Physical Sciences and Mathematics Commons^™

Weighted Networks: Applications From Power Grid Construction To Crowd Control, Thomas Charles Mcandrew

Graduate College Dissertations and Theses

Since their discovery in the 1950's by Erdos and Renyi, network theory (the study of objects and their associations) has blossomed into a full-fledged branch of mathematics.

Due to the network's flexibility, diverse scientific problems can be reformulated as networks and studied using a common set of tools.

I define a network G = (V,E) composed of two parts: (i) the set of objects V, called nodes, and (ii) set of relationships (associations) E, called links, that connect objects in V.

We can extend the classic network of nodes and links by describing the intensity of these associations with weights. …

Temporal Feature Selection With Symbolic Regression, Christopher Winter Fusting

Graduate College Dissertations and Theses

Building and discovering useful features when constructing machine learning models is the central task for the machine learning practitioner. Good features are useful not only in increasing the predictive power of a model but also in illuminating the underlying drivers of a target variable. In this research we propose a novel feature learning technique in which Symbolic regression is endowed with a ``Range Terminal'' that allows it to explore functions of the aggregate of variables over time. We test the Range Terminal on a synthetic data set and a real world data in which we predict seasonal greenness using satellite …

Wronskian And Gram Solutions To Integrable Equations Using Bilinear Methods, Benjamin Wiggins

Graduate College Dissertations and Theses

This thesis presents Wronskian and Gram solutions to both the Korteweg-de Vries and Kadomtsev-Petviashvili equations, which are then scalable to arbitrarily large numbers of interacting solitons.

Through variable transformation and use of the Hirota derivative, these nonlinear partial differential equations can be expressed in bilinear form. We present both Wronskian and Gram determinants which satisfy the equations.

N=1,2,3 and higher order solutions are presented graphically; parameter tuning and the resultant behavioral differences are demonstrated and discussed. In addition, we compare these solutions to naturally occurring shallow water waves on beaches.