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.

Unravelling the evolution of autumn colours: an interdisciplinary approach.

Leaf colour change is commonly observed in temperate deciduous forests in autumn. This is not simply a side effect of leaf senescence, and, in the past decade, several hypotheses have emerged to explain the evolution of autumn colours. Yet a lack of crosstalk between plant physiologists and evolutionary ecologists has resulted in slow progress, and so the adaptive value of this colour change remains a mystery. Here we provide an interdisciplinary summary of the current body of knowledge on autumn colours, and discuss unresolved issues and future avenues of research that might help reveal the evolutionary meaning of this spectacle of nature.

A comparison of breathing patterns of normal full term infants in supine versus right side-lying during quiet and active behavioral sleep states

This study investigated the effect of sleep position on breathing patterns of normal full term infants during quiet and active behavioral sleep states. Tidal volume, percent contribution of rib cage to tidal volume, and respiration rate were measured via respiratory inductive plethysmography (RIP) and pneumotachograph (PNT) in ten infants sleeping in supine versus right side-lying. Data was collected immediately following two consecutive feedings. Paired t tests and ANOVA comparisons showed no significant differences between the two postures (p $<$.05) in mean tidal volume (supine, M = 19.16, right side, M = 22.45), percent contribution of rib cage to tidal volume (supine, M = 30.55, right side M = 33.20), or respiration rate (supine, M = 49.13, right side, M = 49.37) during quiet sleep. Comparisons also showed no significant differences between the two postures (p $<$.05) in mean tidal volume (supine, M = 18.89, right side, M = 20.12), percent contribution of rib cage to tidal volume (supine, M = 6.43, right side, M = 6.97) or respiration rate (supine, M = 62.18, right side, M = 61.04) during active sleep. Therefore, no differences were found in the three respiratory variables measured between the supine and right side-lying positions. These findings suggest that infants may be positioned in either sleep position without detriment to respiratory function. This information may benefit occupational therapists and other health professionals involved in the education of parents on infant positioning and their respective advantages. ^