Physical Sciences and Mathematics Commons^™

Birds And Bioenergy: A Modeling Framework For Managed Landscapes At Multiple Spatial Scales, Jasmine Asha Kreig

Doctoral Dissertations

This dissertation examines the design and management of bioenergy landscapes at multiple spatial scales given numerous objectives. Objectives include biodiversity outcomes, biomass feedstock yields, and economic value.

Our study examined biodiversity metrics for 25 avian species in Iowa, including subsets of these species related to ecosystem services. We used our species distribution model (SDM) framework to determine the importance of predictors related to switchgrass production on species richness. We found that distance to water, mean diurnal temperature range, and herbicide application rate were the three most important predictors of biodiversity overall. We found that 76% of species responded positively to …

Preconditioned Nesterov’S Accelerated Gradient Descent Method And Its Applications To Nonlinear Pde, Jea Hyun Park

Doctoral Dissertations

We develop a theoretical foundation for the application of Nesterov’s accelerated gradient descent method (AGD) to the approximation of solutions of a wide class of partial differential equations (PDEs). This is achieved by proving the existence of an invariant set and exponential convergence rates when its preconditioned version (PAGD) is applied to minimize locally Lipschitz smooth, strongly convex objective functionals. We introduce a second-order ordinary differential equation (ODE) with a preconditioner built-in and show that PAGD is an explicit time-discretization of this ODE, which requires a natural time step restriction for energy stability. At the continuous time level, we show …

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 …

Spatio-Temporal Modeling Of Crime In Chicago, Illinois, Shelby Scott

Doctoral Dissertations

Gun crime is a major public health concern in the United States. In Chicago, Illinois, gun crime incurs a significant cost of life along with monetary costs and community unrest. Due to past legislation, there is limited research applying quantitative methods to gun crime in Chicago. The overall purpose of this work is to create a cellular automata model to observe and project the epidemic spread of gun crime in Chicago. To create that model, t-test analyses of temporal patterns, a Bayesian point process model, a negative binomial Bayesian subset selection, and a k-selection algorithm are used. The cellular automata …

Mathematical Models In Medicine: The Immune Response Of Celiac Disease And The Environmental Transmission Of Clostridioides Difficile In Healthcare Settings, Cara Jill Sulyok

Doctoral Dissertations

Mathematical modeling is a useful technique to describe dynamics happening within events and allows one to address questions and test hypotheses that may be not be feasible to study in reality. This work uses mathematical models to describe two such phenomena, one relating to immunology and the other to the spread of infectious diseases.

Celiac disease is a hereditary autoimmune disease that affects approximately 1 in 133 Americans. It is caused by a reaction to the protein gluten found in wheat, rye, and barley. After ingesting gluten, a patient with celiac disease may experience a range of unpleasant symptoms while …

Data Driven Models Of Hemlock Woolly Adelgid Impacts And Biological Control, Hannah M. Thompson

Doctoral Dissertations

We present two models of the Adelges tsugae, the hemlock woolly adelgid, an invasive insect pest of Tsuga canadensis, eastern hemlock, in the eastern United States. An A. tsugae infestation often results in the death of T. canadensis within years, and has caused significant changes to hemlock forests. We construct two models composed of systems of ordinary differential equations with time dependent parameters to represent seasonality. The first model captures the coupled cycles in T. canadensis health and A. tsugae density. We use field data from Virginia to develop the model and to perform parameter estimation. The mechanisms …