Comparing k Population Means with No Assumption about the Variances

In the analysis of most statistically designed experiments, it is common to assume equal variances along with the assumptions that the sample measurements are independent and normally distributed. Under these three assumptions, a likelihood ratio test is used to test for the difference in population means. Typically, the assumption of independence can be justified based on the sampling method used by the researcher. The likelihood ratio test is robust to the assumption of normality. However, the equality of variances is often difficult to justify. It has been found that the assumption of equal variances cannot be made even after transforming the data. Our interest is to develop a method for comparing k population means assuming the data are independent and normally distributed but without assuming equal variances. This is the Behrens-Fisher problem for k=2. We propose a method that uses the exact distribution of the likelihood ratio (test) statistic. The data is used to estimate this exact distribution to obtain an estimated critical value or an estimated p-value

Flux de l'information en programmation logique

Cette thèse est développée dans le but d'aborder la question du flux de l'information en programmation logique. Les contributions de cette thèse peuvent être divisées en trois parties: 1. Flux de l'information en programmation logique: Nous proposons une base théorique de ce que pourrait être un flux de l'information en programmation logique. Plusieurs définitions de flux d'information (basées sur la réussite / échec, les substitutions réponses, bisimulation entre les arbres de résolution des buts logiques) sont évaluées et comparées. Des problèmes de décision sont donnés pour chaque définition et la complexité est étudiée pour certaines catégories de programmes logiques. 2. Bisimulation de buts logiques: Nous introduisons la notion de bisimulation entre les buts Datalog: deux buts Datalog sont bisimilaires par rapport à un programme Datalog donné lorsque leurs SLD-arbres, considérés comme des structures relationnelles, sont bisimilaires. Nous abordons le problème de décider si deux buts donnés sont bisimilaires à l'égard d'un programme donné. Lorsque les programmes sont hiérarchiques ou restricted, ce problème est décidable en 2EXPTIME. 3. Contrôle préventif de l'inférence dans les bases de données déductives: Nous proposons un mécanisme de sécurité sûr et précis pour les bases de données déductives basé sur la notion de flux de l'information dans la programmation logique.This thesis is developed in order to tackle the issue of information flow in logic programming. The contributions of this thesis can be split into three mains parts: 1. Information flow in logic programming: we propose a theoretical foundation of what could be an information flow in logic programming. Several information flow definitions (based on success/failure, substitution answers, bisimulation between resolution trees of goals) are stated and compared. Decision procedures are given for each definition and complexity is studied for specific classes of logic programs. 2. Bisimulation of logic goals: We introduce the concept of bisimulation between Datalog goals: two Datalog goals are bisimilar with respect to a given Datalog program when their SLD-trees, considered as relational structures, are bisimilar. We address the problem of deciding whether two given goals are bisimilar with respect to given programs. When the given programs are hierarchical or restricted, this problem is decidable in 2EXPTIME. 3. Preventive inference control for deductive databases: We propose a secure and a precise security mechanism for deductive databases based on the notion of information flow in logic programming

Multiple Axisymmetric Solutions for Axially Traveling Waves in Solid Rocket Motors

In this article, we consider the vorticoacoustic flowfield arising in a rightcylindrical porous chamber with uniform sidewall injection. Such configuration is often used to simulate the internal gaseous environment of a solid rocket motor (SRM). Assuming closed-closed acoustic conditions at both fore and aft ends of the domain, the introduction of small disturbances in the mean flow give rise to an axially traveling vortico-acoustically dominated wave structure that our study attempts to elucidate. Although this problem has been formulated before, it is reconsidered here in the context of WKB perturbation expansions in the reciprocal of the crossflow Reynolds number. This enables us to uncover multiple distinguished limits along with new asymptotic solutions that are presented for the first time. Among them are WKB approximations of type II and III that are systematically evaluated and discussed. The WKB solutions are shown to exhibit a peculiar singularity that warrants the use of matched asymptotic expansions to produce uniformly valid representations. Our solutions are obtained for any characteristic mean flow function satisfying Berman’s similarity condition for porous tubes. They are also derived to an arbitrary level of precision using a recursive formulation that can reproduce each of the asymptotic solutions to any prescribed order. Finally, our solutions are verified numerically over a wide range of physical parameters and through limiting process approximations

Green Networking in Cellular HetNets: A Unified Radio Resource Management Framework with Base Station ON/OFF Switching

In this paper, the problem of energy efficiency in cellular heterogeneous networks (HetNets) is investigated using radio resource and power management combined with the base station (BS) ON/OFF switching. The objective is to minimize the total power consumption of the network while satisfying the quality of service (QoS) requirements of each connected user. We consider the case of co-existing macrocell BS, small cell BSs, and private femtocell access points (FAPs). Three different network scenarios are investigated, depending on the status of the FAPs, i.e., HetNets without FAPs, HetNets with closed FAPs, and HetNets with semi-closed FAPs. A unified framework is proposed to simultaneously allocate spectrum resources to users in an energy efficient manner and switch off redundant small cell BSs. The high complexity dual decomposition technique is employed to achieve optimal solutions for the problem. A low complexity iterative algorithm is also proposed and its performances are compared to those of the optimal technique. The particularly interesting case of semi-closed FAPs, in which the FAPs accept to serve external users, achieves the highest energy efficiency due to increased degrees of freedom. In this paper, a cooperation scheme between FAPs and mobile operator is also investigated. The incentives for FAPs, e.g., renewable energy sharing and roaming prices, enabling cooperation are discussed to be considered as a useful guideline for inter-operator agreements.Comment: 15 pages, 9 Figures, IEEE Transactions on Vehicular Technology 201