Now showing items 1-10 of 105
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Exploiting geometry, topology, and optimization for knowledge discovery in big data
Author(s):Ziegelmeier, Lori Beth
In this dissertation, we consider several topics that are united by the theme of topological and geometric data analysis. First, we consider an application in landscape ecology using a well-known vector quantization algorithm ...
Sparse multivariate analyses via ℓ1-regularized optimization problems solved with Bregman iterative techniques
In this dissertation we propose Split Bregman algorithms for several multivariate analytic techniques for dimensionality reduction and feature selection including Sparse Principal Components Analysis, Bisparse Singular ...
Automated detection of circulating cells using low level features
Author(s):Emerson, Tegan Halley
This thesis addresses the problem of detection of high definition circulating tumor cells using data driven feature selection. We propose techniques in pattern analysis and computer vision to achieve this goal. Specifically, ...
Intersections of ψ classes on Hassett spaces of rational curves
Hassett spaces are moduli spaces of weighted stable pointed curves. In this work, we consider such spaces of curves of genus 0 with weights all 1/q , q being a positive integer greater than or equal to 2. These spaces are ...
Abstract hyperovals, partial geometries, and transitive hyperovals
Author(s):Cooper, Benjamin C.
A hyperoval is a (q+2)- arc of a projective plane π, of order q with q even. Let G denote the collineation group of π containing a hyperoval Ω. We say that Ω is transitive if for any pair of points x, y is an element of ...
Analysis of factors affecting student success in Math 160 calculus for Physical Scientists I, An
Author(s):Reinholz, Daniel Lee
The average success rate in MATH 160 Calculus for Physical Scientists I at Colorado State University has been near 60% for at least the past three years. Weak pre-calculus skills are often cited as one of the primary reasons ...
Let k be an algebraically closed field of characteristic p where p is a prime number. The main focus of this work is on properties of Artin-Schreier curves. In particular, we study two invariants of the p-torsion of the ...
Constrained dynamics of rolling balls and moving atoms
This dissertation is devoted to the study of the dynamics, conservation laws and symmetries of rolling spheres, with special attention to applications to atomic and molecular systems. Previously known conservation laws of ...
Lagrangian mixing and transport in hurricanes
This study examines the role of transport and mixing in the dynamics of tropical cyclones from a mathematical viewpoint and their implications for intensity. While this topic has seen extensive study, much of it has lacked ...
Pattern formation in reaction diffusion systems and ion bombardment of surfaces
Author(s):Hashmi, Bahaudin A.
We have analyzed pattern formation in two different systems: (1) Vapor-to-particle reaction diffusion systems and (2) Highly ordered square arrays in ion bombardment. The vapor-to-particle reaction exhibits oscillatory ...