Orientador: José Plínio de Oliveira Santos / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-16T18:39:44Z (GMT). No. of bitstreams: 1 Domingues_DeborahPereira_M.pdf: 925996 bytes, checksum: 6a430acfaa4475e03a36ee7e09bbf42a (MD5) Previous issue date: 2010 / Resumo: Neste trabalho estudamos dois importantes tópicos em combinatória. O primeiro deles é o Teorema Enumerativo de Pólya. No capítulo 2 é dada uma demonstração deste teorema usando o Teorema de Burnside. Também neste capítulo, encontram-se algumas de suas diversas aplicações. O segundo tópico trata de Teoria de Partições. Esta dissertação aborda alguns objetos de estudo desta área. O primeiro objeto é o método de Partition Analisys, usado para achar funções geradoras de vários tipos de interessantes funções de partição. Ainda relacionado a funções geradoras, o capítulo 3 aborda um pouco sobre q-séries. O segundo objeto é o método gráfico, que utiliza a representação gráfica de Ferrers para uma partição. Ainda neste capítulo, são usados os conceitos de quadrado de Durfee e símbolo de Frobenius para provar algumas identidades. / Abstract: This paper presents two important topics in combinatorics. The first one is the Pólya Enumeration Theorem. In chapter 2 is given a demonstration of this theorem by Burnside's Theorem. Also in this chapter are some of their various applications. The second topic deals with the Theory of Partition. This dissertation addresses some aspects of the study on this area. The first is Partition Analysis, this method is used to find the generating functions of various kinds of interesting partition functions. In the third chapter we deal with q-series which is also related to generating functions. The second is the graphical method, which uses a Ferrers's graphical representation of a partition. In addition, we use the concepts of Durfee square and Frobenius's symbol to prove some identities. / Mestrado / Mestre em Matemática

La construction de modèles qui protègent contre les incertitudes dans les données, telles que la variabilité de l'information et l'imprécision est une des principales préoccupations en optimisation sous incertitude. L'incertitude peut affecter différentes domaines, comme le transport, les télécommunications, la finance, etc. ainsi que les différentes parts d'un problème d'optimisation, comme les coefficients de la fonction objectif et /ou les contraintes. De plus, l'ensemble des données incertaines peut être modélisé de différentes façons, comme sous ensembles compactes et convexes de l´espace réel de dimension n, polytopes, produits Cartésiens des intervalles, ellipsoïdes, etc.<p><p>Une des approches possibles pour résoudre des tels problèmes est de considérer les versions minimax regret, pour lesquelles résoudre un problème sous incertitude revient à trouver une solution qui s'écarte le moins possible de la valeur solution optimale dans tout les cas. <p><p>Dans le cas des incertitudes définies par intervalles, les versions minimax regret de nombreux problèmes combinatoires polynomiaux sont NP-difficiles, d'ou l'importance d'essayer de réduire l'espace des solutions. Dans ce contexte, savoir quand un élément du problème, représenté par une variable, fait toujours ou jamais partie d'une solution optimal pour toute réalisation des données (variables 1-persistentes et 0-persistentes respectivement), constitue une manière de réduire la taille du problème. Un des principaux objectifs de cette thèse est d'étudier ces questions pour quelques problèmes d'optimisation combinatoire sous incertitude.<p><p>Nous étudions les versions minimax regret du problème du choix de p éléments parmi m, de l'arbre couvrant minimum et des deux problèmes de plus court chemin. Pour de tels problèmes, dans le cas des incertitudes définis par intervalles, nous étudions le problème de trouver les variables 1- et 0-persistentes. Nous présentons une procédure de pre-traitement du problème, lequel réduit grandement la taille des formulations des versions de minimax regret.<p><p>Nous nous intéressons aussi à la version minimax regret du problème de programmation linéaire dans le cas où les coefficients de la fonction objectif sont incertains et l'ensemble des données incertaines est polyédral. Dans le cas où l'ensemble des incertitudes est défini par des intervalles, le problème de trouver le regret maximum est NP-difficile. Nous présentons des cas spéciaux ou les problèmes de maximum regret et de minimax regret sont polynomiaux. Dans le cas où l´ensemble des incertitudes est défini par un polytope, nous présentons un algorithme pour trouver une solution exacte au problème de minimax regret et nous discutons les résultats numériques obtenus dans un grand nombre d´instances générées aléatoirement.<p><p>Nous étudions les relations entre le problème de 1-centre continu et la version minimax regret du problème de programmation linéaire dans le cas où les coefficients de la fonction objectif sont évalués à l´aide des intervalles. En particulier, nous décrivons la géométrie de ce dernier problème, nous généralisons quelques résultats en théorie de localisation et nous donnons des conditions sous lesquelles certaines variables peuvet être éliminées du problème. Finalement, nous testons ces conditions dans un nombre d´instances générées aléatoirement et nous donnons les conclusions. / Doctorat en sciences, Orientation recherche opérationnelle / info:eu-repo/semantics/nonPublished

No description available.

