This dissertation explores bridge n-sections of knotted surfaces in 4-manifolds by defining invariants that measure the complexity of their topology and by giving geometric constructions that determine Lagrangian surfaces in 4-manifolds under certain conditions. First, we present an elegant geometric construction that generates all triple grid…

A shape grammar is a formalism that has been widely applied, in many different fields, to analyzing designs. Computer implementation of a shape grammar interpreter is vital to both research and application. However, implementing a shape grammar interpreter is hard, especially for parametric shapes defined by open terms. This dissertation…

This thesis investigates and develops a few acceleration techniques for the search engine algorithms used in PageRank and HITS computations. PageRank and HITS methods are two highly successful applications of modern Linear Algebra in computer science and engineering. They constitute the essential technologies accounted for the immense growth and…

Combinatorial scientific computing plays an important enabling role in computational science, particularly in high performance scientific computing. In this thesis, we will describe our work on optimizing matrix-vector multiplication using combinatorial techniques. Our research has focused on two different problems in combinatorial scientific…

This dissertation explores the use of geometric and graphical models for a variety of information search and filtering applications. These models serve to provide an intuitive understanding of the problem domains and as well as computational efficiencies to our solution approaches. We begin by considering a search and rescue scenario where both…

Access to quality mathematics content and instruction has been equated as a civil right (Moses & Cobb, 2001). However, access to empowering mathematics is not a reality for many urban youth. Data show an achievement gap between Black, Hispanic and American Indian students and their peers which, in turn, result in unequal access to education and…