Cette thèse montre des contributions à l'analyse d'algorithmes pour l'optimisation de fonctions bruitées. Les taux de convergences (regret simple et regret cumulatif) sont analysés pour les algorithmes de recherche linéaire ainsi que pour les algorithmes de recherche aléatoires. Nous prouvons que les algorithmes basé sur la matrice hessienne peuvent atteindre le même résultat que certaines algorithmes optimaux, lorsque les paramètres sont bien choisis. De plus, nous analysons l'ordre de convergence des stratégies évolutionnistes pour des fonctions bruitées. Nous déduisons une convergence log-log. Nous prouvons aussi une borne basse pour le taux de convergence de stratégies évolutionnistes. Nous étendons le travail effectué sur les mécanismes de réévaluations en les appliquant au cas discret. Finalement, nous analysons la mesure de performance en elle-même et prouvons que l'utilisation d'une mauvaise mesure de performance peut mener à des résultats trompeurs lorsque différentes méthodes d'optimisation sont évaluées. / This thesis exposes contributions to the analysis of algorithms for noisy functions. It exposes convergence rates for linesearch algorithms as well as for random search algorithms. We prove in terms of Simple Regret and Cumulative Regret that a Hessian based algorithm can reach the same results as some optimal algorithms in the literature, when parameters are tuned correctly. On the other hand we analyse the convergence order of Evolution Strategies when solving noisy functions. We deduce log-log convergence. We also give a lower bound for the convergence rate of the Evolution Strategies. We extend the work on revaluation by applying it to a discrete settings. Finally we analyse the performance measure itself and prove that the use of an erroneus performance measure can lead to misleading results on the evaluation of different methods.

By Banach algebra we mean Banach space enriched with a multiplication operation. It is a mathematical structure that is used in the non-periodic homogenization of composite materials. The theory of classical homogenization studies materials assuming the periodicity of the structure. For real materials, the assumption of a periodicity is not enough and is replaced by the so-called an abstract hypothesis based on a concept composed mainly of the spectrum of Banach algebra and Sigma convergence. This theory was introduced in 2004.

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Dans cette thèse, on étudie la convergence du processus d'exploration de l'arbre généalogique d'un processus de branchement en temps continu non binaire, dans la limite d'une grande population. Dans la première partie, nous donnons une description précise du processus d'exploration de l'arbre non binaire. Ensuite nous décrivons une certaine bijection entre l'ensemble des processus d'exploration et l'ensemble des arbres non binaires. Après renormalisation des paramètres, nous présentons les résultats de convergence du processus de population et du processus d'exploration dans la limite d'une grande population. Dans la deuxième partie, nous établissons d'abord la convergence du processus de population vers un processus de branchement à espace d'état continu avec sauts. Puis, nous montrons la convergence du processus d'exploration normalisé de l'arbre généalogique correspondant vers le processus de hauteur continu défini récemment par Li, Pardoux et Wakolbinger.Dans la dernière partie, on définit un modèle discret de population avec interaction définie par une fonction générale non linéaire f. On fait une renormalisation adéquate du modèle discret pour obtenir en limite un processus de branchement à espace d'état continu généralisé. Ensuite nous renormalisons le processus d'exploration de l'arbre généalogique associé et nous prenons la limite quand la taille de la population tend vers l'infini. / In this thesis, we study the convergence of the exploration process of the non-binary tree associated to a continuous time branching process, in the limit of a large population. In the first part, we give a precise description of the exploration process of the non-binary tree. We then describe a bijection between exploration processes and Galton Watson non-binary trees. After some renormalization, we present the results of convergence of the population process and the exploration process, in the limit of a large populations.In the second part, we first establish the convergence of the population process to a continuous state branching process (CSBP) with jumps. We then show the convergence of the (rescaled) exploration process, of the corresponding genealogical tree towards the continuous height process recently defined by Li, Pardoux and Wakolbinger. In the last part, we consider a population model with interaction defined with a more general non linear function $f.$ We proceed to a renormalization of the parameters model and we obtain in limit a generalized CSBP. We then renormalize the height process of the associated genealogical tree, and take the weak limit as the size of the population tends to infinity.

