Submitted by VINÍCIUS LOURENÇO DA ROCHA null (vinicius.oczrocha@hotmail.com) on 2016-02-17T17:19:26Z No. of bitstreams: 1 Dissertação Final - Vinícius Rocha.pdf: 840133 bytes, checksum: 2e5f5a0242c53770984cfe1fd7c71089 (MD5) / Approved for entry into archive by Sandra Manzano de Almeida (smanzano@marilia.unesp.br) on 2016-02-17T18:15:51Z (GMT) No. of bitstreams: 1 rocha_vl_me_prud.pdf: 840133 bytes, checksum: 2e5f5a0242c53770984cfe1fd7c71089 (MD5) / Made available in DSpace on 2016-02-17T18:15:51Z (GMT). No. of bitstreams: 1 rocha_vl_me_prud.pdf: 840133 bytes, checksum: 2e5f5a0242c53770984cfe1fd7c71089 (MD5) Previous issue date: 2016-02-10 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Baseando-se em trabalhos recentes da literatura, o presente trabalho tem como objetivo estudar limites dinâmicos para operadores de Schrödinger discretos, unidimensionais, com potenciais Sturmianos (modelos quase-periódicos). Tais limites são obtidos das taxas de propagação do pacote de ondas associado a uma partícula sobre a rede unidimensional Z. Utilizando um método desenvolvido por Damanik e Tcheremchantsev, obtém-se um limite dinâmico superior não-trivial para uma família grande de operadores Sturmianos, associados a números de rotação irracionais. Além disso, apresenta-se um limite inferior global para a dimensão fractal superior do espectro desses operadores, o qual é usado para obter um limite dinâmico inferior para tais operadores Sturmianos associados a números irracionais de densidade limitada. Serão utilizados resultados sobre o traço das matrizes de transferência associadas aos operadores de Schrödinger Sturmianos e também propriedades espectrais destes operadores. / By following recent papers in the literature, the present work aims to study dynamical bounds for one dimensional discrete Schrödinger operators with Sturmian potentials by bounding the rates of propagation of the wavepacket. By a method developed by Damanik and Tcheremchantsev, is obtained a non trivial upper bound for almost all Sturmian Schrödinger operator associated with irrational numbers. Moreover, it presents a global lower bound for the upper box counting dimension of the spectrum of these operators, which is used to obtain a lower dynamical bound for such Sturmian Schrödinger operators associated with bounded density irrational numbers. Will be used results about the traces of transfer matrices and spectral properties of Sturmian Schrödinger operators. / FAPESP: 2014/04321-9

abstract: The problem of cooperative radar and communications signaling is investigated. Each system typically considers the other system a source of interference. Consequently, the tradition is to have them operate in orthogonal frequency bands. By considering the radar and communications operations to be a single joint system, performance bounds on a receiver that observes communications and radar return in the same frequency allocation are derived. Bounds in performance of the joint system is measured in terms of data information rate for communications and radar estimation information rate for the radar. Inner bounds on performance are constructed. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2014

