New developments of the odds-theorem

The odds-theorem and the corresponding solution algorithm (odds-algorithm) are tools to solve a wide range of optimal stopping problems. Its generality and tractability have aroused much attention. (Google for instance 'Bruss odds' to obtain a quick overview.) Many extensions and modifications of this result have appeared since its publication in 2000 (see Bruss 2000)). This article reviews the important new developments and applications in this field. The spectrum of application comprises fields as different as secretary problems, more general stopping problems, robotic maintenance problems, and compassionate use clinical trials, amongst others. This review also includes a new contribution of our own. Odds-algorithm; Bruss algorithm; last hitting time; records; © Applied Probability Trust 2013.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Weber's optimal stopping problem and generalizations

One way to interpret the classical secretary problem (CSP) is to consider it as a special case of the following problem. We observe n independent indicator variables I1, I2, In sequentially and we try to stop on the last variable being equal to 1. If Ik=1 it means that the kth observed secretary has smaller rank than all previous ones (and therefore is a better secretary). In the CSP, pk=E(Ik)=1/k and the last k with Ik=1 stands for the best candidate. The more general problem of stopping on a last "1" was studied by Bruss (2000). In what we will call Weber's problem the indicators are replaced by random variables which can take more than 2 values. The goal is now to maximize the probability of stopping on a value appearing for the last time in the sequence. Notice that we do not fix in advance the value taken by the variable on which we stop. We can solve this problem in some cases and provide efficient algorithms to compute the optimal stopping rules. These cases carry generality and are applicable in many concrete situations.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Sequential stopping under different environments of weak information

Notre thèse s’articule autour du thème de l’utilisation optimale de l’information contenue dans un modèle probabiliste flexible. Dans le premier chapitre, nous couvrons des résultats bien connus des martingales comme le théorème de convergence dit L1 des martingales et le théorème d’arrêt. Nous discutons de problèmes ouverts similaires au «last arrival problem» (Bruss et Yor, 2012) qui sont des vrais défis du point de vue théorique et nous ne pouvons que conjecturer la stratégie optimale.Dans les chapitres suivants, nous résolvons des extensions de problèmes d’arrêt optimal proposés par R. R. Weber (U. Cambridge), basés sur le «théorème des odds» (Bruss, 2000). En résumé, il s’agit d’effectuer une seule action (un seul arrêt) lorsque deux suites d’observations indépendantes sont observées simultanément. Nous donnons la solution à ces problèmes pour un nombre (fixé) choisi de processus.Le chapitre suivant passe en revue la plupart des développements récents (depuis 2000) réalisés autour du «théorème des odds» (Bruss, 2000). Le matériel présenté fut publié (2013), il a donc été mis à jour dans cette thèse pour inclure les derniers résultats depuis cette date.Puis nous réservons un chapitre pour une solution explicite pour un cas particulier du Problème d’arrêt optimal de Robbins. Ce chapitre est basé sur un article publié par l’auteur en collaboration avec le professeur Swan (Université de Liège). Ce chapitre offre une belle illustration des difficultés rencontrées lorsque trop d’information sur les variables est contenue dans le modèle. La solution optimale de ce problème dans le cas général n’est pas connue. Par contre, contre-intuitivement, dans le «last arrival problem» mentionné plus haut, moins d’information permet, comme nous le montrons, de trouver en effet la solution optimale.La thèse contient un dernier chapitre sur un problème de nature plus combinatoire que nous pouvons lier à la théorie des graphes dans une certaine mesure. Nous étudions le processus de création d’un graphe aléatoire particulier et les propriétés des cycles créés par celui-ci. Le problème est séquentiel et permet d’envisager des problèmes d’arrêt intéressants. Cette étude a des conséquences en théorie des graphes, en analyse combinatoire ainsi qu’en science de la chimie combinatoire pour les applications. Un de nos résultats est analogue au résultat de Janson (1987) relatif au premier cycle créé pendant la création de graphes aléatoires.Doctorat en Sciencesinfo:eu-repo/semantics/nonPublishe

One step further :an explicit solution to Robbins’ problem when n = 4

info:eu-repo/semantics/publishe

Modelling the changes of scale in industrial materials

International audienc

Viscoelastic behavior and electrical properties of flexible nanofiber filled polymer nanocomposites. Influence of processing conditions

International audienceTwo different types of high aspect ratio flexible nanofibers, cellulose nanofibrils and carbon nanotubes, were dispersed in an amorphous thermoplastic polymer matrix. The mechanical and (in the case of carbon nanotubes filled composites) electrical properties of these composites were investigated. Dynamic mechanical analysis highlighted the influence of entanglements between fibers and of fiber/fiber contact properties on the composite mechanical reinforcement in the rubbery state. In the case of cellulose filled nanocomposites a large mechanical reinforcement effect was observed. This effect was explained by the formation of a rigid nanofibril network linked by strong hydrogen bonds. The formation of this network was assumed to be governed by a percolation mechanism. Conversely, when such bonds between cellulose fibrils were prevented by the process, a lower mechanical reinforcement is observed and can be modeled by a classical mean field approach. On the other hand, both types of composites filled with carbon nanotubes (where no strong interactions are possible) highlighted the fact that entanglements are responsible for a strong increase in thermo-mechanical stability but do not influence the mechanical reinforcement. However, carbon nanotubes are good conductive objects and for such nanocomposites, electrical percolation properties were found. The influence of the process on these electrical properties was highlighted and discussed in term of modification of tubetube contact electrical properties

Carbon nanotube-filled polymer composites. Numerical simulation of electrical conductivity in three-dimensional entangled fibrous networks

International audienceA new modeling approach is presented to simulate direct current electrical conductivity in entangled fibrous networks. Isotropic three-dimensional structures, made up of high aspect ratio non-straight conductive fibers, are generated using a spline calculation; the corresponding volume conductivity is determined by integration using finite element software. The influence of the morphological parameters of fibers - aspect ratio and tortuosity - and of fiber-fiber contact electrical properties on electrical percolation is investigated. The results are then compared to experimental data obtained for nanocomposites composed of carbon nanotubes dispersed in a polymer matrix

Large deformation mechanical behavior of flexible nanofiber filled polymer nanocomposites

International audienceIn the present work, the large deformation behavior of high aspect ratio flexible nanofiber reinforced polymer composites is investigated. Simple or successive tensile tests are performed at room temperature, i.e. in the rubbery state. By studying two different types of fibers, namely cellulose nanofibrils and carbon nanotubes, with two processing routes, the role of entanglements and of interactions existing between fiberswithin the nanofiber network that can be formed in the materialon the composite properties is highlighted. For cellulosic nanofillers, strong hydrogen bonds between fibers lead to a spectacular reinforcement effect combined with a decrease of the composite ultimate strain and an irreversible damage of composite properties after first deformation (rigid network). When such strong interactions between fillers are limited (soft entangled network or simple contacts between non-entangled fibers) the resulted reinforcement is less important and no decrease of the deformation at break is observed. For carbon nanotube fillers, the evolution of the filler network during tensile test is finally highlighted by in situ electrical measurements