Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
Bayesian Topological Machine Learning, Christopher A. Oballe
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
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
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 …
Geographic Disparities Associated With Stroke And Myocardial Infarction In East Tennessee, Ashley Pedigo Golden
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
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 …
Modeling And Simulation Of Value -At -Risk In The Financial Market Area, Xiangyin Zheng
Modeling And Simulation Of Value -At -Risk In The Financial Market Area, Xiangyin Zheng
Doctoral Dissertations
Value-at-Risk (VaR) is a statistical approach to measure market risk. It is widely used by banks, securities firms, commodity and energy merchants, and other trading organizations. The main focus of this research is measuring and analyzing market risk by modeling and simulation of Value-at-Risk for portfolios in the financial market area. The objectives are (1) predicting possible future loss for a financial portfolio from VaR measurement, and (2) identifying how the distributions of the risk factors affect the distribution of the portfolio. Results from (1) and (2) provide valuable information for portfolio optimization and risk management.
The model systems chosen …
Statistical Properties Of Maximum Likelihood Estimates For Accelerated Lifetime Data Under The Weibull Model, Mahmoud A. Yousef
Statistical Properties Of Maximum Likelihood Estimates For Accelerated Lifetime Data Under The Weibull Model, Mahmoud A. Yousef
Doctoral Dissertations
Pipe rehabilitation liners are often installed in host pipes that lie below the water table. As such, they are subjected to external hydrostatic pressure. The external pressure leads to early deformation in the liners, which could ultimately lead to its failing or buckling before its expected service lifetime is achieved. Experiments involving long term buckling behavior of liners are typically accelerated lifetime testing procedures. In an accelerated testing procedure a liner is subjected to a constant external hydrostatic pressure and observed until it fails or for a certain time, t whichever occurs first. Liners that do not fail at time …