Let $G\ensuremath{\mathbin{\raisebox{0.3mm}{$\scriptstyle\square$}}} H$ denote the Cartesian product of the graphs $G$ and $H$. Domination of the Cartesian product of two graphs has received much attention, with a main objective to confirm the truth of Vizing's well-known conjecture. The conjecture states that the domination number of the Cartesian product of two graphs is at least as large as the product of the respective domination numbers. The potential truth of Vizing's conjecture gives rise to investigating the domination of graph products that generalizes the Cartesian product. The generalized prism $\pi G$ of $G$ is the graph consisting of two copies of $G$, with edges between the copies determined by a permutation $\pi$ acting on the vertices of $G$. A generalized Cartesian product $G\ensuremath{\mathbin{\raisebox{0.3mm}{${\scriptstyle \square}$}\hspace{-1.99mm}\raisebox{0.65mm}{${\scriptstyle \pi}$}}} H$ is defined here, incorporating structural properties of both the Cartesian product of two graphs as well as the generalized prism of a graph. Conditions on the isomorphism of two generalized Cartesian products are explored first, establishing a characterization in the case of natural isomorphisms. A comparison of the diameter of the generalized Cartesian product and the corresponding Cartesian product graph is used to illustrate the structural differences between these graph products. This comparison is continued through a study of the validity of an inequality similar to Vizing's conjecture for Cartesian products. Graphs that attain equality in the general bounds for the domination number of the Cartesian product and generalized Cartesian product are investigated in more detail. For any graph $G$ and $n\geq 2$, $\min\{|V(G)|,\gamma(G)+n-2\}\leq\gamma(G\ensuremath{\mathbin{\raisebox{0.3mm}{$\scriptstyle\square$}}} K_{n})\leq n\gamma(G)$. A graph $G$ is called a consistent Cartesian fixer if $\gamma(G\ensuremath{\mathbin{\raisebox{0.3mm}{$\scriptstyle\square$}}} K_{n})=\gamma(G)+n-2$ for each $n$ such that $2\leq n<|V(G)|-\gamma(G)+2$. A graph attaining equality in the stated upper bound on $\gamma(G\ensuremath{\mathbin{\raisebox{0.3mm}{$\scriptstyle\square$}}} K_{n})$ is called a Cartesian $n$-multiplier. Both of these classes are characterized. Concerning the generalized Cartesian product, $\gamma(G\ensuremath{\mathbin{\raisebox{0.3mm}{${\scriptstyle \square}$}\hspace{-1.99mm}\raisebox{0.65mm}{${\scriptstyle \pi}$}}} K_{n})\leq n\gamma(G)$ for any graph $G$, permutation $\pi$ and $n\geq 2$. A graph attaining equality in the upper bound for all $\pi$ is called a universal multiplier. Such graphs are characterized similar to a known result for generalized prisms. A similar problem for the product $G\ensuremath{\mathbin{\raisebox{0.3mm}{${\scriptstyle \square}$}\hspace{-1.99mm}\raisebox{0.65mm}{${\scriptstyle \pi}$}}} C_{n}$ is considered, with conditions on a graph being a so-called cycle multiplier provided. A graph attaining equality in the lower bound $\gamma(G\ensuremath{\mathbin{\raisebox{0.3mm}{${\scriptstyle \square}$}\hspace{-1.99mm}\raisebox{0.65mm}{${\scriptstyle \pi}$}}} H)\geq\gamma(G)$ for some permutation $\pi$ is called a $\pi$-$H$-fixer. A brief investigation is conducted into the existence of universal $H$-fixers, i.e.~graphs that are $\pi$-$H$-fixers for some $H$ and all permuations $\pi$ of $V(G)$, and it is shown that no such graphs exist when $n\geq 3$. A known efficient algorithm for determining $\gamma(G\ensuremath{\mathbin{\raisebox{0.3mm}{$\scriptstyle\square$}}} P_{n})$ is surveyed, and modified to accommodate any Cartesian product $G\ensuremath{\mathbin{\raisebox{0.3mm}{$\scriptstyle\square$}}} H$, thereby establishing a general framework for evaluating the domination number of $G\ensuremath{\mathbin{\raisebox{0.3mm}{$\scriptstyle\square$}}} H$ for a fixed graph $G$ and any $H$. An algorithm to determine $\gamma(G\ensuremath{\mathbin{\raisebox{0.3mm}{$\scriptstyle\square$}}} T)$ for any tree $T$ is provided, and it is observed to be polynomial for trees of bounded maximum degree. The general framework for $G\ensuremath{\mathbin{\raisebox{0.3mm}{$\scriptstyle\square$}}} H$ is also modified to accommodate the generalized Cartesian product $G\ensuremath{\mathbin{\raisebox{0.3mm}{${\scriptstyle \square}$}\hspace{-1.99mm}\raisebox{0.65mm}{${\scriptstyle \pi}$}}} H$. The study diverts from the main topic of domination to investigate the planarity of the generalized Cartesian product graph. If both $G$ and $H$ are 2-connected graphs, then $G\ensuremath{\mathbin{\raisebox{0.3mm}{${\scriptstyle \square}$}\hspace{-1.99mm}\raisebox{0.65mm}{${\scriptstyle \pi}$}}} H$ is nonplanar. A known simple polynomial-time planarity testing algorithm is surveyed, and used to establish conditions on the planarity of $P_{m}\ensuremath{\mathbin{\raisebox{0.3mm}{${\scriptstyle \square}$}\hspace{-1.99mm}\raisebox{0.65mm}{${\scriptstyle \pi}$}}} P_{n}$, the generalized Cartesian product of two paths. This research aims to lay the foundation on which further properties of the generalized Cartesian product and further generalizations may be studied, as well as to provide various open problems to spark interest in the research area.

