Combining geochemical data with physical data produces a powerful method for understanding sources and fluxes of waters to river systems. This study highlights this for river systems in regions of complex hydrogeology, shown here through the identification and quantification of base-flow sources to the Verde River and its tributaries within the middle Verde River watershed. Specifically, geochemical tracers (major solutes, stable and radioactive isotopes) characterize the principal aquifers (C, Redwall-Muav, and Verde Formation) and provide a conceptual understanding of the hydrologic connection between them. For the surface-water system, PCA is utilized to identify potential base-flow sources to the Verde River on a several-kilometer scale. Solute mixing diagrams then provide relative inputs of these sources, and when combined with stream discharge, allow for quantification of water sources. The results of this study provide an improved conceptual model that reveals the complexity of groundwater-surface water exchanges in this river basin.

Land and vegetation changes are part of the continuous and dynamic cycle of earth system variation. This research examines vegetation changes in the 21-county eco-region along coastal Georgia. The Advanced Very High Resolution Radiometer (AVHRR) with Normalized Difference Vegetation Index (NDVI) data is used in tandem with a Principal Component Analysis (PCA) and climatic variables to determine where, and to what extent vegetation and land cover change is occurring. This research is designed around a 16 year time-series from 1990-2005. Findings were that mean NDVI values were either steady or slightly improved, and that PC1 (Healthiness) and PC2 (Time-Change) explained nearly 99 percent of the total mean variance. Healthiness declines are primarily the result of expanding urban districts and decreased soil moisture while increases are the results of restoration, and increased soil moisture. This research aims to use this analysis for the assessment of land changes as the conduit for future environmental research.

<p><font face="F59" size="3"><font face="F59" size="3"> <p align="left">This study examines the relationship between stock returns and market segmentation. Monthly returns of stocks listed on the JSE from 1997-2007 are analysed using mostly the analytic factor and cluster analysis techniques. Evidence supporting the use of multi-index models in explaining the return generating process on the JSE is found. The results provide additional support for Van Rensburg (1997)'s hypothesis on market segmentation on the JSE.</p> </font></font></p>

Molecular dynamics simulations were performed on the influenza A non-structural protein 1 (NS1) RNA binding domain (RBD), a homodimer. Fourteen simulations were performed at 298K, nine ionized with 0.1M KCl and five with no ions. Several analysis techniques were employed to study RBD residue flexibility. The focus of the study was the RNA binding cavity formed by side chains of helix 2 (chain A) and helix 2’ (chain B) and cavity intermonomeric salt bridges. Opening of the salt bridges D29–R46’ and D29’–R46 was observed in several of the trajectories. The RNA binding cavity has large flexibility, where the dimension and shape change during the dynamics. One pair of residues surrounding the cavity and necessary for RNA binding, residues R38 and R38’, have motions during the simulations which cover the top of the cavity. There is correlation between the salt bridge breaking, flexibility of R38 and R38’, and the cavity size and shape changes. Possible RBD small molecule drug targets are these two salt bridges and the pair R38 and R38’. Disrupting the events that occur around these areas could possibly inactivate RNA binding function of the domain. These results could have implications in searching for potential molecules that effectively treat influenza A.