Orientador: Jose Plinio de Oliveira Santos / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-07T19:25:43Z (GMT). No. of bitstreams: 1 Ribeiro_AndreiaCristina_D.pdf: 576297 bytes, checksum: 445154b7e26e801e909854c976d31c45 (MD5) Previous issue date: 2006 / Resumo: Neste trabalho são estudadas varias das identidades do tipo Rogers-Ramanujan dadas por Slater. Em 1985, Andrews, introduziram um método geral para se estender para duas variáveis identidades desse tipo de modo a se obter, como casos especiais, certas importantes funções de Ramanujan. Santos, em 1991, forneceu conjecturas para varias das famílias de polinômios que surgem nestas extensões tendo provado algumas delas. Sills, em sua tese de doutorado, em 2002, implementou procedimentos que permitem a demonstra¸c¿ao das conjecturas dadas por Santos. No presente trabalho, de forma diferente daquela dada por Andrews, s¿ao introduzidos parâmetros nas somas que aparecem nestas identidades, de modo a se obter, em cada caso, funções geradoras que fornecem interpretações combinatórias para partições onde ¿números¿s¿ao vistos como ¿vetores¿e que fornecem, para especiais valores dos parâmetros, interpretações novas para muitas das identidades de Slater / Abstract: In this work many of the identities of the Rogers-Ramanujan type given by Slater are considered. In 1985, Andrews, introduced a general method in other to extend to two variables identities of this type in order to get, as special cases, some important functions of Ramanujan. Santos, in 1991, gave conjectures for many of the family of polynomials that appears in those extensions providing the proofs for some of them. Sills, in his Ph.D. thesis in 2002 ,has implemented procedures allowing the proofs of the conjectures given by Santos. In the present work, in a form different from the one given by Andrews, parameters are introduced in the sums of the identities in such a way to get, in each case, generating functions giving combinatorial interpretations for partitions where ¿numbers¿are represented as ¿vectors¿and that can give, as special cases, combinatorial interpretations for many of the identities given by Slater / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

MSc (Mathematics) / Department of Mathematics and Applied Mathematics / See the attached abstract below

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 1979 / Vita. / Bibliography: leaves 96-98. / Ph. D. / Ph. D. Massachusetts Institute of Technology, Department of Mathematics

The Algorithm Selection Problem is to select the most appropriate way for solving a problem given a choice of different ways. Some of the most prominent and successful applications come from Artificial Intelligence and in particular combinatorial search problems. Machine Learning has established itself as the de facto way of tackling the Algorithm Selection Problem. Yet even after a decade of intensive research, there are no established guidelines as to what kind of Machine Learning to use and how. This dissertation presents an overview of the field of Algorithm Selection and associated research and highlights the fundamental questions left open and problems facing practitioners. In a series of case studies, it underlines the difficulty of doing Algorithm Selection in practice and tackles issues related to this. The case studies apply Algorithm Selection techniques to new problem domains and show how to achieve significant performance improvements. Lazy learning in constraint solving and the implementation of the alldifferent constraint are the areas in which we improve on the performance of current state of the art systems. The case studies furthermore provide empirical evidence for the effectiveness of using the misclassification penalty as an input to Machine Learning. After having established the difficulty, we present an effective technique for reducing it. Machine Learning ensembles are a way of reducing the background knowledge and experimentation required from the researcher while increasing the robustness of the system. Ensembles do not only decrease the difficulty, but can also increase the performance of Algorithm Selection systems. They are used to much the same ends in Machine Learning itself. We finally tackle one of the great remaining challenges of Algorithm Selection -- which Machine Learning technique to use in practice. Through a large-scale empirical evaluation on diverse data taken from Algorithm Selection applications in the literature, we establish recommendations for Machine Learning algorithms that are likely to perform well in Algorithm Selection for combinatorial search problems. The recommendations are based on strong empirical evidence and additional statistical simulations. The research presented in this dissertation significantly reduces the knowledge threshold for researchers who want to perform Algorithm Selection in practice. It makes major contributions to the field of Algorithm Selection by investigating fundamental issues that have been largely ignored by the research community so far.

