Porphyromonas gingivalis, ethanol, and chronic diseases.

This dissertation is an investigation into the relationships among Porphyromonas gingivalis, ethanol, and a series of chronic diseases, focusing primarily on atherosclerosis. It uses evolutionary theory to understand clinical parameters related to chronic disease biology. The initial research question was, If people who drink a glass of wine each day have a lower risk for atherosclerosis, could one explanation involve antibacterial effects on pathogens associated with causing atherosclerosis, namely, Porphyromonas gingivalis? . This dissertation is divided into four chapters. Chapter One provides the foundational information pertinent to the dissertation. Chapter Two describes an in- vitro experiment aimed at understanding how ethanol influences planktonic Porphyromonas gingivalis. Chapter Three details an in-vitro experiment aimed at learning how ethanol influences Porphyromonas gingivalis when it exists in a biofilm. Chapter Four explores how Porphyromonas gingivalis and ethanol influence rheumatoid arthritis, osteoporosis, Alzheimer\u27s disease, chronic kidney disease, and type II diabetes. Chapters Two and Three provide primary information resulting from experiments that I designed and performed, while Chapter Four is more theoretical in nature. The experiments detailed in Chapters Two and Three were designed to understand how ethanol may differentially impact Porphyromonas gingivalis in the bloodstream relative to the oral cavity. The value of this dissertation lies in the synthesis of new ideas related to how the most widely used drug (ethanol) can influence the leading cause of death worldwide, heart disease. The use of ethanol as a systemic antimicrobial agent with regards to chronic infectious diseases has generally been overlooked. The hypothesis that ethanol consumption suppresses P. gingivalis growth in the blood, but not the oral cavity, is supported by experiments and a review of the literature presented in this dissertation

Tuning the Performance of a Computational Persistent Homology Package

In recent years, persistent homology has become an attractive method for data analysis. It captures topological features, such as connected components, holes, and voids from point cloud data and summarizes the way in which these features appear and disappear in a filtration sequence. In this project, we focus on improving the performanceof Eirene, a computational package for persistent homology. Eirene is a 5000-line open-source software library implemented in the dynamic programming language Julia. We use the Julia profiling tools to identify performance bottlenecks and develop novel methods to manage them, including the parallelization of some time-consuming functions on multicore/manycore hardware. Empirical results show that performance can be greatly improved

A geometric representation of continued fractions

Inspired by work of Ford, we describe a geometric representation of real and complex continued fractions by chains of horocycles and horospheres in hyperbolic space. We explore this representation using the isometric action of the group of Moebius transformations on hyperbolic space, and prove a classical theorem on continued fractions

Norms of Möbius maps

We derive inequalities between the matrix, chordal, hyperbolic, three-point and unitary norms of a Möbius map. These extend inequalities proved earlier by Gehring and Martin

The Seidel, Stern, Stolz and Van Vleck Theorems on continued fractions

We unify and extend three classical theorems in continued fraction theory, namely the Stern–Stolz Theorem, the Seidel–Stern Theorem and Van Vleck’s Theorem. Our arguments use the group of Möbius transformations both as a topological group and as the group of conformal isometries of three-dimensional hyperbolic space

Normal Families of Möbius Maps

Several necessary and sufficient conditions for a family of Möbius maps to be a normal family in the extended complex plane are established. Each of these conditions involves collections of two or three points which may vary with the Möbius maps in the family, provided the points satisfy a uniform separation condition. In addition, we derive a sufficient condition for the normality of a family of Möbius maps in terms of the average value of the reciprocal of the chordal derivative

Performance Enhancement of a Computational Persistent Homology Package

In recent years, persistent homology has become an attractive method for data analysis. It captures topological features, such as connected components, holes, voids, etc., from a point cloud by finding out when these features appear and disappear in the filtration sequence. In this project, we focus on improving the performance of Eirene, a fancy computational persistent homology package. Eirene is a 5000-line opensource software implemented by using the dynamic programming language Julia. We use the Julia profiling tools to identify the performance bottlenecks and develop different methods to manage the bottlenecks, including the parallelization of some time-consuming functions on the multicore/manycore hardware. The empirical results show that the performance can be greatly improved