For discrete distributions a variant of rejection from a continuous hat function is presented. The main advantage of the new method, called rejection-inversion, is that no extra uniform random number to decide between acceptance and rejection is required which means that the expected number of uniform variates required is halved. Using rejection-inversion and a squeeze, a simple universal method for a large class of monotone discrete distributions is developed. It can be used to generate variates from the tails of most standard discrete distributions. Rejection-inversion applied to the Zipf (or zeta) distribution results in algorithms that are short and simple and at least twice as fast as the fastest methods suggested in the literature. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

This paper presents an overview of the most powerful universal methods. These are based on acceptance/rejection techniques where hat and squeezes are constructed automatically. Although originally motivated to sample from non-standard distributions these methods have advantages that make them attractive even for sampling from standard distributions and thus are an alternative to special generators tailored for particular distributions. Most important are: the marginal generation time is fast and does not depend on the distribution. They can be used for variance reduction techniques, and they produce random numbers of predictable quality. These algorithms are implemented in a library, called UNURAN, which is available by anonymous ftp. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

Minimum Concave Cost Multicommodity Network Design Problem arises in many application areas, such as transportation planning, distributed energy system and especially both circuit and packet switching backbone network design. Exact concave optimization algorithms have been developed, but these methods are applicable if the network size is small. Therefore, these problems are usually solved by non-exact iterative methods. In this thesis work, methods proposed for circuit switching and packet switching network design are evaluated in detail. After a comprehensive literate survey, Yaged&rsquo / s Linearization, Minoux greedy and Minoux accelerated greedy methods are found to be applicable to circuit switching network design when both solution quality and computational time is considered. Previously, it has been found that Minoux greedy methods may create routings with cycles and in order to eliminate these cycles a modification has been proposed. In this work, this modification is extended and evaluated in detail. Similarly, Gerla and Kleinrock&rsquo / s Concave Branch Elimination, Gersht&rsquo / s greedy and Stacey&rsquo / s Concave Link Elimination methods are investigated within the context of packet switching network design. All of these methods consider aggregate flows on each link simultaneously re-routing more than one commodity in one step. This thesis work also considers an alternative disaggregate approach, where only one commodity is handled at a time. Finally, algorithms proposed for circuit switching network design problem are adapted to the packet switching case and an extensive comparative computational study is performed to point out the best method with respect to time and solution quality for a number of networks and cost structure. Computational results have shown that modification on Minoux greedy to eliminate cycles leads to considerable improvements and the disaggregate approach gives the best result in some networks and cost structure.

Orientador: Alan Rodrigo Panosso / Resumo: O estudo da anisotropia espacial apresenta grande importância na modelagem e mapeamento espacial das variáveis ambientais. Assim, o objetivo do trabalho foi caracterizar a anisotropia espacial da perda de solo e atributos químicos e físicos do solo em diferentes pedoformas com cultivo de cana-de-açúcar, por meio da utilização da dimensão fractal (DF). O estudo foi realizado a partir de um banco de dados legados do Grupo de Pesquisa CSME, referente a uma área de 200 ha, localizada em Tabapuã (SP), Brasil, onde foi estabelecida uma malha de amostragem regular de 50 m, com 623 pontos. Em cada ponto, foi estimada a perda de solo por erosão (A), com a Universal Soil Loss Equation(USLE), bem como os atributos teor de argila (Arg), Areia Total (AT), Capacidade de troca de cátions (CTC), Matéria orgânica (MO) e Fósforo (P). Identificou-se a predominância de condição anisotrópica para todos os atributos na pedoforma convexa nas direções entre 90º e 150º, baseadas nos gráficos de dispersão gerados a partir de diferentes escalas e direções. Porém na pedoforma côncava A, Arg e CTC apresentaram comportamento isotrópico. Obteve-se o melhor ajuste no resultado da validação cruzada de A, na pedoforma côncava no modelo isotrópico e na pedoforma convexa no modelo anisotrópico. Concluiu-se que a pedoforma convexa proporciona maior ocorrência de anisotropia demonstrando que a forma do relevo condiciona padrões diferenciados de anisotropia espacial. / Abstract: The study of spatial anisotropy is of great importance in the modeling and spatial mapping of environmental variables. Thus, the objective of the work was to characterize the spatial anisotropy of soil loss and chemical and physical attributes of the soil in different pedoforms with sugarcane cultivation, using the fractal dimension (DF). The study was carried out from a legacy database of the CSME Research Group, referring to an area of 200 ha, located in Tabapuã (SP), Brazil, where a regular 50 m sampling grid was established, with 623 points . At each point, soil loss by erosion (A) was estimated with the Universal Soil Loss Equation (USLE), as well as the clay content (Arg), Total Sand (AT), Cation exchange capacity (CTC) attributes ), Organic matter (MO) and phosphorus (P). The predominance of anisotropic condition was identified for all attributes in the convex pedoform in the directions between 90º and 150º, based on the scatter plots generated from different scales and directions. However, in the concave pedoform A, Arg and CTC showed isotropic behavior. The best adjustment was obtained in the result of the cross-validation of A, in the concave pedoform in the isotropic model and in the convex pedoform in the anisotropic model. It was concluded that the convex pedoform provides a higher occurrence of anisotropy demonstrating that the shape of the relief conditions different patterns of spatial anisotropy. / Mestre

