<p>Previous studies of agricultural conditions in the Mekong Delta (MD) have identified soil compaction as an obstacle to sustainable production. A conceptual model for soil formation was presented to demonstrate the link between soil hydrology and plant response. Detailed studies of soil moisture dynamics in agricultural fields were conducted using a dynamic process-orientated model. Pressure head and water flow were simulated for three selected sites during a year for which empirical data were available. Daily meteorological data were used as dynamic input and measured pressure head was used to estimate parameter values that satisfied various acceptance criteria. The Generalised Likelihood Uncertainty Estimation (GLUE) approach was applied for calibration procedures with 10,000 runs, each run using random values within the chosen range of parameter values. To evaluate model performance and uncertainty estimation, re-sampling was carried out using coefficient of determination (R2) and mean error (ME) as the criteria. Correlations between parameters and R2 (and ME) and among parameters were also considered to analyse the relationship of the selected parameter set in response to increases/decreases in the acceptable simulations. The method was successful for two of the three sites, with many accepted simulations. For these sites, the uncertainty was reduced and it was possible to quantify the importance of the different parameters.</p><p> </p>

Doctor of Philosophy / Department of Statistics / Wei-Wen Hsu / The classification methods based on a linear combination of multiple biomarkers have been widely used to improve the accuracy in disease screening and diagnosis. However, it is seldom to include covariates such as gender and age at diagnosis into these classification procedures. It is known that biomarkers or patient outcomes are often associated with some covariates in practice, therefore the inclusion of covariates may further improve the power of prediction as well as the classification accuracy. In this study, we focus on the classification methods for multiple biomarkers adjusting for covariates. First, we proposed a covariate-adjusted classification model for multiple cross-sectional biomarkers. Technically, it is a two-stage method with a parametric or non-parametric approach to combine biomarkers first, and then incorporating covariates with the use of the maximum rank correlation estimators. Specifically, these parameter coefficients associated with covariates can be estimated by maximizing the area under the receiver operating characteristic (ROC) curve. The asymptotic properties of these estimators in the model are also discussed. An intensive simulation study is conducted to evaluate the performance of this proposed method in finite sample sizes. The data of colorectal cancer and pancreatic cancer are used to illustrate the proposed methodology for multiple cross-sectional biomarkers. We further extend our classification method to longitudinal biomarkers. With the use of a natural cubic spline basis, each subject's longitudinal biomarker profile can be characterized by spline coefficients with a significant reduction in the dimension of data. Specifically, the maximum reduction can be achieved by controlling the number of knots or degrees of freedom in the spline approach, and its coefficients can be obtained by the ordinary least squares method. We consider each spline coefficient as ``biomarker'' in our previous method, then the optimal linear combination of those spline coefficients can be acquired using Stepwise method without any distributional assumption. Afterward, covariates are included by maximizing the corresponding AUC as the second stage. The proposed method is applied to the longitudinal data of Alzheimer's disease and the primary biliary cirrhosis data for illustration. We conduct a simulation study to assess the finite-sample performance of the proposed method for longitudinal biomarkers.

