This thesis is focused on the topic of assignment problems. The theoretical part presents a summary of the most important previously published findings on linear and quadratic assignment problem. The basic formulations of both problems are introduced, as well as the outline of some methods developed for their solution. Finally both problems are illustrated by practical applications that have appeared in the literature. The practical part gives insight into the issue of assignment of transport orders to drivers in a company and proposes a suitable model that speeds up the process of distributing the orders. The transfers conducted by the company start at the airport and terminate in a hotel in the city centre of Prague or vice versa. When proposing order schedules for the drivers, it is necessary to take into account not only the time of the transfers, but additionally the capacity and the category of the vehicle.

Multi-frame image super-resolution focuses on reconstructing a high-resolution image from a set of low-resolution images with high similarity. Since super-resolution is an ill-posted problem, regularization techniques are widely used to constrain the minimization function. Combining image prior knowledge with fidelity model, Bayesian-based methods can effectively solve this ill-posed problem, which makes this kind of methods more popular than other methods. Our proposed model is based on maximum a posteriori probability (MAP) estimation. In this thesis, we propose a novel initialization method based on median operator to initialize our estimated high-resolution image. For the fidelity term in our proposed algorithm, the half-quadratic estimation is used to choose error norm adaptively instead of using fixed L1 or L2 norm. Furthermore, for our regularization term, we propose a novel regularization method based on Difference Curvature (DC) and Bilateral Total Variation (BTV) to suppress mixed noises and preserve image edges simultaneously. In our experimental results, synthetic data and real data are both tested to demonstrate the superiority of our proposed method in terms of clearer texture and less noise over other state-of-the-art methods.

The diploma thesis focuses on tracing in layout by handlers between assembly lines in new plant for corporation Continental Automotive Czech Republic ltd, where boosters are produced. The theoretical part involves definitions of logistics, supply chain, material flow and handling equipment. Furthermore, methods of mathematic programming and software equipment are described, such as quadratic assignment problem, knapsack problem, travelling salesman problem from graph theory. In the practical part the situation in corporation has been analyzed and the data prepared for further examination. Then layout of plant and internal processes are evaluated and an appropriate model or concept of solution is selected. Subsequently, application in MS Excel is created with support of VBA scripts (3 kinds of layouts). The user manipulates with application followed by Solver for implementation of a new solution into practice. Finally, the models are interpreted and verified by Lingo. The focus of the thesis is the design of a layout change of a new plant including the description of tracing.

M.Ed. / This dissertation is about the instructional approaches used by teachers to teach Grade 11 quadratic equations, errors learners made and misconceptions they possessed. The main topics that I had focused on were solving quadratic equations by factoring, completing a square and using quadratic formula. The intention was to observe teachers’ teaching approaches in quadratic equations and diagnosed types of errors learners displayed and misconceptions they possessed in quadratic equations. Literature review had served as a secondary source of information that was relied upon for the research study. Sources such as scholarly books, government documents, dissertations, professional journals and electronic resources were used to gather the information pertinent to the research topic. Review was also done on how teachers teach quadratic equations, learners’ learning of quadratic equations and teachers teach and learners learn mathematics. This study is action research under qualitative research paradigm in which the information collected was analyzed through thick description and not statistically. Pre-test, self and post test evaluation methods are discussed of quadratic equations by factorization, completing a square and using quadratic formula. Learners were tested on factoring, completing a square and using quadratic formula. In addition to the learners’ class exercises and home work, these scripts were also analysed for errors and misconceptions. Collected data is presented that helped to address errors and misconceptions learners displayed in solving quadratic equations and teachers’ teaching methods and approaches. Data was collected from schools in the neighborhood and the school I was attached as a mathematics teacher. In all schools, five teachers’ three lessons were observed which added up to a total of fifteen. All five teachers were interviewed as well as five learners in each school. Interviews were analyzed by comparing what their teaching approaches with the types of learners’ errors and misconceptions. In classroom observations, Indicator Evaluation Form adopted from Luneta (2006) was used to collect data as well as analyzing it. Questionnaires were prepared for both teachers and learners for interviews.