Dynamic systems for screening, control and identification of different protein-ligand interactions are presented. Dynamic chemistry is used to produce new compounds/constituents in situ that can interact with a target molecule. Several entities can be introduced at the same time and interact with one another. These molecules make a dynamic combinatorial library (DCL) which is used in dynamic combinatorial chemistry (DCC). DCC is a recently introduced approach to generate dynamically interchanging libraries of compounds. These libraries are made of different building blocks that reversibly interact with one another and spontaneously assemble to encompass all possible combinations. If a target molecule, for instance a receptor is added to the system and one or more molecules show affinity to the target species, these compounds will, according to Le Châtelier´s principle, be amplified on the expense of the other non-bonding constituents. To further advance the technique, especially when biological systems are targeted, new reaction types and new screening methods are necessary. This thesis describes the development of different reversible reactions, thiol/disulfide interchange, transthiolesterification and the nitroaldol (Henry) reaction as means of generating reversible covalent bond reactions. Two different types of target proteins are used, enzymes belonging to the hydrolase family and the plant lectin Concanavalin A. Dynamic combinatorial resolution (DCR) is presented. This new concept relies on the consecutive kinetic resolution of dynamic combinatorial libraries, leading to complete amplification and control of dynamically interchangeable processes. By applying a kinetically controlled step to a thermodynamically controlled system, complete transformation and amplification can be obtained. The concept has been demonstrated by developing transthiolesterification and nitroaldol exchange reactions to generate diversity, forming libraries under thermodynamic control, and used in one-pot processes with kinetically controlled enzyme-mediated resolution. The results demonstrate that the reaction types are useful for the generation of dynamic libraries, and that the dynamic combinatorial resolution concept is highly valuable for efficient substrate identification, asymmetric synthesis, and library screening. The thesis also describes three other dynamic chemistry protocols. The first one describes dynamic kinetic resolution (DKR) of nitroaldol adducts by combined lipase catalysis. The second one describes finding lectin inhibitors from a glycodisulfide library and the third one describes finding an inhibitor of acetylcholinesterase using a tandem driven dynamic self-inhibition approach. / <p>QC 20100818</p>

L’objectif de ce projet de trois ans est de proposer des avancées conceptuelles et technologiques dans la résolution de problèmes d’ordonnancement du personnel. L’atteinte de cet objectif passe par la proposition de nouveaux algorithmes basés sur les métaheuristiques et leur implémentation sur les architectures de calcul haute performance. Ce projet s’inscrit en complémentarité du projet HORUS qui bénéficie d’une subvention ANR et qui réunit les expertises scientifiques de deux laboratoires universitaires spécialisés en optimisation et en calcul parallèle : l’équipe SysCom du laboratoire CReSTIC de l’URCA et l’équipe CaRO du laboratoire PRiSM de l’UVSQ. Les avancées technologiques proposées s’appuient également sur les moyens de calcul haute performance offerts par le Centre de Calcul Régional Champagne-Ardenne. / .Many academic and industrial optimization problems are multi-objective and have been of particular interest to researchers in recent years. These problems usually do not have a single optimal solution but a set of best trade-off solutions which form the so-called Pareto front in the objective space. In order to approximate the Pareto front, multi-objective evolutionary algorithms (MOEAs) have been largely investigated in the fields of continuous and combinatorial optimization. Contrary to some classical algorithms, MOEAs have the ability to provide a number of solutions in one single run and are less sensitive to the shape of the Pareto front.As they often require a high amount of computing resources to explore large portions of the search space and handle complex real-life constraints, MOEAs could greatly benefit from today's high-performance computing architectures. Although significant progress has been made in recent years in the design and improvement of parallel models for evolutionary algorithms, most of these models have limited scalability and ability to solve various problems. In fact, solving multi-objective combinatorial optimization problems efficiently on a large number of processors remains a challenge today.This thesis aims to propose an island model which is based on objective space division. The main features of the proposed model are the following (i) An organizer has a global view of the current search via a global archive (ii) Asynchronous cooperation between islands, especially for the exchange of local archives with the organizer to limit model overheads (iii)Control islands to guide the exploration of the search space and improve diversity (iv) A periodic use of a specific local search procedure to improve convergence. Extensive experiments have been conducted to evaluate the performance of the approach and more particularly of each component in the resolution of two classical combinatorial problems, the travelling salesman problem and quadratic assignment problem. Extensibility and quality of the solutions are analyzed compared to state-of-the-art parallel models.

No description available.