Soil suction is one of the most important physical variables affecting the soil engineering behavior, moisture content. Suction has a major controlling influence on soil shear strength. The moisture diffusivity properties of unsaturated properties of soils exert a critical influence on the depth to which seasonal variations of moisture and suction at the ground surface extend into the soil mass. Hence, a study of moisture diffusion coefficient is pivotal. In this research the drying test originally proposed by Mitchell (1979) has been validated by back calculating the moisture diffusion values using the empirical relation established by Lytton (2003). The non-linear flow through unsaturated soils has been simplified to a linear problem for simplicity in this study. Owing to this simplification, certain refinements have therefore been applied in the determination of diffusion coefficient. Thermocouple psychrometer was used to measure the soil suction along the length of the sample and at different times in the laboratory. Initial suction measurements were done using the filter paper test. Curve fitting procedure established by (Aubeny and Lytton, 2003), has been used for the determination of the diffusion coefficient. Analytical validation of the moisture diffusion coefficient, required coefficient of permeability, ??k??, slope of suction water characteristic curve ??S?? and air entry value ??ho?? as the major input parameters. Mitchell (1979) assumed the value of ??ho?? to be 100 cm. In this research air entry value, ??ho?? has been re-evaluated and it comes out to be higher than the pre estimated value. The value of slope of suction water characteristic curve, ??S?? obtained from pressure plate tests, compares well to the empirical equation of Lytton (2003). The results of moisture diffusion coefficient obtained from the empirical equation come out in the same range as obtained from the refined Mitchell??s (1979) drying test. The refinements includes introduction of constant temperature environment. Owing to the least variation in temperature, more reliable and reproducible data was obtained. The range of moisture diffusion coefficient, ??-values obtained from empirical equation, comes out to be coherent with the laboratory data. Hence, it can be concluded that the research was successful.

The current design procedure for cantilever structures on spread footings in the Texas Department of Transportation (TxDOT) is based on horizontal pressure that is calculated by using Rankine's and Coulomb's theory. These are classical Geotechnical Engineering methods. Horizontal earth pressure due to moisture and volume change in high plasticity soil is not determined by these classical methods. However, horizontal pressure on most of the cantilever retaining structures in Texas is determined by following the classical methods. In recent years, a number of consultants have considered the horizontal pressure due to swelling on cantilever retaining structures in Texas. However, the proposed horizontal pressure by consultants is 10-20 times higher than the classical horizontal pressure. This method of cantilever retaining structure design without knowing the real pressure and stress pattern increases the thickness of the wall, and raises the cost of construction. This study focuses on providing adequate patterns of lateral earth pressure distribution on cantilever retaining structures in expansive soil. These retaining wall structures are subject to swelling pressures which cause horizontal pressures that are larger than the classical especially near the ground surface. Beside the prediction of lateral earth pressure distribution, the relations between water content, volume change and suction change are determined. Based on the laboratory testing program conducted, Soil Water Characteristic Curves (SWCC) are determined for a site located at the intersection of I-35 and Walters Street in San Antonio, Texas. Additionally, relations between volume change with confining pressure curve, water content change with the change of confining pressure curve, water content change with change of matric suction and volume change with change of matric suction curves are generated based on laboratory tests. There are a number of available mass volume measurement methods that use mostly mercury or paraffin to obtain volume measurements. Although these methods are reported in the literature, they are not used in practice due to application limitations like safety, time, and cost. In order to overcome these limitations, a new method was developed to measure the volume of soil mass by using sand displacement. This new method is an inexpensive, safe, and simple way to measure mass volume by Ottawa sand.

Previous studies of agricultural conditions in the Mekong Delta (MD) have identified soil compaction as an obstacle to sustainable production. A conceptual model for soil formation was presented to demonstrate the link between soil hydrology and plant response. Detailed studies of soil moisture dynamics in agricultural fields were conducted using a dynamic process-orientated model. Pressure head and water flow were simulated for three selected sites during a year for which empirical data were available. Daily meteorological data were used as dynamic input and measured pressure head was used to estimate parameter values that satisfied various acceptance criteria. The Generalised Likelihood Uncertainty Estimation (GLUE) approach was applied for calibration procedures with 10,000 runs, each run using random values within the chosen range of parameter values. To evaluate model performance and uncertainty estimation, re-sampling was carried out using coefficient of determination (R2) and mean error (ME) as the criteria. Correlations between parameters and R2 (and ME) and among parameters were also considered to analyse the relationship of the selected parameter set in response to increases/decreases in the acceptable simulations. The method was successful for two of the three sites, with many accepted simulations. For these sites, the uncertainty was reduced and it was possible to quantify the importance of the different parameters.