Nous nous sommes intéressés dans cette étude à l'estimation de la loi de la durée de séjour en prenant en compte les individus sur lesquels l'évènement d'intérêt et la censure peuvent se produire dans un même intervalle et être observés. Pour cela, nous avons proposé deux approches d'estimation non paramétrique basées sur une approximation asymptotique quand la longueur de l'intervalle entre deux dates consécutives d'observation tend vers 0. La première est basée sur une relation intégrale et la deuxième est basée sur une restauration des durées de séjour. Nous nous sommes servis de ces approches pour monter un modèle de croissance des fruits du cacaoyer en fonction du climat. Nous avons également estimé la sensibilité (probabilité de pénétration et de réussite d'infection) des fruits en fonction de leur stade et le potentiel infectieux (nombre moyen de spores sur un fruit) par date. Ce potentiel infectieux nous permettrait de monter un modèle du potentiel infectieux en fonction des fruits attaqués. La connaissance du potentiel infectieux en fonction des fruits attaqués, de l'estimation de la sensibilité suivant les stades, de l'estimation du modèle de croissance permettra alors de monter un modèle dynamique du potentiel infectieux pour prédire le risque d'évolution de la pourriture brune des fruits du cacaoyer / We are interested in this study in estimating the lifetime distribution by taking into consideration individuals on which the interest event and the censorship can occur in the same intervaland both events were then observed. We proposed two nonparametric approaches based on an asymptotic approximation when the lengthbetween two consecutive observation days tends to 0. The first one was based on an integral relationship and the second one on a lifetime restoration. We used theses approaches to build a fruitgrowth model depending on climatic variables. We also estimated the susceptibility (success probability of attack by a spore on a fruit) of the fruit depending of its developmental stage and theinfectious potential of the disease over time.This infectious potential could help to build a model of infectious potential depending on infected fruits. The knowledge of the infectious potential depending on infected fruits, the estimation of the susceptibility of the fruit and the model of growth will allow to built a dynamic model of infectious potential to predict the evolution risk of disease progression

Nesta dissertação, discute-se o problema de otimização de carteiras de investimento para estratégia passiva de Index Tracking. Os objetivos principais são (i) apresentar um modelo de otimização de Index Tracking e (ii) a solucionar esse modelo com uso do método heurístico de Algoritmos Genéticos (AG) para formação de carteiras com número reduzido de ativos. O índice de referência utilizado é o Ibovespa, para o período de Janeiro/2009 a Julho/2012, com um total de 890 observações diárias de preços. A partir de uma amostra de 67 ativos, são formadas carteiras sem limite de ativos e limitadas a 40, 30, 20, 10 e 05 ativos; os intervalos de rebalanceamento das carteiras são 20, 40 e 60 períodos (dias úteis), ou seja, rebalanceamento mensal, bimestral e trimestral. É verificado que, para essa amostra, não é possível formar carteiras de 20 ou menos ativos via otimização direta com o solver Cplex com menos de 1 hora de processamento e gap abaixo de 5%. Com uso da heurística de Algoritmos Genéticos, são formadas carteiras de 10 e 05 ativos com tempo de processamento em torno de 5 minutos; nesse caso, o gap médio fica abaixo de 10% para ambos os tipos de carteira. E, com tempo de processamento do AG um pouco maior, em torno de 8 minutos, o algoritmo fornece soluções para carteiras de 10 e 05 ativos com gap médio abaixo de 5%. / In this master’s thesis it is discussed the portfolio optimization problem using the passive investment strategy of Index Tracking. The main goals are (i) to present an optimization model for the Index Tracking problem and (ii) to solve this model using the heuristic approach of Genetic Algorithms (GA) to create portfolios with reduced amount of stocks. The benchmark used is the Ibovespa Index (main reference for the Brazilian Stock Market), during the period from January/2009 to July/2012 (using a total of 890 daily stock prices). The sample contains 67 assets, and the model is used to build portfolios without limit in the amount of assets and portfolios limited to 40, 30, 20, 10 and 05 assets; the ranges of time to rebalance the portfolios are 20, 40, and 60 trading days, which means to rebalance monthly, bimonthly and quarterly. The results show that, considering this sample, it is not possible to build portfolios with 20 stocks (or less than 20) through direct optimization using the solver Cplex with computational processing time less than 1 hour and results with gap below 5%. On the other hand, using the Genetic Algorithms heuristic approach, portfolios limited to 10 and 05 stocks are built with computational time close to 5 minutes; for both types of portfolio, the solutions provided by the GA have average gap below 10%. Also, with a computational time slightly bigger, close to 8 minutes, the algorithm provides solutions with average gap below 5% for portfolios limited to 10 and 05 stocks.

