Statistical analysis and optimal classification of blood cell populations using Gaussian distributions

This dissertation develops a new figure of merit to measure the similarity (or dissimilarity) of Gaussian distributions through a novel concept that relates the Fisher distance to the percentage of data overlap. The derivations are expanded to provide a generalized mathematical platform for determining an optimal separating boundary of Gaussian distributions in multiple dimensions. Real-world data used for implementation and in carrying out feasibility studies were provided by Beckman-Coulter. It is noted that although the data used is flow cytometric in nature, the mathematics are general in their derivation to include other types of data as long as their statistical behavior approximate Gaussian distributions. ^ Because this new figure of merit is heavily based on the statistical nature of the data, a new filtering technique is introduced to accommodate for the accumulation process involved with histogram data. When data is accumulated into a frequency histogram, the data is inherently smoothed in a linear fashion, since an averaging effect is taking place as the histogram is generated. This new filtering scheme addresses data that is accumulated in the uneven resolution of the channels of the frequency histogram. ^ The qualitative interpretation of flow cytometric data is currently a time consuming and imprecise method for evaluating histogram data. This method offers a broader spectrum of capabilities in the analysis of histograms, since the figure of merit derived in this dissertation integrates within its mathematics both a measure of similarity and the percentage of overlap between the distributions under analysis. ^

Calculations on the end-group conformational barrier in carotenoids and a study of the bioavailability of xanthophyll esters in humans

The present study measures the increase in serum carotenoid concentration in 30 healthy individuals after supplementation with a low dose xanthophyll ester (3 and 6 mg of lutein equivalent/per day) when compared to a placebo. Serum levels of carotenoids were measured using HPLC and showed an increase in the concentration of lutein, zeaxanthin and four lutein metabolites proportional to dose. In order to further assess the importance of the end-group structure in carotenoids we have investigated the influence of the end-group type and functionality on the conformational energy barrier. We used the density functional method implemented on GAUSSIAN 98 to calculate the conformational energy curves for rotation of the P-ring or the E-ring relative to short polyene chains around the C6-C7 single bond. A large barrier is observed for the interconversion of conformers in the E-rings (8 kcal/mol) when compared to beta rings (2.3-3 kcal/mol).