Dans ce travail, nous proposons des procédures de test paramétriques et nonparamétriques localement et asymptotiquement optimales au sens de Hajek et Le Cam, pour deux modèles de données de panel. Notre approche est fondée sur la théorie de Le Cam d'une part, pour obtenir les propriétés de normalité asymptotique, bases de la construction des tests paramétriques optimaux, et la théorie de Hajek d'autre part, qui, via un principe d'invariance, permet d'obtenir les procédures nonparamétriques. Dans le premier chapitre, nous considérons un modèle à erreurs composées et nous nous intéressons au problème qui consiste à tester l'absence de l'effet individuel aléatoire. Nous établissons la propriété de normalité locale asymptotique (LAN), ce qui nous permet de construire des procédures paramétriques localement et asymptotiquement optimales (“les plus stringentes”) pour le problème considéré. L'optimalité de ces procédures est liée à la densité-cible f1. Ces propriétés d'optimalité sont hautement paramétriques puisqu'elles requièrent que la densité sous-jacente soit f1. De plus, ces procédures ne seront valides que si la densité-cible f1 et la densité sous-jacent g1 coincïdent. Or, en pratique, une spécification correcte de la densité sous-jacente g1 est non réaliste, et g1 doit être considérée comme un paramètre de nuissance. Pour éliminer cette nuisance, nous adoptons l'argument d'invariance et nous nous restreignons aux procédures fondées sur des statistiques qui sont mesurables par rapport au vecteur des rangs. Les tests que nous obtenons restent valide quelle que soit la densité sous-jacente et sont localement et asymptotiquement les plus stringents. Afin d'avoir des renseignements sur l'efficacité des tests fondés sur les rangs sous différentes lois, nous calculons les efficacités asymptotiques relatives de ces tests par rapport aux tests pseudo-gaussiens, sous des densités g1 quelconques. Enfin, nous proposons quelques simulations pour comparer les performances des procédures proposées. Dans le deuxième chapitre, nous considérons un modèle à erreurs composées avec autocorrélation d'ordre 1 et nous montrons que ce modèle jouit de la propriété LAN. A partir de ce résultat, nous construisons des tests optimaux, au sens local et asymptotique, pour trois problèmes de tests importants dans ce contexte : (a) test de l'absence d'effet individuel et d'autocorrélation; (b) test de l'absence d'effet individuel en présence d'une autocorrélation non spécifiée; et (c) test de l'absence d'autocorrélation en présence d'un effet individuel non spécifié. Enfin, nous proposons quelques simulations pour comparer les performances des tests pseudogaussiens et des tests classiques.

In order to design robust controllers, H-infinity synthesis is a common tool to use. The controllers that result from these algorithms are typically of very high order, which complicates implementation. However, if a constraint on the maximum order of the controller is set, that is lower than the order of the plant, the problem is no longer convex and it is then relatively hard to solve. These problems become very complex, even when the order of the system to be controlled is low. The approach used in the thesis is based on formulating the constraint on the maximum order of the plant as a polynomial equation. By using the fact that the polynomial is non-negative on the feasible set, the problem is reformulated as an optimization problem where the nonconvex polynomial function is to be minimized over a convex set defined by linear matrix inequalities. To solve this optimization problem, two methods have been proposed. The first method is a barrier method and the second one is a method based on a primal-dual framework. These methods have been evaluated on several problems and compared with a well-known method found in the literature. To motivate this choice of method, we have made a brief survey of available methods available for solving the same or related problems. The proposed methods emerged as the best methods among the three for finding lower order controllers with the same or similar performance as the full order controller. When the aim is to find the lowest order controller with no worse than +50% increase in the closed loop H-infinity norm, then the three compared methods perform equally well.

<p>&nbsp / </p> <p align="left">The groups we consider in this study belong to the class <font face="F30">X</font><font face="F25" size="1"><font face="F25" size="1">0 </font></font><font face="F15">of all finitely generated groups with finite commutator subgroups.</font></p>

The Kappa coefficient is widely used in assessing categorical agreement between two raters or two methods. It can also be extended to more than two raters (methods).  When using Kappa, the shortcomings of this coefficient should be not neglected.  Bias and prevalence effects lead to paradoxes of Kappa. These problems can be avoided by using some other indexes together, but the solutions of the Kappa problems are not satisfactory. This paper gives a critical survey concerning the Kappa coefficient and gives a real life example. A useful alternative statistical approach, the Rank-invariant method is also introduced, and applied to analyze the disagreement between two raters.

