Physical Sciences and Mathematics Commons^™

Machine Learning With Topological Data Analysis, Ephraim Robert Love

Doctoral Dissertations

Topological Data Analysis (TDA) is a relatively new focus in the fields of statistics and machine learning. Methods of exploiting the geometry of data, such as clustering, have proven theoretically and empirically invaluable. TDA provides a general framework within which to study topological invariants (shapes) of data, which are more robust to noise and can recover information on higher dimensional features than immediately apparent in the data. A common tool for conducting TDA is persistence homology, which measures the significance of these invariants. Persistence homology has prominent realizations in methods of data visualization, statistics and machine learning. Extending ML with …

Bayesian Topological Machine Learning, Christopher A. Oballe

Doctoral Dissertations

Topological data analysis encompasses a broad set of ideas and techniques that address 1) how to rigorously define and summarize the shape of data, and 2) use these constructs for inference. This dissertation addresses the second problem by developing new inferential tools for topological data analysis and applying them to solve real-world data problems. First, a Bayesian framework to approximate probability distributions of persistence diagrams is established. The key insight underpinning this framework is that persistence diagrams may be viewed as Poisson point processes with prior intensities. With this assumption in hand, one may compute posterior intensities by adopting techniques …

Data Analysis Methods Using Persistence Diagrams, Andrew Marchese

Doctoral Dissertations

In recent years, persistent homology techniques have been used to study data and dynamical systems. Using these techniques, information about the shape and geometry of the data and systems leads to important information regarding the periodicity, bistability, and chaos of the underlying systems. In this thesis, we study all aspects of the application of persistent homology to data analysis. In particular, we introduce a new distance on the space of persistence diagrams, and show that it is useful in detecting changes in geometry and topology, which is essential for the supervised learning problem. Moreover, we introduce a clustering framework directly …

On The Quantification Of Complexity And Diversity From Phenotypes To Ecosystems, Zachary Harrison Marion

Doctoral Dissertations

A cornerstone of ecology and evolution is comparing and explaining the complexity of natural systems, be they genomes, phenotypes, communities, or entire ecosystems. These comparisons and explanations then beget questions about how complexity should be quantified in theory and estimated in practice. Here I embrace diversity partitioning using Hill or effective numbers to move the empirical side of the field regarding the quantification of biological complexity.

First, at the level of phenotypes, I show that traditional multivariate analyses ignore individual complexity and provide relatively abstract representations of variation among individuals. I then suggest using well-known diversity indices from community ecology …

Social Fingerprinting: Identifying Users Of Social Networks By Their Data Footprint, Denise Koessler Gosnell

Doctoral Dissertations

This research defines, models, and quantifies a new metric for social networks: the social fingerprint. Just as one's fingers leave behind a unique trace in a print, this dissertation introduces and demonstrates that the manner in which people interact with other accounts on social networks creates a unique data trail. Accurate identification of a user's social fingerprint can address the growing demand for improved techniques in unique user account analysis, computational forensics and social network analysis.

In this dissertation, we theorize, construct and test novel software and methodologies which quantify features of social network data. All approaches and methodologies are …

Metabr: An R Script For Linear Model Analysis Of Quantitative Metabolomic Data, Ben Ernest, Jessica R. Gooding, Shawn R. Campagna, Arnold M. Saxton, Brynn H. Voy

Chemistry Publications and Other Works

Background

Metabolomics is an emerging high-throughput approach to systems biology, but data analysis tools are lacking compared to other systems level disciplines such as transcriptomics and proteomics. Metabolomic data analysis requires a normalization step to remove systematic effects of confounding variables on metabolite measurements. Current tools may not correctly normalize every metabolite when the relationships between each metabolite quantity and fixed-effect confounding variables are different, or for the effects of random-effect confounding variables. Linear mixed models, an established methodology in the microarray literature, offer a standardized and flexible approach for removing the effects of fixed- and random-effect confounding variables from …

Geographic Disparities Associated With Stroke And Myocardial Infarction In East Tennessee, Ashley Pedigo Golden

Doctoral Dissertations

Stroke and myocardial infarction (MI) are serious conditions whose burdens vary by socio-demographic and geographic factors. Although several studies have investigated and identified disparities in burdens of these conditions at the county and state levels, little is known regarding their geographic epidemiology at the neighborhood level. Both conditions require emergency treatments and therefore timely geographic accessibility to appropriate care is critical. Investigation of disparities in geographic accessibility to stroke and MI care and the role of Emergency Medical Services (EMS) in reducing treatment delays are vital in improving health outcomes. Therefore, the objectives of this work were to: (i) classify …

Energy Functional For Nuclear Masses, Michael Giovanni Bertolli

Doctoral Dissertations

An energy functional is formulated for mass calculations of nuclei across the nuclear chart with major-shell occupations as the relevant degrees of freedom. The functional is based on Hohenberg-Kohn theory. Motivation for its form comes from both phenomenology and relevant microscopic systems, such as the three-level Lipkin Model. A global fit of the 17-parameter functional to nuclear masses yields a root- mean-square deviation of χ[chi] = 1.31 MeV, on the order of other mass models. The construction of the energy functional includes the development of a systematic method for selecting and testing possible functional terms. Nuclear radii are computed within …