Os problemas de corte e empacotamento são muito comuns nas indústrias e na logística. Dado um conjunto de N itens com diferentes pesos e um conjunto de M contentores com capacidade C, o problema de empacotamento unidimensional consiste em determinar o menor número de contentores a serem utilizados para alocar todos os itens respeitando a restrição de capacidade dos contentores. Nesse estudo pretende-se resolver o problema com instâncias benchmark da literatura, por meio de sessenta heurísticas diferentes, que são comparadas a quatro limitantes inferiores propostos na literatura com o intuito de avaliar a qualidade da solução heurística. Quatro limitantes inferiores e dez heurísticas construtivas diferentes foram programados em C++ num mesmo ambiente computacional, permitindo sua comparação tanto em termos de qualidade das soluções, quanto em termos dos tempos de processamento. Uma heurística simples de troca de itens entre contentores chamada Diferença-de-Quadrados foi proposta para melhorar as soluções iniciais do problema. A metaheurística simulated annealing foi acionada para melhorar a solução inicial quando o limitante inferior não foi atingido. Os parâmetros dos simulated annealing foram determinados com os dados das instâncias de forma diferente da utilizada na literatura. As combinações entre as dez soluções iniciais, a heurística Diferença-de-Quadrados e o simulated annealing geraram um conjunto de sessenta heurísticas diferentes. Os resultados mostraram que o algoritmo proposto é eficiente para resolver o problema com tempos de processamento adequados a tomada de decisão. / Cutting and packing problems are very common in industries and logistics. Given a set of N items with different weights and a set of M bins with full capacity C, the one-dimensional bin packing problem consists of determining the smallest number of bins capable to allocate all items respecting the capacity constraint of the bins. that impose that the sum of the weights of the items allocated to the bin is less than or equal to their capacity. In this study we intend to solve the problem with benchmark instances of the literature, by means of sixty different heuristics, which are compared to four lower bounds proposed in the literature in order to evaluate the quality of the heuristic solution. Four lower bounds and ten different constructive heuristics were programmed in C++ in the same computational environment, allowing their comparison both in terms of the quality of the solutions and in terms of processing times. A simple heuristic of item exchange between bins called Difference-of-Squares was proposed to improve the initial solutions of the problem. The simulated annealing metaheuristic was triggered to improve the initial solution when the lower bounds was not reached. The parameters of the simulated annealing were determined with the data of the instances differently from that used in the literature. The combinations of the ten initial solutions, the Difference-of-Squares heuristic and the simulated annealing generated a set of sixty different heuristics. The results showed that the proposed algorithm is efficient to solve the problem with adequate processing times for decision making.

A singularly perturbed reaction diffusion problem is considered. The small diffusion coefficient generically leads to solutions with boundary layers. The problem is discretized by a vertex-centered finite volume method. The anisotropy of the solution is reflected by using \emph{anisotropic meshes} which can improve the accuracy of the discretization considerably. The main focus is on \emph{a posteriori} error estimation. A residual type error estimator is proposed and rigorously analysed. It is shown to be robust with respect to the small perturbation parameter. The estimator is also robust with respect to the mesh anisotropy as long as the anisotropic mesh sufficiently reflects the anisotropy of the solution (which is almost always the case for sensible discretizations). Altogether, reliable and efficient \emph{a posteriori} error estimation is achieved for the finite volume method on anisotropic meshes.

This paper is a first attempt to empirically evaluate some competing hypotheses for the Austrian growth performance. We find that the real appreciations, gross investment, a low duration of unemployment and high youth employment exhibit a significant influence on economic growth. This validates the hard currency policy hypothesis, the macroeconomic management hypothesis, and the microinstitutions hypothesis, whilst all other fail according to this exercise. In particular, we find the Schulmeister-thesis of loose money and the deficit spending hypothesis are even counterfactual. Summarizing, we find that economic policy had its share in promoting growth in the Austrian economy. As a byproduct from our analysis, we find that low levels of unemployment have a significant and positive impact on the growth rate of real GDP, which calls for further theoretical research in this direction. (author's abstract) / Series: Working Papers Series "Growth and Employment in Europe: Sustainability and Competitiveness"

