Dans un premier temps, nous introduisons une classe de champs réels appelés champs de Lévy multifractionnaires au moyen d'une représentation harmonisable. Cette classe contient à la fois celle des champs de Lévy fractionnaires et le mouvement brownien multifractionnaire (MBM en abrégé). Elle fournit notamment des exemples de champs non gaussiens du second ordre ayant des propriétés semblables à celles du MBM. En particulier, les champs de Lévy multifractionnaires sont localement autosimilaires et leur exposant de Hölder ponctuel peut varier le long d'une trajectoire. Par ailleurs, leurs propriétés sont gouvernées par leur fonction multifractionnaire. Par suite, d'un point de vue statistique, un problème naturel est l'identification de cette fonction. Comme dans le cas du MBM, elle peut être identifiée au moyen des variations quadratiques localisées et généralisées. Dans la deuxième partie, nous nous sommes intéressés à la simulation de la partie non gaussienne d'un champ de Lévy multifractionnaire. La méthode proposée est basée sur une représentation en série de bruits généralisés. Cependant, dans certains cas, on approche aussi une partie du champ de Lévy multifractionnaire par un MBM. Enfin, la dernière partie introduit un champ $X_(H,\be)$ localement autosimilaire avec un comportement atypique en $0$. En effet, alors qu'en tout point $x\ne0$, le champ tangent à $X_(H,\be)$ est un mouvement brownien fractionnaire, en général en $x=0$ le champ tangent à $X_(H,\be)$ est de nature bien différente. De plus, le champ $X_(H,\be)$ satisfait une propriété d'autosimilarité à grandes échelles et son étude est ensuite complétée par celle de la régularité des trajectoires et de la dimension de Hausdorff de ses graphes.

Soit \M un espace de modules de groupes p-divisibles introduit par Rapoport et Zink. Supposons que cet espace \M soit non-ramifié de type EL ou PEL unitaire ou symplectique. Soit \Mrig la fibre générique de Berthelot de \M. C'est un espace rigide analytique au-dessus duquel il existe une tour de revêtements étales finis (\M_K)_K qui classifient les structures de niveau. On définit un morphisme déterminant \det_K de la tour (\M_K)_K vers une tour d'espaces rigides analytiques étales de dimension 0 associée au cocentre du groupe réductif relié à cet espace. C'est un analogue local en des places non-archimédiennes du morphisme déterminant pour les variétés de Shimura défini par Deligne. Comme pour les variétés de Shimura, on montre que les fibres géométriques du morphisme déterminant \det_K sont les composantes connexes géométriques de \M_K. On définit aussi les morphismes puissances extérieures qui généralisent le morphisme déterminant sur la tour d'espaces rigides analytiques associée à un espace de Lubin-Tate.

I give explicit estimates of the Lp-norm of a mean zero infinitely divisible random vector taking values in a Hilbert space in terms of a certain mixture of the L2- and Lp-norms of the Levy measure. Using decoupling inequalities, the stochastic integral driven by an infinitely divisible random measure is defined. As a first application utilizing the Lp-norm estimates, computation of Ito Isomorphisms for different types of stochastic integrals are given. As a second application, I consider the discrete time signal-observation model in the presence of an alpha-stable noise environment. Formulation is given to compute the optimal linear estimate of the system state.

We propose a new construction of point processes, which generalizes the class of infinitely divisible point processes. Examples are the quantum Boson and Fermion gases as well as the classical Gibbs point processes, where the interaction is given by a stable and regular pair potential.

In this thesis, the focus is on the development of scheduling algorithms for Sim-PETEK which is a framework for parallel and distributed execution of simulations. Since it is especially designed for running parameter sweep applications in a heterogeneous distributed computational environment, multi-round and adaptive scheduling approaches are followed. Five different scheduling algorithms are designed and evaluated for scheduling purposes of Sim-PETEK. Development of these algorithms are arranged in a way that a newly developed algorithm provides extensions over the previously developed and evaluated ones. Evaluation of the scheduling algorithms is handled by running a Wireless Sensor Network (WSN) simulation over Sim-PETEK in a heterogeneous distributed computational system formed in TUBITAK UEKAE ILTAREN. This evaluation not only makes comparisons among the scheduling algorithms but it also and rates them in terms of the optimality principle of divisible load theory which mentions that in order to obtain optimal processing time all the processors used in the computation must stop at the same time. Furthermore, this study adapts a scheduling approach, which uses statistical calibration, from literature to Sim-PETEK and makes an assessment between this approach and the most optimal scheduling approach among the five algorithms that have been previously evaluated. The approach which is found to be the most efficient is utilized as the Sim-PETEK scheduler.

In this dissertation, we study semi-stable representations of G(Q(p)) and their mod p-reductions, which is a part of the problem in which we construct deformation spaces whose characteristic 0 closed points are the semi-stable lifts with Hodge-Tate weights (0, 1, 2) of a fixed absolutely irreducible residual representation ρ : G(Q(p)) → GL₃(F(p)). We first classify the isomorphism classes of semi-stable representations of G(Q(p)) with regular Hodge-Tate weights, by classifying admissible filtered (phi,N)-modules with Hodge-Tate weights (0, r, s) for 0 < r < s. We also construct a Galois stable lattice in some irreducible semi-stable representations with Hodge-Tate weights (0, 1, 2), by constructing strongly divisible modules, which is an analogue of Galois stable lattices on the filtered (ɸ, N)-module side. We compute the reductions mod p of the corresponding Galois representations to the strongly divisible modules we have constructed, by computing Breuil modules, which is, roughly speaking, mod p-reduction of strongly divisible modules. We also determine which Breuil modules corresponds to irreducible mod p representations of G(Q(p)).