As equações diferencias parciais tem origem na modelagem do problemas nas ciências e engenharia, tais como a equação do calor, equação da onda, equação de Poisson, entre outras. Para muitas destas equações não é tão simples obter uma técnica analítica para achar sua solução e nestes casos é necessário uso de soluções aproximadas obtidas pelo computador. Existem técnicas tradicionais para solução numérica de uma grande classe de equações diferenciais, mas quando esta equação está na forma implícita, muitas destas técnicas já não podem ser aplicadas. Frequentemente as equações diferenciais parciais de segunda ordem tem maior estudo que as equações de primeira ordem sendo uma das razões que os modelos envolvem derivadas de segunda ordem. No caso das equações diferenciais parciais de primeira ordem implícitas a não linearidade em alguns casos não permite determinar uma solução de forma simples. O trabalho desenvolvido faz uma revisão do método das características para estabelecer as condições necessárias e suficientes, que permitam encontrar uma solução, ao mesmo tempo evidencia a complexidade de determinar uma solução clássica. Dentro das aplicações existentes relacionadas com as Equações Diferenciais Parciais Implícitas de Primeira Ordem, podemos mencionar a Equação cinemática e a Equação de Hamilton-Jacobi que podem-se associar com o movimento de partículas. Para a solução de uma Equação Diferencial Implícita de Primeira Ordem o método das características tem uma estrutura de solução que permite resolver a equação de forma analítica e numérica, desde que se verifique o Teorema de Cauchy. O objetivo deste trabalho de mestrado é obter um método numérico para a solução de equações diferenciais parciais de primeira ordem implícitas. Nós propomos um método numérico do tipo previsor-corretor que resolve uma EDP de primeira ordem implícita, utilizando o sistema característico em conjunto com as condições de banda, para reduzir o erro global nas iterações. / Partial differential equations arise in the modeling of problems in science and engineering, such as the heat equation, wave equation, Poisson equation, among others. For many of these equations it is not so simple to obtain an analytical technique to find a solution in these cases and it is necessary to use a computer to obtain approximate solutions. There are traditional techniques for numerical solution of a large class of differential equations, but when this equation is in implicit form, many of these techniques can no longer be applied. Often partial differential equations of second order are more studied than first order equations the reason being that one of the models involve secondorder derivatives. In the case of implicit partial differential equations of first order the non-linearity in some cases does not allow for a solution in simple from to be determined. The work reviews the method of characteristics to establish the necessary and sufficient conditions that will find a solution at the same time demonstrates the complexity of determining classical solution. Within existing applications related to Partial Differential Equations of First Order Implicit, we can mention the textit kinematic equation and textit equation Hamilton-Jacobi that can be associated with the movement of particles. For the solution of a differential equation First Implicit Order the method of characteristics has a solution framework that enables solve the equation analytically and numerically, provided there is the Cauchy theorem. The objective of this master thesis is to obtain a numerical method for the solution of partial differential equations first order implicit. We propose a numerical method of predictor-corrector type that resolves a EDP first implicate order, using the characteristic system in conjunction with the band conditions, to reduce the overall error in iterations.

A mecânica dos solos não saturados tem se tornado um importante tema de pesquisas dedicadas a entender o comportamento dos solos não saturados e otimizar sua utilização em várias obras civis. A curva de retenção de água, definida como a relação entre a sucção e a quantidade de água presente no solo, é considerada um elemento chave na interpretação do comportamento e propriedades dos solos não saturados tais como a condutividade hidráulica e a resistência ao cisalhamento. Este trabalho apresenta a estrutura de um banco de dados projetado para armazenar informações de solos brasileiros com enfoque nas características de retenção de água. O banco de dados inclui a curva de retenção e os parâmetros de ajuste das equações de van Genuchten (1980) e Fredlund & Xing (1994), assim como informações das características dos solos como índices físicos, classificações dos solos, análises granulométricas, índices de consistência e localização e estado da amostra. Além da estimativa da função condutividade hidráulica, o banco de dados oferece duas ferramentas que permitem a pesquisa rápida ou detalhada das informações e os dados armazenados podem ser mostrados na tela ou em relatórios impressos / Unsaturated soil mechanics has become an important subject of research devoted to understand the behavior of unsaturated soils and optimize their use in several civil works. The soil-water characteristic curve, defined as the relationship between the suction and the amount of water present in the soil, is considered as the key in the interpretation of the behavior and properties of unsaturated soils, such as the hydraulic conductivity and the shear strength. This paper presents the structure of a database designed to store information of brazilian soils with focus in the characteristics of water retention. The database includes the retention curves and the parameters of adjusted van Genuchten and Fredlund & Xing equations and also information of soil characteristics such as physical indexes, soil classifications, particle-size analysis, consistency indexes and location and kind of used samples. Beyond the estimate of hydraulic conductivity, the database presents two search tools that allow for quick and detailed recovering of information and stored data can be displayed on screen or in printed reports