Orientador: Paulo Roberto Brumatti / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-04T02:10:19Z (GMT). No. of bitstreams: 1 Veloso_MarceloOliveira_M.pdf: 605567 bytes, checksum: 5882cdcae8b9c04096f915755c89a683 (MD5) Previous issue date: 2005 / Resumo: O objetivo principal deste trabalho é o estudo do número de soluções de equações polinomiais definidas sobre corpos finitos. Para isto utilizamos resultados básicos sobre a soma de Caracteres e resultados sobre o número de soluções de uma Forma Quadrática. Na nossa abordagem procuramos utilizar técnicas bem elementares, apesar disto implicar num número maior de cálculos. Contudo este método permitiu estudar e determinar fórmulas para o número de soluções de determinadas equações polinomiais muito estudadas, sem a necessidade de ferramentas mais elaboradas. Dentre as aplicações das fórmulas obtidas, temos alguns exemplos de curvas algébricas planas cujo número de pontos racionais atingem a cota de Weil, ou seja, curvas maximais que são de grande interesse em teoria dos códigos. Também conseguimos exemplos de variedades projetivas sobre corpos finitos cujo número de pontos atingem a cota de Weil-Deligne / Abstract: The main objective of this work is to study the number of solutions of polynomial equations over finite fields. For that we used basic results on Character sums and on the number of solutions of a Quadratic Form. This approach uses elementary techniques even considering the increasing on computations. Therefore this method allowed us to study and determine formulae for the number of solutions of certain polynomial equations well known, without the need of more sophisticated tools. Among the applications of the obtained formulae, we have some examples of plane algebraic curves which number of rational points achieve the Weil bound, that is, maximal curves which are of great interest in code theory. In addition, other examples were obtained of projective manifolds over finite fields which number of points achieve the Weil-Deligne bound / Mestrado / Algebra / Mestre em Matemática

Orientador: Antonio Carlos Moretti, Margarida Pinheiro Mello / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-18T11:43:39Z (GMT). No. of bitstreams: 1 Oliveira_WashingtonAlvesde_D.pdf: 1534705 bytes, checksum: 351c92a12c85da49389a18880da92ee7 (MD5) Previous issue date: 2011 / Resumo: Existem na literatura diversos conceitos e definições que caracterizam e dão condições de otimalidade para as soluções de um problema de programação multiobjetivo. A mais importante é a condição necessária de primeira ordem, que generaliza a condição clássica do tipo Karush-Kuhn-Tucker em otimização não linear. Esta condição garante a existência de uma vizinhança arbitrária onde uma solução ótima está contida. No entanto, para se obter condições suficientes de otimalidade, tanto local como global, é necessário impor hipóteses adicionais sobre as funções objetivo e o conjunto de restrições, como convexidade ou as suas generalizações. Em determinados problemas tais hipóteses podem ser muito restritivas. Neste trabalho, introduzimos um conceito alternativo para identificar a vizinhança de uma solução ótima local em problemas de programação multiobjetivo. Em uma primeira etapa, usando este conceito, obtemos condições necessárias e suficientes de otimalidade para as soluções de um problema particular, onde cada função objetivo é constituída de um quociente de funções quadráticas e o conjunto de restrições é formado por desigualdades lineares. Então, mostramos como calcular o maior raio da região esférica centrada em uma solução ótima local na qual esta solução é ótima. Nesse processo, podemos concluir que esta solução também é globalmente ótima. Em uma segunda etapa, usando o gradiente e a Hessiana de cada função quadrática, caracterizamos as soluções ótimas locais. Em uma terceira etapa, obtemos condições suficientes de otimalidade global impondo algumas hipóteses adicionais, porém essas hipóteses não