Nesse trabalho estudamos dois tipos de modelos para a descrição dos sistemas magnéticos modulados. O primeiro é o modelo ANNNI (\"Axial Next-Nearest-Neighbor Ising\"). Dentro dos limites da aproximação de campo médio estudamos vários efeitos que surgem quando as interações intraplanares são menores que as interações interplanares. Investigamos em particular a ocorrência de fases desordenadas, assim denominadas por apresentar planos com magnetização nula. Estudamos ainda o comportamento dos pontos de acumulação de pontos de ramificação que determinam o limite entre as transições do tipo comensurável-comensurável e comensurável-incomensurável. Também investigamos dois variantes do modelo ANNNI, um com spin qualquer e outro com spin 1 e anisotropia de campo cristalino. O segundo tipo de modelo estudado, apropriado para sistemas apresentando modulações helicoidais das magnetizações, é um modelo planar clássico com interações competitivas entre primeiros e segundos vizinhos numa direção axial. Restringimos o nosso estudo ao zero absoluto de temperatura. Fizemos expansões das magnetizações em série de Fourier para campos baixos e altos. Também fizemos análise de estabilidade das fases comensuráveis, dentro de uma aproximação contínua, utilizando a teoria dos sólitons. Finalmente, estudamos numericamente o diagrama de fases do modelo aplicando o método dos potenciais efetivos. / In this work we have studied two types of models for the description of modulated magnetic systems. The first is the ANNNI (Axial NextNearest-Neighbor Ising) model. Within the mean-field approximation we have studied various effects which comes about when the intralayer interactions are weaker than the interlayer interactions. We have investigated in particular the possibility of partially disordered phases, characterized by the presence of layers with zero magnetization. We also have studied the behavior of the accumulation points of the branching points, which separates the commensurate-commensurate transitions from the commensurate-incommensurate transitions. We have also investigated two variants of the ANNNI model, one with an arbitrary spin and the other with spin 1 and a term of crystal-field anisotropy. The second type of the model we have studied, appropriate for systems presenting helicoidal modulation of the magnetization, is a classical planar model with nearest and next-nearest interactions along an axial direction. \\\'Ve have restricted our study to the absolute zero of the temperature. The magnetization is expanded in Fourier series for high and low fields. We also analyse the stability of the commensurate phases, within a continuum approximation, using the soliton theory. Finally, we construct numerically the phase diagram of the model using the method of effective potentials.

O interesse geral de nosso grupo é estudar sistemas moleculares em fase líquida. Para isto existem vários métodos de simulação. Dentre eles, os mais utilizados são o método Monte Carlo Matropolis e Dinâmica Molecular. Porém ambos necessitam do conhecimento prévio do potencial de interação molecular. Neste trabalho, estudamos um método de simulação recente que embora tenha sido idealizado em 1968 por Kaplow et al. só foi formalizado em 1988 por McGreevy et al. Este método é hoje chamado de Monte Carlo Reverso. A vantagem deste método é que ele não necessita do potencial de interação, mas sim do fator de estrutura ou da função de distribuição radial que podem ser obtidos experimentalmente por meio de espalhamento de raio-X ou de nêutrons. A desvantagem é que ainda existem algumas dúvidas sobre sua confiabilidade e aplicabilidade para sistemas líquidos. Neste trabalho, realizamos um estudo investigativo procurando adquirir conhecimento a respeito deste método para podermos obter nossas próprias experiências e conclusões. Inicialmente, desenvolvemos um código computacional utilizando o método Monte Carlo Reverso. Depois realizamos simulações de argônio líquido com a finalidade de testar nosso programa e posteriormente aplicarmos o método para o oxigênio líquido. Baseados nos resultados que obtivemos, concluímos que apesar do método Monte Carlo Reverso não ser capaz de descrever a termodinâmica do sistema, ele gera estruturas configuracionais com as mesmas características que as geradas com o Monte Carlo Metropolis. No futuro pretendemos analisar se as configurações geradas com o Monte Carlo Reverso são capazes de reproduzir as propriedades quânticas (dipolo, espectro de absorção, etc) da mesma maneira que o Monte Carlo Metropolis / Implementation and applications of the reverse Monte Carlo method for homogeneous liquids

Discovering the associations between genetic variables and disease status can help reduce the burden of disease on society. This thesis focuses on the methods required to detect maternal genetic effects (an effect where the genes of the mother affect the disease risk of the child) and interaction effects between these maternal genes and environmental variables in trio data consisting of parents and an affected child. A simulation study was conducted to determine the extent to which testing for these effects is affected by violations to the mating symmetry assumption required for two current methods when control parents are not available.. This study showed that methods for maternal effect estimation are not robust to these violations; however, the interaction test is robust to the violation. Finally, a candidate gene study on orofacial clefts was conducted to evaluate maternal gene-environment interactions in international consortium data. Significant effects were found but the large magnitude of the effect estimates raises concerns about the validity of the results. This thesis tries also discusses the lack of methods and software available to estimate maternal gene environment interactions.