Naive Bayes classifier and maximum likelihood hypotheses in Bayesian learning are considered when the errors have non-normal distribution. For location and scale parameters, efficient and robust estimators that are obtained by using the modified maximum likelihood estimation (MML) technique are used. In naive Bayes classifier, the error distributions from class to class and from feature to feature are assumed to be non-identical and Generalized Secant Hyperbolic (GSH) and Generalized Logistic (GL) distribution families have been used instead of normal distribution. It is shown that the non-normal naive Bayes classifier obtained in this way classifies the data more accurately than the one based on the normality assumption. Furthermore, the maximum likelihood (ML) hypotheses are obtained under the assumption of non-normality, which also produce better results compared to the conventional ML approach.

Made available in DSpace on 2014-06-11T19:31:37Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-11-16Bitstream added on 2014-06-13T21:02:57Z : No. of bitstreams: 1 barbosa_l_dr_botfca.pdf: 2587351 bytes, checksum: 76e343f1e0edbbbee5cb996188d8efd2 (MD5) / É bastante comum na área agrícola, experimentos cujas variáveis respostas são contagens ou proporções. Para esse tipo de dados, utiliza-se a metodologia de modelos lineares generalizados quando as respostas são independentes. Por outro lado, quando as respostas são dependentes, há uma correlação entre as observações e isso tem que ser levado em consideração na análise, para evitar inferências incorretas sobre os coeficientes de regressão. Na literatura há técnicas disponíveis para a modelagem e análise desses dados, sendo os modelos disponíveis extensões dos modelos lineares generalizados. No presente trabalho, utiliza-se a metodologia de equação de estimação generalizada, que inclui no modelo uma matriz de correlação para a obtenção de um melhor ajuste. Outra alternativa, também abordada neste trabalho, é a utilização de um modelo linear generalizado misto, no qual o uso de efeitos aleatórios também introduz uma correlação entre observações que tenham algum efeito em comum. Essas duas metodologias são aplicadas a um conjunto de dados obtidos de um experimento para avaliar certas condições na germinação de sementes de mamona da cultivar AL Guarany 2002, com o objetivo de se verificar qual o melhor modelo de estimação para esses dados / Experiments whose response variables are counts or proportions are very common in agriculture. For this type of data, if the observational units are independent, the methodology of generalized linear models can be appropriate. On the other hand, when responses are dependent or clustered, there is a correlation between the observations and that has to be taken into consideration in the analysis to avoid incorrect inferences about the regression coefficients. In the literature there are techniques available for modeling and analyzing such type data, the models being extensions of generalized linear models. The present study explores the use of: 1) generalized estimation equations, that includes a correlation matrix to obtain a better fit; 2) generalized linear mixed models, that introduce a correlation between clustered observations though the addition of random effects in the model. These two methodologies are applied to a data set obtained from an experiment to evaluate certain conditions on the germination of seeds of castor bean cultivar AL Guarany 2002 with the objective of determining the best estimation model for such data