The primary objective of this thesis is to develop a model for quantification of weather-related railway embankments hazards. The model for quantification of embankment hazards constitutes an essential component of a decision support system that is required for the management of railway embankment hazards. A model for the deterministic and probabilistic assessment of weather-related geo-hazards (W-GHA model) is proposed based on concepts of unsaturated soil mechanics and hydrology. The model combines a system of two-dimensional partial differential equations governing the thermo-hydro-mechanical behaviour of saturated/unsaturated soils and soil-atmosphere coupling equations. A Dynamic Programming algorithm for slope stability analysis (Safe-DP) was developed and incorporated into the W-GHA model. Finally, an efficient probabilistic and sensitivity analysis framework based on an alternative point estimate method was proposed. According to the W-GHA model framework, railway embankment hazards are assessed based on factors of safety and probabilities of failures computed using soil property variability and case scenarios. <p> A comprehensive study of unsaturated property variability is presented. A methodology for the characterization and assessment of unsaturated soil property variability is proposed. Appropriate fitting equations and parameter were selected. Probability density functions adequate for representing the unsaturated soil parameters studied were determined. Typical central tendency measures, variability measures, and correlation coefficients were established for the unsaturated soil parameters. The inherent variability of the unsaturated soil properties can be addressed using the probabilistic analysis framework proposed herein. <p> A large number of hypothetical railway embankments were analysed using the proposed model. The embankment analyses were undertaken in order to demonstrate the application of the proposed model and in order to determine the sensitivity of the factor of safety to the uncertainty in several input variables. The conclusions drawn from the sensitivity analysis study resulted in important simplifications of the W-GHA model. It was shown how unsaturated soil mechanics can be applied for the assessment of near ground surface stability hazards. The approach proposed in this thesis forms a protocol for application of unsaturated soil mechanics into geotechnical engineering practice. This protocol is based on predicted unsaturated soil properties and based on the use of case scenarios for addressing soil property uncertainty. Other classes of unsaturated soil problems will benefit from the protocol presented in this thesis.

