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 effect of mobile technology as an active student response system on the acquisition of U.S. history content of secondary students with specific learning disabilities

Students with specific learning disabilities (SLD) typically learn less history content than their peers without disabilities and show fewer learning gains. Even when they are provided with the same instructional strategies, many students with SLD struggle to grasp complex historical concepts and content area vocabulary. Many strategies involving technology have been used in the past to enhance learning for students with SLD in history classrooms. However, very few studies have explored the effectiveness of emerging mobile technology in K-12 history classrooms. ^ This study investigated the effects of mobile devices (iPads) as an active student response (ASR) system on the acquisition of U.S. history content of middle school students with SLD. An alternating treatments single subject design was used to compare the effects of two interventions. There were two conditions and a series of pretest probesin this study. The conditions were: (a) direct instruction and studying from handwritten notes using the interactive notebook strategy and (b) direct instruction and studying using the Quizlet App on the iPad. There were three dependent variables in this study: (a) percent correct on tests, (b) rate of correct responses per minute, and (c) rate of errors per minute. ^ A comparative analysis suggested that both interventions (studying from interactive notes and studying using Quizlet on the iPad) had varying degrees of effectiveness in increasing the learning gains of students with SLD. In most cases, both interventions were equally effective. During both interventions, all of the participants increased their percentage correct and increased their rate of correct responses. Most of the participants decreased their rate of errors. ^ The results of this study suggest that teachers of students with SLD should consider a post lesson review in the form of mobile devices as an ASR system or studying from handwritten notes paired with existing evidence-based practices to facilitate students’ knowledge in U.S. history. Future research should focus on the use of other interactive applications on various mobile operating platforms, on other social studies subjects, and should explore various testing formats such as oral question-answer and multiple choice. ^