Orientador: Luiza Aparecida Trinca / Banca: Liciana Vaz da Arruda / Banca: Osmar Delmanto Junior / Banca: Célia Regina Lopes Zimback / Banca: Marli Teixeira de A. Minhoni / Resumo: É bastante comum na área agrícola, experimentos cujas variáveis respostas são contagens ou proporções. Para esse tipo de dados, utiliza-se a metodologia de modelos lineares generalizados quando as respostas são independentes. Por outro lado, quando as respostas são dependentes, há uma correlação entre as observações e isso tem que ser levado em consideração na análise, para evitar inferências incorretas sobre os coeficientes de regressão. Na literatura há técnicas disponíveis para a modelagem e análise desses dados, sendo os modelos disponíveis extensões dos modelos lineares generalizados. No presente trabalho, utiliza-se a metodologia de equação de estimação generalizada, que inclui no modelo uma matriz de correlação para a obtenção de um melhor ajuste. Outra alternativa, também abordada neste trabalho, é a utilização de um modelo linear generalizado misto, no qual o uso de efeitos aleatórios também introduz uma correlação entre observações que tenham algum efeito em comum. Essas duas metodologias são aplicadas a um conjunto de dados obtidos de um experimento para avaliar certas condições na germinação de sementes de mamona da cultivar AL Guarany 2002, com o objetivo de se verificar qual o melhor modelo de estimação para esses dados / Abstract: Experiments whose response variables are counts or proportions are very common in agriculture. For this type of data, if the observational units are independent, the methodology of generalized linear models can be appropriate. On the other hand, when responses are dependent or clustered, there is a correlation between the observations and that has to be taken into consideration in the analysis to avoid incorrect inferences about the regression coefficients. In the literature there are techniques available for modeling and analyzing such type data, the models being extensions of generalized linear models. The present study explores the use of: 1) generalized estimation equations, that includes a correlation matrix to obtain a better fit; 2) generalized linear mixed models, that introduce a correlation between clustered observations though the addition of random effects in the model. These two methodologies are applied to a data set obtained from an experiment to evaluate certain conditions on the germination of seeds of castor bean cultivar AL Guarany 2002 with the objective of determining the best estimation model for such data / Doutor

The random walk is a powerful model. Chemistry, Physics, and Finance are just a few of the disciplines that model with the random walk. It is clear from its varied uses that despite its simplicity, the simple random walk it very flexible. There is one major drawback, however, to the simple random walk and the geometric random walk. The limiting distribution is either normal, lognormal, or a levy process with infinite variance. This thesis introduces an new random walk aimed at overcoming this drawback. Because the simple random walk and the geometric random walk are special cases of the proposed walk, it is called a generalized random walk. Several properties of the generalized random walk are considered. First, the limiting distribution of the generalized random walk is shown to include a large class of distributions. Second and in conjunction with the first, the generalized random walk is compared to the geometric random walk. It is shown that when parametrized properly, the generalized random walk does converge to the lognormal distribution. Third, and perhaps most interesting, is one of the limiting properties of the generalized random walk. In the limit, generalized random walks are closely connected with a u function. The u function is the key link between generalized random walks and its difference equation. Last, we apply the generalized random walk to option pricing.

No description available.

The generalized linear model (GLM) is a popular model in many research areas. In the GLM, each outcome of the dependent variable is assumed to be generated from a particular distribution function in the exponential family. The mean of the distribution depends on the independent variables. The link function provides the relationship between the linear predictor and the mean of the distribution function. In this dissertation, two semiparametric extensions of the GLM will be developed. In the first part of this dissertation, we have proposed a new model, called a semiparametric generalized linear model with a log-concave random component (SGLM-L). In this model, the estimate of the distribution of the random component has a nonparametric form while the estimate of the systematic part has a parametric form. In the second part of this dissertation, we have proposed a model, called a generalized semiparametric single-index mixed model (GSSIMM). A nonparametric component with a single index is incorporated into the mean function in the generalized linear mixed model (GLMM) assuming that the random component is following a parametric distribution. In the first part of this dissertation, since most of the literature on the GLM deals with the parametric random component, we relax the parametric distribution assumption for the random component of the GLM and impose a log-concave constraint on the distribution. An iterative numerical algorithm for computing the estimators in the SGLM-L is developed. We construct a log-likelihood ratio test for inference. In the second part of this dissertation, we use a single index model to generalize the GLMM to have a linear combination of covariates enter the model via a nonparametric mean function, because the linear model in the GLMM is not complex enough to capture the underlying relationship between the response and its associated covariates. The marginal likelihood is approximated using the Laplace method. A penalized quasi-likelihood approach is proposed to estimate the nonparametric function and parameters including single-index coe±cients in the GSSIMM. We estimate variance components using marginal quasi-likelihood. Asymptotic properties of the estimators are developed using a similar idea by Yu (2008). A simulation example is carried out to compare the performance of the GSSIMM with that of the GLMM. We demonstrate the advantage of my approach using a study of the association between daily air pollutants and daily mortality adjusted for temperature and wind speed in various counties of North Carolina. / Ph. D.