Carbon-infiltrated carbon nanotube (CICNT) forests are carbon nanotube (CNT) forests infiltrated with pyrolytic carbon to increase durability by becoming a solid material. This material can be tuned to maintain the nanotube geometry of a CNT forest and can also be fabricated on a variety of materials and geometries. Additionally, the present work has indicated that CICNT forests may resist bacterial proliferation and biofilm formation. This phenomenon is not due to the CICNT chemistry; it is presumably due to the CICNT nanostructure morphology. Thus, both silicon and stainless steel substrates were used to investigate CICNT's structural resistance to Methicillin-resistant Staphylococcus aureus (MRSA) biofilm. From in vitro experimental testing, CICNT on both these substrates resisted MRSA cell attachment and biofilm proliferation. The discovery of this non-pharmaceutical biofilm resistance expands the potential applications of CICNT to include medical devices that are prone to infection and/or devices that contribute to infection. Two representative applications were investigated: external fixator pins and scalpel blades. CICNT-coated versions of these applications underwent additional MRSA biofilm resistance testing as well as mechanical testing. In particular, external fixator pins were identified as a high potential application of CICNT surface coating technology. Previous work on both CNT and CICNT forests has largely been performed on planar structures. However, any potential medical device applications involve curved substrates. In particular, concave curvatures are challenging due to the potential for stress-related CICNT forest defects. Thus, the present work also included a study of the incidence rates and determining factors of these defects. SEM images of the cross-sections revealed different types of microscale forest defects while the top surface showed morphologies that are largely consistent with flat substrates. CICNT forest height and substrate curvature were identified as contributing factors to CICNT forest defect incidence rates. Thus, the present work advances the understanding of bacterial resistance and microstructure-related properties of CICNT surface coatings, with applications in medical devices.

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We develop and evaluate algorithms for generating random variates for simulation input. One group called automatic, or black-box algorithms can be used to sample from distributions with known density. They are based on the rejection principle. The hat function is generated automatically in a setup step using the idea of transformed density rejection. There the density is transformed into a concave function and the minimum of several tangents is used to construct the hat function. The resulting algorithms are not too complicated and are quite fast. The principle is also applicable to random vectors. A second group of algorithms is presented that generate random variates directly from a given sample by implicitly estimating the unknown distribution. The best of these algorithms are based on the idea of naive resampling plus added noise. These algorithms can be interpreted as sampling from the kernel density estimates. This method can be also applied to random vectors. There it can be interpreted as a mixture of naive resampling and sampling from the multi-normal distribution that has the same covariance matrix as the data. The algorithms described in this paper have been implemented in ANSI C in a library called UNURAN which is available via anonymous ftp. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

Orientador: Márcio Ricardo Alves Gouveia / Resumo: O presente trabalho trata de conceitos relacionados com a medida generalizada de Hausdorff, onde o principal objetivo consiste na obtenção de conjuntos cuja dimensão seja um número positivo não inteiro. Ele começa com uma definição sobre as propriedades que uma função de conjunto deve satisfazer para ser considerada uma medida de Carathéodory, suas implicações e consequências. Após a explicação destes conceitos iniciais, dá-se alguns exemplos de funções de conjunto contínuas e monótonas com a apresentação da função de escala logarítmica, que é peça chave para o desenvolvimento de conjuntos de medidas positivas não inteiras, além da introdução da medida de Hausdorff com seus desdobramentos. Algumas hipóteses sobre funções côncavas são apresentadas juntamente com fórmulas deduzidas com bases nestas hipóteses e na concavidade da função. Utiliza-se a função de escala logarítima para a determinação da dimensão de vários conjuntos, inclusive o conjunto de Cantor. Posteriormente, há uma adaptação dos conceitos trabalhados para o tratamento de dimensões relacionadas à números diádicos irracionais. Por fim, os conceitos tratados sobre a reta real são estendidos para produtos cartesianos, com especial enfoque para conjuntos planares. / Abstract: The present work deals with concepts related to the generalized Hausdorff measure, where the main objective is to obtain sets whose dimension is a positive non integer number. It begins with a definition of the properties that a set function must satisfy to be considered a Carathéodory measure, their implications and consequences. Following the explanation of these initial concepts, some examples of continuous and monotonous set functions are given with the presentation of the logarithmic scale function, which is key to the development of non-integer positive measure sets, in addition to the introduction of the Hausdorff measure with its developments. Some assumptions about concave functions are presented together with formulas derived from these assumptions and the concavity of the function. The logarithmic scale function is used to determine the dimension of various sets, including the Cantor set. Later, there is an adaptation of the concepts worked for the treatment of dimensions related to irrational dyadic numbers. Finally, the concepts treated on the real line are extended to Cartesian products, with special focus on planar sets. / Mestre

Sont concernes les problèmes d'optimisation non convexe et non différentiable du type d.c canonique. L'aspect théorique et l'aspect algorithmique sont abordés