Cette thèse aborde plusieurs questions relatives à l’évolution biologique au moyen de modèles mathématiques et d’algorithmes de calcul les utilisant. Elle se trouve donc à l’intersection des mathématiques, de l’informatique et de la biologie. La question principale étudiée dans la thèse est la mise en évidence de signatures moléculaires de la convergence évolutive qui est le phénomène par lequel des espèces éloignées développent indépendamment des caractères similaires. Nous proposons une approche originale permettant de détecter les positions des protéines potentiellement impliquées dans la convergence d’un caractère binaire donné. Celle-ci repose sur une mesure du “niveau de convergence” des positions, qui est une espérance déterminée sous des modèles Markoviens d’évolution protéique. Nous donnons un algorithme de calcul polynomial de cet indice et montrons (i) qu’il discrimine mieux que les méthodes précédentes, les positions convergentes des “neutres” sur des simulations et (ii) que notre approche donne des résultats qui font sens biologiquement sur un exemple réel.Dans le but de pouvoir traiter à terme de la convergence de caractères continus, comme le poids ou la taille, nous nous sommes ensuite intéressés à la détection de changements de tendance évolutive le long d’un arbre représentant l’évolution des espèces. Nous proposons une nouvelle méthode qui, à notre connaissance, est la première à être basée sur un principe de parcimonie où l’on cherche à déterminer la position du changement permettant de minimiser un certain coût évolutif sur l’arbre. / In this thesis, we studied questions about biological evolution by using mathematical models and bio-informatic algorithms. This work is at the intersection of mathematics, computer science and biology.The major question addressed in this thesis is the detection molecular basisof phenotypic convergence. Evolutionary convergence is the process by which independent species develop similar traits. This evolutionary process is strongly related to fundamental questions such as the role of adaptation .After pointing out different biological concepts linked to evolutionary convergence, we proposed a novel approach combining an original measure of the extent to which a site supports a phenotypic convergence to a binary trait. Thismeasure is based on the “convergence level” of a site which is a mathematical expectation under Markov evolutionary model. We proposed a polynomial time algorithm to compute this index. Our algorithm outperformed two previous algorithms in distinguishing simulated convergent sites from non-convergent ones. With the aim to study the evolutionary convergence of continuous traits, like weight and size, we tried to detect change in evolutionary trends of continuous characters along the tree of life. We proposed a novel method based on anasymmetric version of the linear parsimony, for determining the position of the change in trend which minimizes the total evolutionary cost of the tree. By using the approach on two biological datasets, we obtained results consistentwith those given by previous stochastic approaches.

Maintaining global warming to 2 degrees Celsius above pre-industrial levels is vital. Whether the convergence hypothesis holds for carbon dioxide emissions is important for policymakers facing this issue. This paper investigates the convergence behavior of carbon dioxide emissions for 39 countries in the Americas from 1960-2016. A linear regression test of convergence which looks for conditional sigma convergence is employed, and a clustering algorithm is used to identify convergence clubs. The results show evidence of convergence in the region for the long run. Convergence clubs are identified for the short run. The convergence clubs show some relation to spatial distribution and income level. Possible factors determining the formation of convergence clubs are investigated through logistic regression. Initial level of emissions and energy intensity were found to have the largest impact determining what convergence club a country belongs to. Per capita GDP, trade openness, and renewable energy were all found to be highly significant factors determining what convergence club a country belongs to as well. Different results were found for urbanization’s impact in determining the formation of convergence clubs. These findings show that policymakers should promote allocation schemes for carbon dioxide emissions. Policymakers should also aim to reduce carbon footprint based on the economy’s structural characteristics.

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No / Media content is becoming ubiquitous and globally accessible, and can be held and accessed just as easily on a global network as on local devices which are increasingly intelligent and network ready. Digital intelligence is becoming seamless and invisible, enabling more attention to be paid to the content and the user’s interaction with it. The effects of convergence on the media landscape are substantial. Traditional media distribution channels are increasingly in the hands of the consumer rather than the distributor. News information can be generated by the general public by means of mobile devices and have a dynamic global impact via social networking sites. Political elections are being influenced in real time by information circulating on social networks in addition to the more formal statements of policy. This paper explores some of these transformative effects, the disruptive effects on traditional business models, and their implications for the future.

In this Ph.D. thesis we discuss results concerning variational convergences for functionals and differential operators on Lipschitz continuous vector fields. The convergences taken into account are gamma-convergence (for functionals) and H-convergence (for differential operators).

The focus of this thesis is the theory of periodic homogenization of partial differential equations and some applicable concepts of convergence. More precisely, we study parabolic problems exhibiting both spatial and temporal microscopic oscillations and a vanishing volumetric heat capacity type of coefficient. We also consider a hyperbolic-parabolic problem with two spatial microscopic scales. The tools used are evolution settings of multiscale and very weak multiscale convergence, which are extensions of, or closely related to, the classical method of two-scale convergence. The novelty of the research in the thesis is the homogenization results and, for the studied parabolic problems, adapted compactness results of multiscale convergence type.