The major Hot-Mix Asphalt (HMA) input for mechanistic-empirical (M-E) flexible pavement design is the dynamic complex modulus obtained from either the uniaxial or triaxial compressive dynamic modulus test. Furthermore, as part of the performance-based mix design process, the triaxial dynamic modulus has been selected to predict rutting and fatigue cracking, and the Indirect Tension (IDT) creep compliance test to predict low-temperature thermal cracking. The creep compliance and dynamic modulus are measured responses (viscoelastic functions) of viscoelastic materials under transient and cyclic loading, respectively. Under the assumptions of linearity, linear viscoelastic functions are equivalent. Moreover, these properties should be the same whether they are obtained from a uniaxial compressive or IDT test. For this dissertation, we tested the applicability of linear viscoelastic (LVE) theory to HMA mixes and determined whether HMA need to be modeled as a bimodular material to analyze IDT creep compliance test results. The need to model HMA as a bimodular material is a result of a number of studies that suggest that HMA tensile and compressive properties are different. A testing program was developed to experimentally measure the uniaxial compression, and IDT creep compliance, and the uniaxial compression dynamic modulus for different HMA mixes. The uniaxial compressive creep compliance and dynamic modulus master curves are constructed and the shift factors obtained from each test are compared. Interconversion between the creep compliance and dynamic modulus experimental results confirm the applicability of LVE theory for the HMA mixes investigated. Based on the applicability of LVE theory, a methodology to determine HMA LVE properties from the combined creep compliance and dynamic modulus test results was developed. As a practical application that is relevant to the M-E flexible pavement design procedure, LVE theory was used and compared to proposed approximate methods to perform the conversion of testing frequency to loading time. Specifically, dynamic modulus results were converted to relaxation modulus, creep compliance, and resilient modulus. Finally, the HMA IDT creep compliance test results at low and intermediate temperature (<20oC) were successfully analyzed using a HMA bimodular material model based on the Ambartsumyan model. The difference between the compressive modulus and the modulus calculated from the IDT test using Hondros' stress distribution is calculated. In addition, a method to determine the compressive-to-tensile modulus ratio using uniaxial compressive and IDT test results is illustrated for one of the tested HMA mixes. / Ph. D.

<p>Proučaveni su uop&scaron;teni slučajni procesi na različitim prostorima uop&scaron;tenih funkcija i date njihove reprezentacije. Dati su potrebni i dovoljni uslovi za različite konvergencije niza uop&scaron;tenih slučajnih procesa. Data je ekstenzija Gausovog uop&scaron;tenog slučajnog procesa na Hilbertovom prostoru.</p> / <p>Generalized random processes on different&nbsp; spaces of generalized functions are considered. The representation of such processes are given. Necessary and sufficient conditions for different convergence of a a sequence of generalized random pocesses are obtained. Extension of a Gaussian generalized random pocess to a Hilbert space is obtained.</p>

<p>Postpartum depression has become a major public health concern for women within a specific time period after delivery. Depression is possibly associated with some risk factors such as socioeconomic status, social support, maternal mental and physical health, and history of anxiety. TOMIS III, funded by the Canadian Institutes of Health Research, is a prospective cohort to study the associations between delivery method and health and health resource utilization.</p> <p>Clinically, we investigated the associations between mode of delivery and outcome of postnatal depression, maternal and infant health, and we implied the risk predictors for outcomes by statistical methodology of marginal model with generalized estimating equations (GEE). Statistically, a variety of regression models, namely, generalized linear mixed effect model (GLMM), hierarchical generalized linear model (HGLM) and Bayesian hierarchical model were applied for this analysis and results were compared with GEEs. Some imputation strategies, namely, mean imputation, last observation carrying forward (LOCF), hot-deck imputation and multiple imputation were employed for handling missing values in this study.</p> <p>Analysis results demonstrated that there was no statistically significant association between mode of delivery and postpartum depression [OR 0.99, 95% CI (0.73, 1.34)]. However, the development of postpartum depression was found to be associated with low income, low mental and physical health functioning, lack of social support, the low number of unmet learning needs in hospital, and English or French spoken at home. Results were consistent for all regression models but GEE provided the best fit and an excellent discriminative ability. GEE models were constructed on different datasets imputed by mean, LOCF, hot-deck and multiple imputation, and LOCF was recommended to handle the missing data in this longitudinal study.</p> <p>Analyses on the outcome of maternal health and infant health stated that method of delivery had a statistically significant influence on maternal health but no significant impact on infant health. Risks of maternal health problems were associated with cesarean delivery, good/fair/poor infant health, low maternal mental and physical health functioning, lack of care for maternal mental health, and good/fair/poor health before pregnancy. Risks of infant health problems were associated with good/fair/poor maternal health before pregnancy and after discharge, inadequate care or help for infant health, fair/poor community services after discharge, low maternal mental health functioning, non-English or non-French spoken at home, and mothers born outside of Canada.</p> / Master of Science (MSc)