance. This thesis seeks to determine, what are the exogenous risk factorsthat impact the performance of all companies in the Dominican Republic? Thesefactors differentially affect the micro, small and medium enterprises according to theirbusiness sector. What is the risk on each of the most representative sub-sectors ofthe Dominican companies? We found that the most statistically significant riskfactors are the household consumption expenditure, the interest rate of commercialbanks, the total investment, the DOP to USD exchange rate and the deficit on thetrade balance. The composition and importance of the factors significantly variesdepending on the size of the company and the sub-sector to which it belongs. Also,large firms are on average less risky than medium, small and micro regardless of thesub-sector they belong. / Muchos de los estudios de gestión sobre el performance de la empresa se enfocanen explicar la relación que existe entre los factores o características intrínsecas de laempresa (nivel de endeudamiento, diversificación de productos, estrategiacompetitiva, etc.) y el performance de la misma. Esta tesis busca determinar¿cuáles son los factores exógenos de riesgo que impactan el performance de lasempresas de la República Dominicana? Si estos factores afectan de forma diferentea la micro, pequeña y mediana empresa según su actividad empresarial. ¿Cuál es elriesgo que tiene cada uno de los sub-sectores más representativos de las empresasdominicanas? Encontramos que los factores de riesgo estadísticamente mássignificativos son el consumo de los hogares, la tasa de interés de los bancoscomerciales, la inversión total, la tasa de cambio de DOP a USD y el déficit en labalanza comercial. La importancia y composición de los factores varíasignificativamente según el tamaño de la empresa y el sub-sector al que pertenece.También, en promedio, las empresas grandes tienen menos riesgos que lasmedianas, pequeñas y micro sin importar al sub-sector que pertenezcan.