With the development of DNA microarray technology, scientists can now measure the expression levels of thousands of genes (features or genomic biomarkers) simultaneously in one single experiment. Robust and accurate gene selection methods are required to identify differentially expressed genes across different samples for disease diagnosis or prognosis. The problem of identifying significantly differentially expressed genes can be stated as follows: Given gene expression measurements from an experiment of two (or more)conditions, find a subset of all genes having significantly different expression levels across these two (or more) conditions. Analysis of genomic data is challenging due to high dimensionality of data and low sample size. Currently several mathematical and statistical methods exist to identify significantly differentially expressed genes. The methods typically focus on gene by gene analysis within a parametric hypothesis testing framework. In this study, we propose three flexible procedures for analyzing microarray data. In the first method we propose a parametric method which is based on a flexible distribution, Generalized Logistic Distribution of Type II (GLDII), and an approximate likelihood ratio test (ALRT) is developed. Though the method considers gene-by-gene analysis, the ALRT method with distributional assumption GLDII appears to provide a favourable fit to microarray data. In the second method we propose a test statistic for testing whether area under receiver operating characteristic curve (AUC) for each gene is greater than 0.5 allowing different variances for each gene. This proposed method is computationally less intensive and can identify genes that are reasonably stable with satisfactory prediction performance. The third method is based on comparing two AUCs for a pair of genes that is designed for selecting highly correlated genes in the microarray datasets. We propose a nonparametric procedure for selecting genes with expression levels correlated with that of a ``seed" gene in microarray experiments. The test proposed by DeLong et al. (1988) is the conventional nonparametric procedure for comparing correlated AUCs. It uses a consistent variance estimator and relies on asymptotic normality of the AUC estimator. Our proposed method includes DeLong's variance estimation technique in comparing pair of genes and can identify genes with biologically sound implications. In this thesis, we focus on the primary step in the gene selection process, namely, the ranking of genes with respect to a statistical measure of differential expression. We assess the proposed approaches by extensive simulation studies and demonstrate the methods on real datasets. The simulation study indicates that the parametric method performs favorably well at any settings of variance, sample size and treatment effects. Importantly, the method is found less sensitive to contaminated by noise. The proposed nonparametric methods do not involve complicated formulas and do not require advanced programming skills. Again both methods can identify a large fraction of truly differentially expressed (DE) genes, especially if the data consists of large sample sizes or the presence of outliers. We conclude that the proposed methods offer good choices of analytical tools to identify DE genes for further biological and clinical analysis.

With the development of DNA microarray technology, scientists can now measure the expression levels of thousands of genes (features or genomic biomarkers) simultaneously in one single experiment. Robust and accurate gene selection methods are required to identify differentially expressed genes across different samples for disease diagnosis or prognosis. The problem of identifying significantly differentially expressed genes can be stated as follows: Given gene expression measurements from an experiment of two (or more)conditions, find a subset of all genes having significantly different expression levels across these two (or more) conditions. Analysis of genomic data is challenging due to high dimensionality of data and low sample size. Currently several mathematical and statistical methods exist to identify significantly differentially expressed genes. The methods typically focus on gene by gene analysis within a parametric hypothesis testing framework. In this study, we propose three flexible procedures for analyzing microarray data. In the first method we propose a parametric method which is based on a flexible distribution, Generalized Logistic Distribution of Type II (GLDII), and an approximate likelihood ratio test (ALRT) is developed. Though the method considers gene-by-gene analysis, the ALRT method with distributional assumption GLDII appears to provide a favourable fit to microarray data. In the second method we propose a test statistic for testing whether area under receiver operating characteristic curve (AUC) for each gene is greater than 0.5 allowing different variances for each gene. This proposed method is computationally less intensive and can identify genes that are reasonably stable with satisfactory prediction performance. The third method is based on comparing two AUCs for a pair of genes that is designed for selecting highly correlated genes in the microarray datasets. We propose a nonparametric procedure for selecting genes with expression levels correlated with that of a ``seed" gene in microarray experiments. The test proposed by DeLong et al. (1988) is the conventional nonparametric procedure for comparing correlated AUCs. It uses a consistent variance estimator and relies on asymptotic normality of the AUC estimator. Our proposed method includes DeLong's variance estimation technique in comparing pair of genes and can identify genes with biologically sound implications. In this thesis, we focus on the primary step in the gene selection process, namely, the ranking of genes with respect to a statistical measure of differential expression. We assess the proposed approaches by extensive simulation studies and demonstrate the methods on real datasets. The simulation study indicates that the parametric method performs favorably well at any settings of variance, sample size and treatment effects. Importantly, the method is found less sensitive to contaminated by noise. The proposed nonparametric methods do not involve complicated formulas and do not require advanced programming skills. Again both methods can identify a large fraction of truly differentially expressed (DE) genes, especially if the data consists of large sample sizes or the presence of outliers. We conclude that the proposed methods offer good choices of analytical tools to identify DE genes for further biological and clinical analysis.