caracterizam nenhum tipo de convexidade generalizada sobre as funções objetivo. Finalizamos com alguns resultados de dualidade. Este problema particular, envolvendo otimização fracional, surge frequentemente em aplicações nos processos de tomada de decisão em Ciência da Gestão, por exemplo, quando se deseja otimizar razões como desempenho/custo, lucro/investimento, custo/tempo, etc. Por isso, também propomos ao longo do texto vários métodos computacionais derivados dos nossos resultados que podem ser usados na obtenção de soluções para esses tipos de aplicações / Abstract: In the literature there are several concepts and definitions that characterize and give optimality conditions for solutions of a multiobjective programming problem. The most important is the necessary first-order optimality condition that generalizes the Karush-Kuhn-Tucker conditions. This condition ensures the existence of an arbitrary neighborhood that contains an optimal solution. However, in order to obtain optimality sufficient conditions, both local and global, it is necessary to impose additional assumptions on the objective functions and on the feasible set such as convexity and its generalizations. Sometimes, in some problems, such assumptions are too restrictive. In this work, we introduce an alternative concept to identify the local optimal solution neighborhood in multiobjective programming problems. In a first step, using this concept, we obtain necessary and sufficient optimality conditions for the solutions of a particular problem, where each objective function consists of a ratio quadratic functions and the feasible set is defined by linear inequalities. Then we show how to calculate the largest radius of the spherical region centered on a local optimal solution in which the local solution is optimal. In this process we may conclude that the solution is also globally optimal. In a second step, using the gradient and the Hessian of each quadratic function, we characterize the local optimal solutions. In a third step, we obtain global optimality sufficient conditions by imposing some additional assumptions but these assumptions do not characterize any kind of generalized convexity on the objective functions. We conclude this work with some results of the duality. This particular problem, involving fractional optimization, arises frequently in the decision making of the management science applications, for example, if you want to otimize the performance/cost ratio, or profit/investment, or cost/time, etc.. Therefore, we also propose throughout the text various computational methods derived from our results. These methods can be used to obtain solutions to these types of applications / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

Orientador: Antonio Jose Engler / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-14T13:32:53Z (GMT). No. of bitstreams: 1 PapaNeto_Angelo_D.pdf: 939822 bytes, checksum: 40aedb2e25f1f22956a7ff182038cae3 (MD5) Previous issue date: 2007 / Resumo: Um corpo ordenado é uma estrutura algébrica similar à do corpo dos números reais. No entanto, ao contrário dos reais, um corpo arbitrário F pode admitir mais de uma ordem, inclusive um número infinito e não enumerável de ordens. A cada elemento x do corpo F podemos associar uma forma quadrática binária [1, x], chamada 1-forma de Pfister. Os elementos de F = F 0} representados por [1, x], constituem um grupo que chamamos grupo de valores da forma e denotamos por D[1,x]. Um elemento d S F é chamado rígido se D[1, d] = F2 U dF2 , onde F2 é o subgrupo de F formado pelos quadrados. Um elemento d é dito birígido se d e -d são rígidos. O presente trabalho tem como objetivo principal obter um teorema de estrutura para o anel de Witt (das classes de equivalência de formas quadráticas) de um corpo ordenado F admitindo um elemento rígido que não é birígido e que é negativo em relação à pelo menos uma das ordens do corpo. Mais precisamente, obtemos uma decomposição do anel de Witt