The thesis examines the problem of joint receive and transmit beamforming for a wireless network which consists of one relay node equipped with multiple antennas. The transmitter and the receiver are single antenna systems. The communication system consists of two phases. In the first phase the transmitter sends the information symbol to the relay while in the second phase, the relay re-transmits a linearly transformed version of the vector of its received signals. The concept of general-rank beamforming is applied to this communication scheme for the case of the uplink (transmitter-relay) and downlink (relay-receiver) channel vectors being statistically independent and statistically dependent. In the general-rank beamforming approach, the multi-antenna relay multiplies the received signal vector with a general-rank complex weight matrix and re-transmits each entry of the output vector on the corresponding antenna. The thesis presents a closed form solution to the general-rank beamforming power minimization problem with proof that for statistically independent uplink and downlink channels, the general-rank beamforming approach results in a rank-one solution for the beamforming matrix. The simulation results have shown that when the generalrank beamformer is applied to the case of statistically dependent uplink and downlink channels, the general-rank beamforming technique significantly outperforms the separable receive and transmit beamforming method. / UOIT

Network coding has emerged as a new paradigm for communication in networks, allowing packets to be algebraically combined at internal nodes, rather than simply routed or replicated. The very nature of packet-mixing, however, makes the system highly sensitive to error propagation. Classical error correction approaches are therefore insufficient to solve the problem, which calls for novel techniques and insights. The main portion of this work is devoted to the problem of error control assuming an adversarial or worst-case error model. We start by proposing a general coding theory for adversarial channels, whose aim is to characterize the correction capability of a code. We then specialize this theory to the cases of coherent and noncoherent network coding. For coherent network coding, we show that the correction capability is given by the rank metric, while for noncoherent network coding, it is given by a new metric, called the injection metric. For both cases, optimal or near-optimal coding schemes are proposed based on rank-metric codes. In addition, we show how existing decoding algorithms for rank-metric codes can be conveniently adapted to work over a network coding channel. We also present several speed improvements that make these algorithms the fastest known to date. The second part of this work investigates a probabilistic error model. Upper and lower bounds on capacity are obtained for any channel parameters, and asymptotic expressions are provided in the limit of long packet length and/or large field size. A simple coding scheme is presented that achieves capacity in both limiting cases. The scheme has fairly low decoding complexity and a probability of failure that decreases exponentially both in the packet length and in the field size in bits. Extensions of the scheme are provided for several variations of the channel. A final contribution of this work is to apply rank-metric codes to a closely related problem: securing a network coding system against an eavesdropper. We show that the maximum possible rate can be achieved with a coset coding scheme based on rank-metric codes. Unlike previous schemes, our scheme has the distinctive property of being universal: it can be applied on top of any communication network without requiring knowledge of or any modifications on the underlying network code. In addition, the scheme can be easily combined with a rank-metric-based error control scheme to provide both security and reliability.

Det är idag vanligt inom verksamheter som skola och omsorg att använda rankningar för att utvärdera kvalitet och skapa beslutsunderlag, något som är behäftat med stor osäkerhet. Trots det redovisas ofta dessa utan speciellt tagen hänsyn till den närvarande slumpvariationen. Mot bakgrund av det har vi varit speciellt intresserade av sådana data och har för uppsatsen haft tillgång till skoldata samt tre olika sjukvårdsdata. För att identifiera om och när en rankning kan vara meningsfull har vi för samtliga data jämfört länsnivå med lägre nivåer. Uppsatsen behandlar den slumpmässiga variation som framträder i samband med upprättandet av rankningslistor. Då små enheter är mer mottagliga för naturlig variation, förväntas denna har särskild betydelse för placeringen och inte sällan återfinns dessa i toppen eller botten av tabellen. Två i grund olika metoder som båda är konstruerade för att hantera osäkerheten i rankningar testas empiriskt i uppsatsen. Uppsatsen finner att det i samtliga fall är förenat med stora svårigheter att skapa meningsfulla och entydiga rankningar. Dels till följd av slumpmässig variation men även för att de skillnader som observeras mellan enheter är alltför små för att kunna göra åtskillnader i kvalitet. Speciellt krävs mycket stora stickprov för att göra en rankning mindre osäker.