Cette thèse traite de la théorie spectrale des opérateurs de Schrödinger discrets H(λ) := - Δ + b sur Zd et plus généralement sur des graphes pondérés infinis. Plus précisément, nous étudions le comportement des fonctions spectrales qui représentent les bornes du spectre de ces opérateurs. Un des principaux résultats est l'obtention d'une condition nécessaire et suffisante sur le potentiel b pour que le bas du spectre soit strictement positif. L'étude du haut du spectre est également considérée.Nous étudions tout d'abord ces questions pour les opérateurs de Schrödinger discrets sur Zd. La régularité de cet espace permet alors d'obtenir des résultats spécifiques dans ce cas particulier. Nous généralisons ensuite nos travaux au cas des graphes infinis pondérés. Les techniques développées dans ce cadre nous permettent également d'étudier le comportement asymptotique du bas du spectre pour les grandes valeurs de λ. / This thesis deals with the spectral theory of discrete Schrödinger operators H(λ) := - Δ + b on Zd and more generally on in#nite weighted graphs. Precisely, we study the behavior of the spectral functions which represent the spectral bounds of these operators. One of the main results is the obtention of a necessary and sufficient condition on the potential b such that the bottom of the spectrum is stricly positive.The study of the top of the spectrum is also treated.We first study these questions for discrete Schrödinger operators on Zd. The regularity of this space provides specific results in this particular case. Then we extend our work to the case of infinite weighted graphs. Moreover, the technics developed in this framework allow us to study the asymptotic behavior of the bottom of the spectrum for large values of λ.

Ce travail présente une méthode générale fournissant des bornes garanties de l'erreur de discrétisation sur une quantité locale issue d'un calcul éléments finis. Formulée dans un cadre général, la méthode est illustrée sur un cas 2D d'élastoplasticité. Le cadre non-linéaire de cette implémentation a soulevé des problèmes d'un type nouveau au sein de la thématique de vérification. Après avoir défini les problèmes miroir et central, nous proposons des solutions pour les résoudre.La mise en place de l'outil introduit est détaillée. Ainsi, des bornes garanties de l'erreur locale sur une composante de la déformation plastique sont calculées. Une première étude sur des cas académiques est présentée avant de s'intéresser à un cas plus complexe. Enfin une amélioration de la méthode est introduite, permettant l'obtention de bornes plus pertinentes. / This work presents a general method providing good control on the discretization error on a local quantity of a finite element solution. Formulated using a general formulation, this method is illustrated in a 2D case of elastoplasticity. Nonlinear part of this implementation has raised issues of a new type in the subject of verification. Mirror and the central problems are defined, and we offer solutions for both.The implementation of this tool is introduced in detail. Thus, the guarantees bounds of the local error on a component of plastic deformation are calculated. An initial study on academic case is presented before focusing on a more complex one. Finally an improved method is introduced, allowing the calculation of more relevant bounds.

Doctor en Sistemas de Ingeniería / En esta tesis se presentan los resultados del trabajo desarrollado por el autor durante el periodo en que fue estudiante de doctorado en el Departamento de Industrias de la Universidad de Chile. El trabajo se centra en la aplicación de técnicas de optimización entera-mixtas a problemas de planificación estratégica del sector eléctrico, donde el problema de corto plazo correspondiente al predespacho de unidades de generación en sistemas térmicos es el tema central en estudio. En lo relativo al modelamiento del problema de predespacho de unidades, se considera el análisis de las distintas formulaciones entera-mixtas disponibles en la literatura junto con una nueva basada en un formulaciones extendidas tipo red. Se investiga su desempeño sobre un conjunto de instancias reales desde el punto de vista de su eficiencia computacional al ser resueltas con softwares comerciales. Lo anterior incluye análisis de tiempos de solución, nodos utilizados e iteraciones de simplex realizadas para distintas tolerancias requeridas. Los experimentos muestran la calidad de la aproximación propuesta, siendo esta completamente competitiva respecto a las ya documentadas. Este resultado era esperable, dada la estructura totalmente unimodular de gran parte de la formulación propuesta, pero para nada justificable debido al tamaño de la misma. Lo anterior muestra que el efecto del preproceso de los softwares comerciales puede ser fundamental en algunas formulaciones. Por otro lado, respecto a la función objetivo del problema de predespacho de unidades, que por lo general se representa como una función cuadrática de la generación, se presenta una nueva manera de linealizar su comportamiento de modo que su inclusión en una formulación entera-mixta lineal tradicional sea eficiente. Esto último debe entenderse a partir de la necesidad que el tamaño de la aproximación no crezca de manera desmedida si el error requerido para la misma decrece. Si bien ya existía la posibilidad de hacer esto mediante la aplicación de la aproximación desarrollada por Ben-Tal y Nemirovsky para conos de segundo orden [2], acá se presenta un método alternativo, con mejores propiedades numéricas, un orden de magnitud mejor en calidad de aproximación, y cuya aplicación a problemas reales de predespacho de unidades genera mejores resultados respecto de las aproximaciones tradicionales. Por último, con el fin de mejorar el desempeño de la formulación entera-mixta presentada, se realiza el análisis poliedral de una de sus subestructuras esperando identificar desigualdades válidas que permitan mejorar su cota dual. Esta subestructura corresponde al knapsack semicontinuo con restricciones adicionales del tipo generalized upper bound. Se demuestra que bajo supuestos simples es posible identificar facetas tipo generalized flow cover en espacios restringidos de dimensión inferior. Luego se llevan estas desigualdades al espacio original utilizando procedimientos de lifting multidimensional independiente de la secuencia [38, 27, 16, 17] y se iii prueba que con supuestos adicionales también son facetas allí. Experimentos computacionales en instancias derivadas de problemas de UC muestran su eficiencia, donde más de un 50% del gap integral del nodo raíz se reduce aplicando en promedio solo tres de estos cortes. Además, en este contexto, también se ha implementado un solver ad-hoc para la solución eficiente de las relajaciones lineales de la formulación tipo red, con un speed-up del orden de 4x a 8x respecto a CPLEX barrier optimizer, pero que aún no está documentado.

