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. ^

The relationship between faculty perceptions and implementation of elements of transactional distance theory and online web-based course completion rates

The purpose of this study was to explore the relationship between faculty perceptions, selected demographics, implementation of elements of transactional distance theory and online web-based course completion rates. This theory posits that the high transactional distance of online courses makes it difficult for students to complete these courses successfully; too often this is associated with low completion rates. Faculty members play an indispensable role in course design, whether online or face-to-face. They also influence course delivery format from design through implementation and ultimately to how students will experience the course. This study used transactional distance theory as the conceptual framework to examine the relationship between teaching and learning strategies used by faculty members to help students complete online courses. Faculty members' sex, number of years teaching online at the college, and their online course completion rates were considered. A researcher-developed survey was used to collect data from 348 faculty members who teach online at two prominent colleges in the southeastern part of United States. An exploratory factor analysis resulted in six factors related to transactional distance theory. The factors accounted for slightly over 65% of the variance of transactional distance scores as measured by the survey instrument. Results provided support for Moore's (1993) theory of transactional distance. Female faculty members scored higher in all the factors of transactional distance theory when compared to men. Faculty number of years teaching online at the college level correlated significantly with all the elements of transactional distance theory. Regression analysis was used to determine that two of the factors, instructor interface and instructor-learner interaction, accounted for 12% of the variance in student online course completion rates. In conclusion, of the six factors found, the two with the highest percentage scores were instructor interface and instructor-learner interaction. This finding, while in alignment with the literature concerning the dialogue element of transactional distance theory, brings a special interest to the importance of instructor interface as a factor. Surprisingly, based on the reviewed literature on transactional distance theory, faculty perceptions concerning learner-learner interaction was not an important factor and there was no learner-content interaction factor.

Development, validation and uncertainty analysis of quantitative structure and activity relationship models for Log P of disinfection by -products

Hydrophobicity as measured by Log P is an important molecular property related to toxicity and carcinogenicity. With increasing public health concerns for the effects of Disinfection By-Products (DBPs), there are considerable benefits in developing Quantitative Structure and Activity Relationship (QSAR) models capable of accurately predicting Log P. In this research, Log P values of 173 DBP compounds in 6 functional classes were used to develop QSAR models, by applying 3 molecular descriptors, namely, Energy of the Lowest Unoccupied Molecular Orbital (ELUMO), Number of Chlorine (NCl) and Number of Carbon (NC) by Multiple Linear Regression (MLR) analysis. The QSAR models developed were validated based on the Organization for Economic Co-operation and Development (OECD) principles. The model Applicability Domain (AD) and mechanistic interpretation were explored. Considering the very complex nature of DBPs, the established QSAR models performed very well with respect to goodness-of-fit, robustness and predictability. The predicted values of Log P of DBPs by the QSAR models were found to be significant with a correlation coefficient R2 from 81% to 98%. The Leverage Approach by Williams Plot was applied to detect and remove outliers, consequently increasing R 2 by approximately 2% to 13% for different DBP classes. The developed QSAR models were statistically validated for their predictive power by the Leave-One-Out (LOO) and Leave-Many-Out (LMO) cross validation methods. Finally, Monte Carlo simulation was used to assess the variations and inherent uncertainties in the QSAR models of Log P and determine the most influential parameters in connection with Log P prediction. The developed QSAR models in this dissertation will have a broad applicability domain because the research data set covered six out of eight common DBP classes, including halogenated alkane, halogenated alkene, halogenated aromatic, halogenated aldehyde, halogenated ketone, and halogenated carboxylic acid, which have been brought to the attention of regulatory agencies in recent years. Furthermore, the QSAR models are suitable to be used for prediction of similar DBP compounds within the same applicability domain. The selection and integration of various methodologies developed in this research may also benefit future research in similar fields.

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.

The Relationship between Faculty Perceptions and Implementation of Elements of Transactional Distance Theory and Online Web-Based Course Completion Rates

The purpose of this study was to explore the relationship between faculty perceptions, selected demographics, implementation of elements of transactional distance theory and online web-based course completion rates. This theory posits that the high transactional distance of online courses makes it difficult for students to complete these courses successfully; too often this is associated with low completion rates. Faculty members play an indispensable role in course design, whether online or face-to-face. They also influence course delivery format from design through implementation and ultimately to how students will experience the course. This study used transactional distance theory as the conceptual framework to examine the relationship between teaching and learning strategies used by faculty members to help students complete online courses. Faculty members’ sex, number of years teaching online at the college, and their online course completion rates were considered. A researcher-developed survey was used to collect data from 348 faculty members who teach online at two prominent colleges in the southeastern part of United States. An exploratory factor analysis resulted in six factors related to transactional distance theory. The factors accounted for slightly over 65% of the variance of transactional distance scores as measured by the survey instrument. Results provided support for Moore’s (1993) theory of transactional distance. Female faculty members scored higher in all the factors of transactional distance theory when compared to men. Faculty number of years teaching online at the college level correlated significantly with all the elements of transactional distance theory. Regression analysis was used to determine that two of the factors, instructor interface and instructor-learner interaction, accounted for 12% of the variance in student online course completion rates. In conclusion, of the six factors found, the two with the highest percentage scores were instructor interface and instructor-learner interaction. This finding, while in alignment with the literature concerning the dialogue element of transactional distance theory, brings a special interest to the importance of instructor interface as a factor. Surprisingly, based on the reviewed literature on transactional distance theory, faculty perceptions concerning learner-learner interaction was not an important factor and there was no learner-content interaction factor.