A mathematical resolution to log transformations and the binning effect in applied processing of data in flow cytometry

This dissertation develops a new mathematical approach that overcomes the effect of a data processing phenomenon known as “histogram binning” inherent to flow cytometry data. A real-time procedure is introduced to prove the effectiveness and fast implementation of such an approach on real-world data. The histogram binning effect is a dilemma posed by two seemingly antagonistic developments: (1) flow cytometry data in its histogram form is extended in its dynamic range to improve its analysis and interpretation, and (2) the inevitable dynamic range extension introduces an unwelcome side effect, the binning effect, which skews the statistics of the data, undermining as a consequence the accuracy of the analysis and the eventual interpretation of the data. ^ Researchers in the field contended with such a dilemma for many years, resorting either to hardware approaches that are rather costly with inherent calibration and noise effects; or have developed software techniques based on filtering the binning effect but without successfully preserving the statistical content of the original data. ^ The mathematical approach introduced in this dissertation is so appealing that a patent application has been filed. The contribution of this dissertation is an incremental scientific innovation based on a mathematical framework that will allow researchers in the field of flow cytometry to improve the interpretation of data knowing that its statistical meaning has been faithfully preserved for its optimized analysis. Furthermore, with the same mathematical foundation, proof of the origin of such an inherent artifact is provided. ^ These results are unique in that new mathematical derivations are established to define and solve the critical problem of the binning effect faced at the experimental assessment level, providing a data platform that preserves its statistical content. ^ In addition, a novel method for accumulating the log-transformed data was developed. This new method uses the properties of the transformation of statistical distributions to accumulate the output histogram in a non-integer and multi-channel fashion. Although the mathematics of this new mapping technique seem intricate, the concise nature of the derivations allow for an implementation procedure that lends itself to a real-time implementation using lookup tables, a task that is also introduced in this dissertation. ^

A mathematical resolution to log transformations and the binning effect in applied processing of data in flow cytometry

This dissertation develops a new mathematical approach that overcomes the effect of a data processing phenomenon known as "histogram binning" inherent to flow cytometry data. A real-time procedure is introduced to prove the effectiveness and fast implementation of such an approach on real-world data. The histogram binning effect is a dilemma posed by two seemingly antagonistic developments: (1) flow cytometry data in its histogram form is extended in its dynamic range to improve its analysis and interpretation, and (2) the inevitable dynamic range extension introduces an unwelcome side effect, the binning effect, which skews the statistics of the data, undermining as a consequence the accuracy of the analysis and the eventual interpretation of the data. Researchers in the field contended with such a dilemma for many years, resorting either to hardware approaches that are rather costly with inherent calibration and noise effects; or have developed software techniques based on filtering the binning effect but without successfully preserving the statistical content of the original data. The mathematical approach introduced in this dissertation is so appealing that a patent application has been filed. The contribution of this dissertation is an incremental scientific innovation based on a mathematical framework that will allow researchers in the field of flow cytometry to improve the interpretation of data knowing that its statistical meaning has been faithfully preserved for its optimized analysis. Furthermore, with the same mathematical foundation, proof of the origin of such an inherent artifact is provided. These results are unique in that new mathematical derivations are established to define and solve the critical problem of the binning effect faced at the experimental assessment level, providing a data platform that preserves its statistical content. In addition, a novel method for accumulating the log-transformed data was developed. This new method uses the properties of the transformation of statistical distributions to accumulate the output histogram in a non-integer and multi-channel fashion. Although the mathematics of this new mapping technique seem intricate, the concise nature of the derivations allow for an implementation procedure that lends itself to a real-time implementation using lookup tables, a task that is also introduced in this dissertation.

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. ^

Forecasting Responses of Seagrass Distributions to Changing Water Quality Using Monitoring Data

Extensive data sets on water quality and seagrass distributions in Florida Bay have been assembled under complementary, but independent, monitoring programs. This paper presents the landscape-scale results from these monitoring programs and outlines a method for exploring the relationships between two such data sets. Seagrass species occurrence and abundance data were used to define eight benthic habitat classes from 677 sampling locations in Florida Bay. Water quality data from 28 monitoring stations spread across the Bay were used to construct a discriminant function model that assigned a probability of a given benthic habitat class occurring for a given combination of water quality variables. Mean salinity, salinity variability, the amount of light reaching the benthos, sediment depth, and mean nutrient concentrations were important predictor variables in the discriminant function model. Using a cross-validated classification scheme, this discriminant function identified the most likely benthic habitat type as the actual habitat type in most cases. The model predicted that the distribution of benthic habitat types in Florida Bay would likely change if water quality and water delivery were changed by human engineering of freshwater discharge from the Everglades. Specifically, an increase in the seasonal delivery of freshwater to Florida Bay should cause an expansion of seagrass beds dominated by Ruppia maritima and Halodule wrightii at the expense of the Thalassia testudinum-dominated community that now occurs in northeast Florida Bay. These statistical techniques should prove useful for predicting landscape-scale changes in community composition in diverse systems where communities are in quasi-equilibrium with environmental drivers.

Experimental deuteron momentum distributions with reduced final state interactions

This dissertation presents a study of the D( e, e′p)n reaction carried out at the Thomas Jefferson National Accelerator Facility (Jefferson Lab) for a set of fixed values of four-momentum transfer Q 2 = 2.1 and 0.8 (GeV/c)2 and for missing momenta pm ranging from pm = 0.03 to pm = 0.65 GeV/c. The analysis resulted in the determination of absolute D(e,e′ p)n cross sections as a function of the recoiling neutron momentum and it's scattering angle with respect to the momentum transfer [vector] q. The angular distribution was compared to various modern theoretical predictions that also included final state interactions. The data confirmed the theoretical prediction of a strong anisotropy of final state interaction contributions at Q2 of 2.1 (GeV/c)2 while at the lower Q2 value, the anisotropy was much less pronounced. At Q2 of 0.8 (GeV/c)2, theories show a large disagreement with the experimental results. The experimental momentum distribution of the bound proton inside the deuteron has been determined for the first time at a set of fixed neutron recoil angles. The momentum distribution is directly related to the ground state wave function of the deuteron in momentum space. The high momentum part of this wave function plays a crucial role in understanding the short-range part of the nucleon-nucleon force. At Q2 = 2.1 (GeV/c)2, the momentum distribution determined at small neutron recoil angles is much less affected by FSI compared to a recoil angle of 75°. In contrast, at Q2 = 0.8 (GeV/c)2 there seems to be no region with reduced FSI for larger missing momenta. Besides the statistical errors, systematic errors of about 5–6 % were included in the final results in order to account for normalization uncertainties and uncertainties in the determi- nation of kinematic veriables. The measurements were carried out using an electron beam energy of 2.8 and 4.7 GeV with beam currents between 10 to 100 &mgr; A. The scattered electrons and the ejected protons originated from a 15cm long liquid deuterium target, and were detected in conicidence with the two high resolution spectrometers of Hall A at Jefferson Lab.^