Network coding has emerged as a new paradigm for communication in networks, allowing packets to be algebraically combined at internal nodes, rather than simply routed or replicated. The very nature of packet-mixing, however, makes the system highly sensitive to error propagation. Classical error correction approaches are therefore insufficient to solve the problem, which calls for novel techniques and insights. The main portion of this work is devoted to the problem of error control assuming an adversarial or worst-case error model. We start by proposing a general coding theory for adversarial channels, whose aim is to characterize the correction capability of a code. We then specialize this theory to the cases of coherent and noncoherent network coding. For coherent network coding, we show that the correction capability is given by the rank metric, while for noncoherent network coding, it is given by a new metric, called the injection metric. For both cases, optimal or near-optimal coding schemes are proposed based on rank-metric codes. In addition, we show how existing decoding algorithms for rank-metric codes can be conveniently adapted to work over a network coding channel. We also present several speed improvements that make these algorithms the fastest known to date. The second part of this work investigates a probabilistic error model. Upper and lower bounds on capacity are obtained for any channel parameters, and asymptotic expressions are provided in the limit of long packet length and/or large field size. A simple coding scheme is presented that achieves capacity in both limiting cases. The scheme has fairly low decoding complexity and a probability of failure that decreases exponentially both in the packet length and in the field size in bits. Extensions of the scheme are provided for several variations of the channel. A final contribution of this work is to apply rank-metric codes to a closely related problem: securing a network coding system against an eavesdropper. We show that the maximum possible rate can be achieved with a coset coding scheme based on rank-metric codes. Unlike previous schemes, our scheme has the distinctive property of being universal: it can be applied on top of any communication network without requiring knowledge of or any modifications on the underlying network code. In addition, the scheme can be easily combined with a rank-metric-based error control scheme to provide both security and reliability.

We obtain a tight upper bound for the genus of a partition, and calculate the number of partitions of maximal genus. The generating series for genus zero and genus one rooted hypermonopoles is obtained in closed form by specializing the genus series for hypermaps. We discuss the connection between partitions and rooted hypermonopoles, and suggest how a generating series for genus one partitions may be obtained via the generating series for genus one rooted hypermonopoles. An involution on the poset of genus one partitions is constructed from the associated hypermonopole diagrams, showing that the poset is rank-symmetric. Also, a symmetric chain decomposition is constructed for the poset of genus one partitions, which consequently shows that it is strongly Sperner.

This thesis develops a semiunification-based type inference procedure for the rank 2 fragment of System F, with an emphasis on practical considerations for the adoption of such a procedure into existing programming languages. Current semiunification-based rank 2 inference procedures (notably that of Kfoury and Wells) are limited in several ways, which hinder their use in real-world settings. First of all, the translation from an instance of the type inference problem to an instance of the semiunification problem (SUP) is indirect; in particular, because of a series of source-level transformations that take place before translation, the translation is not syntax-directed. As a result, type errors discovered during the semiunification process cannot be cleanly translated back to specific subexpressions of the source program that caused the error. Also, because the rank 2 fragment of System F lacks a principal types property, an inference procedure cannot output a single type that encompasses all of a given term's derivable types. The procedure must therefore either rely on user assistance to produce the right type, or simply choose arbitrarily one of the given term's possible types. The algorithm of Kfoury and Wells in particular makes degenerate type assumptions in the absence of user assistance, and consequently produces types that are of no practical use. We build up our system in stages; we begin by improving the SUP translation. Whereas termination for the Kfoury-Wells rank 2 inference procedure is assured by translating terms into instances of the acyclic semiunification problem (a decidable subset of SUP, which is undecidable in general), we formulate and target the R-acyclic semiunification problem---a larger decidable subset of SUP that facilitates a more concise translation from source terms. We next eliminate the source-level transformation of terms, in order to formulate a truly syntax-directed translation from a source term to a set of SUP-like constraints. In doing so, we find that even the full SUP itself is not sufficiently equipped to support such a translation. We formulate USUP, a superset of SUP that incorporates a new class of identifier we call an unknown. We formulate decidable subsets of USUP, and then formulate a truly syntax-directed translation from source terms into USUP, with guaranteed termination. Finally, to address the principal types problem, we introduce a notation for types in which we allow a particular class of variable to stand for type constructors, rather than ordinary types (an idea based on the so-called third-order lambda-calculus). We show that, with third-order types we can not only output large sets of useful types for a given term, without programmer assistance, but the types we output also generalize over more System F types than any type within System F itself can do, and still be a valid type for the source term. Thus, our system increases opportunities for separate compilation and code reuse beyond any existing system of which we are aware. Our system is sound, though incomplete in certain well-characterized ways, despite which our system performs exactly as one would hope on a variety of examples, which we illustrate in this thesis.