Mathematics
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Item Solving, Generating, and Modeling Arc Routing Problems(2017) Lum, Oliver; Golden, Bruce; Wasil, Edward; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Arc routing problems are an important class of network optimization problems. In this dissertation, we develop an open source library with solvers that can be applied to several uncapacitated arc routing problems. The library has a flexible architecture and the ability to visualize real-world street networks. We also develop a software tool that allows users to generate arc routing instances directly from an open source map database. Our tool has a visualization capability that can produce images of routes overlaid on a specific instance. We model and solve two variants of the standard arc routing problem: (1) the windy rural postman problem with zigzag time windows and (2) the min-max K windy rural postman problem. In the first variant, we allow servicing of both sides of some streets in a network, that is, a vehicle can service a street by zigzagging. We combine insertion and local search techniques to produce high-quality solutions to a set of test instances. In the second variant, we design a cluster-first, route-second heuristic that compares favorably to an existing heuristic and produces routes that are intuitively appealing. Finally, we show how to partition a street network into routes that are compact, balanced, and visually appealing.Item Applications of parametric and semi-parametric models for longitudinal data analysis(2014) Talukder, Hisham; Corrada Bravo, Héctor; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)A wide range of scientific applications involve analyses of longitudinal data. Whether it is time or location, careful considerations need to be made when applying different statistical tools. One such challenge is to correctly estimate variance components in observed data. In this dissertation, I apply statistical tools to solve problems involving longitudinal data in the field of Biology, Healthcare and Networks. In the second chapter, I apply SSANOVA models to find regions in the genome that have a specific biological trait. We introduce a direct approach of estimating genomic longitudinal data of two different biological groups. Using SSANOVA we then produce a novel method to estimate the difference between the two groups and find regions (location or time) where this difference is biologically significant. In the third chapter, we analyze longitudinal network data using an overdispersed Poisson model. We build a network of musical writers yearly for a 42 year period. Using statistical models, we predict network level topology changes and find covariates that explain these changes. Network level characteristics used for this chapter include average node degree, clustering coefficient and network density. We also build a visualization tool using R-Shiny. The fourth chapter uses data partitioning to study the difference between insured patients and uninsured patients in health outcomes. There is a disparity in health outcomes depending on an individual's type of insurance. The level of risk for an injury is the longitudinal aspect of this dataset. We partition the data into four pre-defined risk categories and evaluate the disparity between insured and uninsured patients using logistic regression models.