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. ^

Computer program for the analysis of non-prismatic beams

One of the major problems in the analysis of beams with Moment of Inertia varying along their length, is to find the Fixed End Moments, Stiffness, and Carry-Over Factors. In order to determine Fixed End Moments, it is necessary to consider the non-prismatic member as integrated by a large number of small sections with constant Moment of Inertia, and to find the M/EI values for each individual section. This process takes a lot of time from Designers and Structural Engineers. The object of this thesis is to design a computer program to simplify this repetitive process, obtaining rapidly and effectively the Final Moments and Shears in continuous non-prismatic Beams. For this purpose the Column Analogy and the Moment Distribution Methods of Professor Hardy Cross have been utilized as the principles toward the methodical computer solutions. The program has been specifically designed to analyze continuous beams of a maximum of four spans of any length, integrated by symmetrical members with rectangular cross sections and with rectilinear variation of the Moment of Inertia. Any load or combination of uniform and concentrated loads must be considered. Finally sample problems will be solved with the new Computer Program and with traditional systems, to determine the accuracy and applicability of the Program.