de F como produto de anéis de Witt de duas extensões H ¿ F e K ¿ F, ambas contidas no fecho quadrático de F. Os anéis de Witt de H e K têm estrutura mais simples que a do anel de Witt de F. Obtemos os corpos H e K construindo subgrupos Rd e Sd associados ao elemento rígido d e exigindo que valha uma propriedade de decomposição: F = Rd· Sd. O corpo H é uma henselização de F relativa a um anel de valorização (A;mA) de F tal que Rd = (1 + mA) F2 . O corpo K é pitagórico e tem espaço de ordens XK homeomorfo ao espaço X/Sd das ordens de F que contém Sd. Obtemos ainda uma condição necessária e suficiente para que ocorra a decomposição F = Rd · Sd, que depende do grupo de valores e do corpo de resíduos do anel de valorização A. / Abstract: An ordered field is an algebraic structure like the field of real numbers. However, while the field of real numbers have only one ordering, an arbitrary ordered field F may have more than one ordering, and also a infinite and uncountble number of orderings is allowed. To each element x Î F one can associate an binary quadratic form [1, x], called Pfister 1-fold form. The set of elements in F = F 0} which are represented by [1, x] is a group D[1,x], called value group of [1,x]. An element d S F is called rigid if D[1, d] = F2 U dF2, where F 2 denotes the subgroup of squares in F . An element d is called birigid if d and -d are both rigid. The main purpose of this thesis is to prove an structure theorem for Witt ring (of equivalence classes of quadratic forms) of an ordered field F with a rigid element which is not birigid and is negative in at least one ordering of F, that is, we get a decomposition of the Witt ring of F as a product of Witt rings of extensions H ¿ F and K ¿ F, both inside the quadratic closure of F. The Witt rings of H and K have a simpler structure than Witt ring of F. We get fields H and K by builting subgroups Rd and Sd associated to the rigid element d and making the addicional assumption that F = Rd·Sd holds. The field H is a henselization of F relative to a valuation ring (A;mA) of F such that Rd = (1 + mA) F2. The pythagorean field K has space of orderings XK homeomorphic to X/Sd, the space of orderings of F which contain Sd. Moreover, we settle an necessary and suficient condiction to decomposition F = Rd·Sd holds, relative to value group and residue field of valuation ring A. / Doutorado / Algebra / Doutor em Matemática

Orientador: Mario Antonio Bernal Rodriguez / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-30T22:42:12Z (GMT). No. of bitstreams: 1 TelloCajiao_JohnJames_M.pdf: 2614936 bytes, checksum: e5bdfc91b42434b003cad0b5fa850afb (MD5) Previous issue date: 2016 / Resumo: O objetivo deste trabalho é estudar a influência da conformação do DNA na probabilidade de dano direto produzido por partículas ionizantes. Além disso, os fundamentos mecanicísticos do modelo Linear-Quadrático são investigadas através de um modelo biofísico desenvolvido neste trabalho, baseado na TADR (Teoria da Ação Dual da Radiação). Para este fim, três modelos geométricos do material genético foram construídos. Os modelos têm resolução atomística e levam em conta ? 10^9 pares de base (bps) nas configurações A,B e Z do DNA. A partir de um único bp, os diferentes níveis organizacionais no interior do núcleo da célula foram criados por meio de transformações lineares. Em seguida, o código Monte Carlo (MC) GEANT4-DNA foi usado para simular o transporte de prótons de 0.5, 1, 5, 7 e 10 MeV assim como de partículas alfa de 2, 5, 7 e 10M eV . O número de partículas em cada caso é de tal modo que as doses absorvidas estão entre 0.5 ? 