[pt] Esse artigo investiga como o emprego público afeta a alocação de habilidades na economia. Construímos um modelo de Roy onde trabalhadores se selecionam entre os setores público e privado baseados nas suas produtividades e aversões ao risco. O setor privado é caracterizado por pareamento positivos entre habilidades e tarefas, mas tem retornos incertos, o que pode criar um trade-off para os trabalhadores. Estimamos esse modelo para o Brazil usando dados no nível do trabalhadores para os anos de 2011-2014 e fazemos um exercício contra-factual. Resultados mostram que reduzir o tamanho do setor público aumento a produtividade média do setor privado e reduz o prêmio por fazer ensino superior, mas aumenta a desigualdade salarial. / [en] This paper investigates how public sector employment affects the allocation of skills in the economy. We develop a Roy model where workers self-select into either public or private sectors based on their productivity and risk aversion. The private sector is characterized by positive assortative matching between skills and tasks, but it has uncertain returns, which potentially creates a trade-off for workers. We estimate the model using Brazilian worker level data for the years of 2011-2014 and use it to perform counter-factual exercises. We show that reducing the size of the public sector increases private sector average productivity, decreases the college wage premium, but increases wage inequality.

The purpose of this paper is to derive minimal sufficient statistics for the balanced incomplete block design and the group divisible partially balanced incomplete block design when the Eisenhart Model III (mixed model) is assumed. The results are identical to Hultquist and Graybill's (1965) and Hirotsu's (1965) for the same model without interaction, except for the addition of a statistic, ∑ijY2ij•.

A design is a set of points, V, together with a set of subsets of V called blocks. A classic type of design is a balanced incomplete block design, where every pair of points occurs together in a block the same number of times. This ‘balanced’ condition can be replaced with other properties. An adesign is a design where instead every pair of points occurs a different number of times together in a block. The number of times a specified pair of points occurs together is called the pair frequency. Here, a special type of adesign is explored, called a Sarvate-Beam design, named after its founders D.G. Sarvate and W. Beam. In such an adesign, the pair frequencies cover an interval of consecutive integers. Specifically the existence of Sarvate-Beam group divisible designs are investigated. A group divisible design, in the usual sense, is a set of points and blocks where the points are partitioned into subsets called groups. Any pair of points contained in a group have pair frequency zero and pairs of points from different groups have pair frequency one. A Sarvate-Beam group divisible design, or SBGDD, is a group divisible design where instead the frequencies of pairs from different groups form a set of distinct nonnegative consecutive integers. The SBGDD is said to be uniform when the groups are of equal size. The main result of this dissertation is to completely settle the existence question for uniform SBGDDs with blocks of size three where the smallest pair frequency, called the starting frequency, is zero. Higher starting frequencies are also considered and settled for all positive integers except when the SBGDD is partitioned into eight groups where a few possible exceptions remain. A relationship between these designs and graph decompositions is developed and leads to some generalizations. The use of matrices and linear programming is also explored and give rise to related results. / Graduate

In this dissertation, we focus on multiple levels of optimized resource management techniques. We first consider a classic resource management problem, namely the scheduling of data-intensive applications. We define the Divisible Load Scheduling (DLS) problem, outline the system model based on the assumption that data staging and all communication with the sites can be done in parallel, and introduce a set of optimal divisible load scheduling algorithms and the related fault-tolerant coordination algorithm. The DLS algorithms introduced in this dissertation exploit parallel communication, consider realistic scenarios regarding the time when heterogeneous computing systems are available, and generate optimal schedules. Performance studies show that these algorithms perform better than divisible load scheduling algorithms based upon sequential communication. We have developed a self-organization model for resource management in distributed systems consisting of a very large number of sites with excess computing capacity. This self-organization model is inspired by biological metaphors and uses the concept of varying energy levels to express activity and goal satisfaction. The model is applied to Pleiades, a service-oriented architecture based on resource virtualization. The self-organization model for complex computing and communication systems is applied to Very Large Sensor Networks (VLSNs). An algorithm for self-organization of anonymous sensor nodes called SFSN (Scale-free Sensor Networks) and an algorithm utilizing the Small-worlds principle called SWAS (Small-worlds of Anonymous Sensors) are introduced. The SFSN algorithm is designed for VLSNs consisting of a fairly large number of inexpensive sensors with limited resources. An important feature of the algorithm is the ability to interconnect sensors without an identity, or physical address used by traditional communication and coordination protocols. During the self-organization phase, the collision-free communication channels allowing a sensor to synchronously forward information to the members of its proximity set are established and the communication pattern is followed during the activity phases. Simulation study shows that the SFSN ensures the scalability, limits the amount of communication and the complexity of coordination. The SWAS algorithm is further improved from SFSN by applying the Small-worlds principle. It is unique in its ability to create a sensor network with a topology approximating small-world networks. Rather than creating shortcuts between pairs of diametrically positioned nodes in a logical ring, we end up with something resembling a double-stranded DNA. By exploiting Small-worlds principle we combine two desirable features of networks, namely high clustering and small path length.