Abstract not available

Thesis (M. Phil.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.

Testing main effects and interaction effects in factorial designs are basic content in statistics textbooks and widely used in various fields. In balanced designs there is general agreement on the appropriate main effect and interaction sums of squares and these are typically displayed in an analysis of variance (ANOVA). A number of methods for analyzing unbalanced designs have been developed, but in general they do not lead to unique results. For example, in SAS one can get three different main effect sums of squares in an unbalanced design. I, If these results are viewed from the theory of the general linear model, then it is typically the case that the different sums of squares all lead to F-tests, but they are testing different linear hypotheses. In particular, if one clearly specifies the linear hypothesis being tested, then linear model theory leads to one unique deviation sum of squares. One exception to this statement is an ANOVA, called an unweighted means ANOVA (UANOVA) introduced by Yates (1934). The deviation sum of squares in a UNANOVA typically does not lead to an F-test and hence does not reduce to a usual deviation sum of squares for some linear hypothesis. The UANOVA tests have been suggested by several writers as an alternative to the usual tests. Almost all of these results are limited to the one-way model or a two-way model with interaction, and hence the UANOVA procedure is not available for a general linear model. This thesis generalizes the UANOVA test prescribed in the two-way model with interaction to a general linear model. In addition, the properties of the test are investigated. It is found, similar to the usual test, that computation of the UANOVA test statistic does not depend on how the linear hypothesis is formulated. It is also shown that the numerator of the UANOVA test is like a linear combination of independent chi-squared random variables as opposed to a single chi-squared random variable in the usual test. In addition we show how the Imhof (1961) paper can be used to determine critical values, p-values and power for the UANOVA test. Comparisons with the usual test are also included. It is found that neither test is more powerful than the other. Even so, for most circumstances our general recommendation is that the usual test is probably superior to the UANOVA test. / Graduation date: 2002

Environmental monitoring poses two challenges to statistical analysis: complex data and complex survey designs. Monitoring for system health involves measuring physical, chemical, and biological properties that have complex relations. Exploring these relations is an integral part of understanding how systems are changing under stress. How does one explore high dimensional data? Many of our current methods rely on "black-box" mathematical methods. Visualization techniques on the other hand are either restricted to low dimensions or hopelessly out of context. The first topic explored in this dissertation suggests a direct search method for use in projection pursuit guided tours. In Chapter 2 a direct search method for index optimization, the multidirectional pattern search, was explored for use in projection pursuit guided tours. The benefit of this method is that it does not require the projection pursuit index to be continuously differentiable; in contrast to existing methods that require differentiability. Computational comparisons with test data revealed the feasibility and promise of the method. It successfully found hidden structure in 4 of 6 test data sets. The study demonstrates that the direct search method lends itself well to use in guided tours and allows for non-differentiable indices. Evaluating estimators of the population variance is covered in Chapter 3. Good estimates of the population variance are useful when designing a survey. These estimates may come from a pilot project or survey. Often in environmental sampling simple random sampling is not possible;�� instead complex designs are used. In this case there is no clear estimator for the population variance. We propose an estimator that is (1) based on a methods of moments approach and (2) extendible to more complex variance component models. Several other estimators have been proposed in the literature. This study compared our method of moment estimator to other variance estimators. Unfortunately our estimator did not do as well as some of the other estimators that have been suggested implying that these estimators do not perform similarly as the literature suggests they do. Two estimators, the sample variance and a ratio estimator based on the Horvitz-Thompson Theorem and a consistency argument, proved to be favorable. / Graduation date: 2000

Thesis (Ph. D.)--Oregon Graduate Center, 1973.

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2002. / Includes bibliographical references. Also available in electronic version. Access restricted to campus users.

Thesis (Ph. D.)--California Institute of Technology, 2003. Thesis (Ph. D.). PQ #3093487. / Includes bibliographical references. Also available via the World Wide Web. http://www.fluff.info/klemens