16Gy. Os três modelos foram consistentes com as dimensões das estruturas reais. Em particular, os modelos foram compatíveis com a exigência de que o diâmetro da cromatina seja de 30 nm, bem como com os volumes bp reportados em outros trabalhos. Os rendimentos tanto das quebras totais quanto das quebras duplas (TSBY e DSBY) foram obtidos para cada qualidade de radiação. Além disso, a probabilidade de impacto (SHP) definida como a razão entre o volume do DNA e o volume núcleo, foi calculada teoricamente e a partir das simulações. O modelo biofísico em conjunto com as simulações MC forneceu o número de lesões letais (N_LL) em função da dose, para prótons de 0,5 e 10 MeV, e para partículas alfa de 2 e 10 MeV . Os N_LL puderam ser divididos em aqueles criados por uma única trajetória e aqueles originados pela interacção de duas trajetórias. Concluiu-se que o TSBY é praticamente determinada pela SHP e depende fracamente da qualidade de radiação incidente. No entanto, o DSBY mostrou forte dependência tanto da conformação do DNA quanto da qualidade de radiação. Isto é devido à relação entre a capacidade de agrupamento das deposições de energia para uma radiação dada e o empacotamento do DNA. Por outro lado, a análise dos mecanismos de produção de dano, baseada na TADR e testada com o modelo biofísico desenvolvido, mostraram que os efeitos de uma única trajetória (de primeira ordem) dependem linearmente com a dose. Além disso, os efeitos inter-trajetórias seguem um comportamento quadrático com a dose, com um termo linear que influencia o mecanismo de primeira ordem. Isto significa que o comportamento linear-quadrático do N_LL com a dose, tem fundamentos mecanicistas, pelo menos, na primeira fase do dano / Abstract: The aim of this work is to study the influence of the DNA conformation on the probability of direct damage induction by ionizing particles. Also, the mechanistic grounds of the Linear-Quadratic radiobiological model are investigated through the eyes of a home-made biophysical model based on the DRAT (Dual Radiation Action Theory). To this end, three geometrical models of the genetic material were constructed. The models have atomistic resolution and account for ? 10^9 base pairs (bps) in the A-, B- and Z-DNA configurations. Starting from a single bp, the different organizational levels inside the cell nucleus were created by means of linear transformations. Next, the Monte Carlo (MC) code GEANT4-DNA was used to simulate the transport of protons of 0.5, 1, 5, 7 and 10 MeV , and alpha particles of 2, 5, 7 and 10 MeV. The number of particles in each case is such that the absorbed doses range between 0.5 Gy and 16 Gy. The three models proved to be consistent with the dimensions of the real structures. In particular, the models were compatible with the 30 nm chromatin fiber diameter requirement as well as with the bp volumes reported in other works. The Total and Double Strand Break Yields (TSBY and DSBY) were obtained for every radiation quality. Also, the Site-Hit Probability (SHP) defined as the total target to the nucleus volume ratio, was computed theoretically and from the simulations. The biophysical model in conjunction with the MC simulations furnished the number of lethal lesions (N_LL) as a function of dose, for protons of 0.5 and 10 MeV , and for alpha particles of 2 and 10 MeV . The N_LL could be split into those created by a single track and those originated by interaction of two tracks. It is concluded that the TSBY is practically determined by the SHP and depends weakly on the incident radiation quality. Nevertheless, the DSBY showed strong dependence on both the DNA conformation and the radiation quality. This is due to the interplay between the energy deposition clustering capacity of a given radiation and the DNA spatial packing. On the other hand, the analysis of the mechanisms of damage production based on the DRAT and tested with the biophysical model developed, showed that single-track (first order) effects depend linearly on the dose. Moreover, inter-track effects follows a quadratic behavior with the dose, having a linear term that influences the first order mechanism. This means that the Linear-Quadratic behavior of the N_LL with the dose, has mechanistic groundings at least at the first stage of the damage / Mestrado / Física / Mestre em Física / 1370449/2014 / CAPES