Fluorescence techniques are being considered for the detection and identification of bacterial spores. This thesis sets out to empirically characterize the detailed autofluorescence spectroscopic properties of spores and their target molecules. The multiwavelength fluorescence studies from a unique endogenous biomarker, dipicolinic acid (DPA) and its calcium salt (CaDPA) in bacterial spores are found to be useful for fluorescence characterization of spores. A systematic determination of the fluorescence profile of the major chemical components of Bacillus spores and the effect of UV irradiation on them has been performed in dry samples, wet paste and in aqueous solution. The thesis applies reliable tools for accurately describing complex nature of spectral profile from bacterial spores, and for interpreting and identifying their spectral properties. We show that multiwavelength fluorescence technique combined with Principal Component Analysis (PCA) clearly indicates identifiable grouping among dry and wet Bacillus spore species. Differences are also observed between dried, wet and redried spores, indicating the stark effect of hydration on fluorescence fingerprints. The study revealed that changes in fluorescence of spores due to hydration/drying were reversible and supports a recent model of a dynamic and dormant spore structure. The spectra were analysed with PCA, revealing several spectroscopically characteristic features enabling spore species separation. The identified spectral features could be attributed to specific spore chemical components by comparing the spore sample signals with spectra obtained from the target molecules. PCA indicated underlying spectral patterns strongly related to species and the derived components were correlated with the chemical composition of the spore samples. More importantly, we examined and compared the fluorescence of normal spores with a mutant of the same strain whose spores lack DPA. We discovered that the dramatic fluorescence enhancement of Bacillus spores can be caused by UV irradiation in the spectral region of this unique biomarker without any pre treatment. Differences between spectra of spores, spore strains and other biological samples are very marked and are due to the dominance of the dipicolinate features in the spore spectra. This could lead to a cheap, more sensitive, faster and reagentless bacterial spore detector.

The goal of this research was to improve the speed and accuracy of reporting by clinical radiologists. By applying a technique known as eigenimage processing to chest radiographs, abnormal findings were enhanced and a classification scheme developed. Results confirm that the method is feasible for clinical use. Eigenimage processing is a popular face recognition routine that has only recently been applied to medical images, but it has not previously been applied to full size radiographs. Chest radiographs were chosen for this research because they are clinically important and are challenging to process due to their large data content. It is hoped that the success with these images will enable future work on other medical images such as those from CT and MRI. Eigenimage processing is based on a multivariate statistical method which identifies patterns of variance within a training set of images. Specifically it involves the application of a statistical technique called principal components analysis to a training set. For this research, the training set was a collection of 77 normal radiographs. This processing produced a set of basis images, known as eigenimages, that best describe the variance within the training set of normal images. For chest radiographs the basis images may also be referred to as 'eigenchests'. Images to be tested were described in terms of eigenimages. This identified patterns of variance likely to be normal. A new image, referred to as the remainder image, was derived by removing patterns of normal variance, thus making abnormal patterns of variance more conspicuous. The remainder image could either be presented to clinicians or used as part of a computer aided diagnosis system. For the image sets used, the discriminatory power of a classification scheme approached 90%. While the processing of the training set required significant computation time, each test image to be classified or enhanced required only a few seconds to process. Thus the system could be integrated into a clinical radiology department.

The thesis consists of four papers that address likelihood-based unit root tests for panel data with cross-sectional dependence arising from common factors. In the first three papers, we derive Lagrange multiplier (LM)-type tests for common and idiosyncratic unit roots in the exact factor models based on the likelihood function of the differenced data. Also derived are the asymptotic distributions of these test statistics. The finite sample properties of these tests are compared by simulation with other commonly used unit root tests. The results show that our LM-type tests have better size and local power properties. In the fourth paper, we estimate the spaces spanned by the common factors and the spaces spanned by the idiosyncratic components of the static factor model by using the quasi-maximum likelihood (ML) method and compare it with the widely used method of principal components (PC). Next, by simulation, we compare the size and power properties of established tests for idiosyncratic unit roots, using both the ML and PC methods. Simulation results show that the idiosyncratic unit root tests based on the likelihood-based residuals generally have better size and higher size-adjusted power, especially when the cross-sectional dimension is small and the time series dimension is large.