We study and answer questions related to the complexity of various important problems such as: multi-frontal solvers of hp-adaptive finite element method, sorting and majority. We advocate the use of dynamic programming as a viable tool to study optimal algorithms for these problems. The main approach used to attack these problems is modeling classes of algorithms that may solve this problem using a discrete model of computation then defining cost functions on this discrete structure that reflect different complexity measures of the represented algorithms. As a last step, dynamic programming algorithms are designed and used to optimize those models (algorithms) and to obtain exact results on the complexity of the studied problems. The first part of the thesis presents a novel model of computation (element partition tree) that represents a class of algorithms for multi-frontal solvers along with cost functions reflecting various complexity measures such as: time and space. It then introduces dynamic programming algorithms for multi-stage and bi-criteria optimization of element partition trees. In addition, it presents results based on optimal element partition trees for famous benchmark meshes such as: meshes with point and edge singularities. New improved heuristics for those benchmark meshes were ob- tained based on insights of the optimal results found by our algorithms. The second part of the thesis starts by introducing a general problem where different problems can be reduced to and show how to use a decision table to model such problem. We describe how decision trees and decision tests for this table correspond to adaptive and non-adaptive algorithms for the original problem. We present exact bounds on the average time complexity of adaptive algorithms for the eight elements sorting problem. Then bounds on adaptive and non-adaptive algorithms for a variant of the majority problem are introduced. Adaptive algorithms are modeled as decision trees whose depth reflects the worst-case time complexity and average depth indicates the average-case time complexity. Non-adaptive algorithms are represented as decision tests whose size expresses the worst-case time complexity. Finally, we present a dynamic programming algorithm that finds a minimum decision test (minimum reduct) for a given decision table.

A singularly perturbed reaction diffusion problem is considered. The small diffusion coefficient generically leads to solutions with boundary layers. The problem is discretized by a vertex-centered finite volume method. The anisotropy of the solution is reflected by using \emph{anisotropic meshes} which can improve the accuracy of the discretization considerably. The main focus is on \emph{a posteriori} error estimation. A residual type error estimator is proposed and rigorously analysed. It is shown to be robust with respect to the small perturbation parameter. The estimator is also robust with respect to the mesh anisotropy as long as the anisotropic mesh sufficiently reflects the anisotropy of the solution (which is almost always the case for sensible discretizations). Altogether, reliable and efficient \emph{a posteriori} error estimation is achieved for the finite volume method on anisotropic meshes.