Principal Components Analysis is a standard tool in data analysis, widely used in data-rich fields such as computer vision, data mining, bioinformatics, and econometrics. For a set of vectors in n dimensions and a natural number k less than n, the method returns a subspace of dimension k whose average squared distance to that set is as small as possible. Besides saving computation by reducing the dimension, projecting to this subspace can often reveal structure that was hidden in high dimension. This thesis considers several novel extensions of PCA, which provably reveals hidden structure where standard PCA fails to do so. First, we consider Robust PCA, which prevents a few points, possibly corrupted by an adversary, from having a large effect on the analysis. When applied to learning noisy logconcave mixture models, the algorithm requires only slightly more separation between component means than is required for the noiseless case. Second, we consider Isotropic PCA, which can go beyond the first two moments in identifying ``interesting' directions in data. The method leads to the first affine-invariant algorithm that can provably learn mixtures of Gaussians in high dimensions, improving significantly on known results. Thirdly, we define the ``Subgraph Parity Tensor' of order r of a graph and reduce the problem of finding planted cliques in random graphs to the problem of finding the top principal component of this tensor.

In this dissertation, application of multi-way analysis is extended into new areas of environmental chemistry, microbiology, electrochemistry and organometallic chemistry. Additionally new practical aspects of some of the multi-way analysis methods are discussed. Parallel Factor Analysis Two (PARAFAC2) is used to classify a wide range of weathered petroleum oils using GC-MS data. Various chemical and data analysis issues exist in the current methods of oil spill analysis are discussed and the proposed method is demonstrated to have potential to be employed in identification of source of oil spills. Two important practical aspects of PARAFAC2 are exploited to deal with chromatographic shifts and non-diagnostic peaks.GEneralized Multiplicative ANalysis Of VAriance (GEMANOVA) is applied to assess the bactericidal activity of new natural antibacterial extracts on three species of bacteria in different structure and oxidation forms and different concentrations. In this work while the applicability of traditional ANOVA is restricted due to the high interaction amongst the factors, GEMANOVA is shown to return robust and easily interpretable models which conform to the actual structure of the data. Peptide-modified electrochemical sensors are used to determine three metal cations of Cu2+, Cd2+ and Pb2+ simultaneously. Two sets of experiments are performed using a four-electrode system returning a three-way array of size (sample ?? current ?? electrode) and a single electrode resulting in a two-way data set of size (sample ?? current). The data of former is modeled by N-PLS and that latter using PLS. Despite the presence of highly overlapped voltammograms and several sources of non-linearity N-PLS returns reasonable models while PLS fails. An intramolecular hydroamination reaction is catalyzed by several organometallic catalysts to identify the most effective catalysts. The reaction of starting material in the presence of 72 different catalysts is monitored by UV-Vis at two time points, before and after heating the mixtures in an oven. PARAFAC is applied to the three-way data set of (sample ?? wavelength ?? time) to resolve the overlapped UV-Vis peaks and to identify the effective catalysts using the estimated relative concentration of product (loadings plot of the sample mode).

This thesis presents the results of research into the use of factor models for stationary economic time series. Two basic scenarios are considered. The first is a situation where a large number of observations are available on a relatively small number variables, and a dynamic factor model is specified. It is shown that a dynamic factor model may be derived as a representation of a VARMA model of reduced spectral rank observed subject to measurement error. In some cases the resulting factor model corresponds to a minimal state-space representation of the VARMA plus noise model. Identification is discussed and proved for a fairly general class of dynamic factor model, and a frequency domain estimation procedure is proposed which has the advantage of generalising easily to models with rich dynamic structures. The second scenario is one where both the number of variables and the number of observations jointly diverge to infinity. The principal components estimator is considered in this case, and consistency is proved under assumptions which allow for much more error cross-correlation than the previously published theorems. Ancillary results include finite sample/variables bounds linking population principal components to population factors, and consistency results for principal components in a dual limit framework under a `gap' condition on the eigenvalues. A new factor model, named the Grouped Variable Approximate Factor Model, is introduced. This factor model allows for arbitrarily strong correlation between some of the errors, provided that the variables corresponding to the strongly correlated errors may be arranged into groups. An approximate instrumental variables estimator is proposed for the model and consistency is proved.