Prostate cancer (PCa) recurrences are often predicted by assessing the status of surgical margins (SM) – positive surgical margins (PSM) increase the chances of biochemical recurrence by 2-4 times which may lead to PCa recurrence. At present,...
Continual improvements to clinical breast imaging technologies have led to ever earlier detections and increasingly accurate localizations of female breast cancers. While these advancements have certainly improved the prognoses of many patients,...
Magnetic susceptibility imaging of magnetic nanoparticles (mNPs) has many potential applications in biomedicine such as contrast enhanced imaging and image guidance for magnetic hyperthermia therapy. This thesis describes three imaging methods...
At the heart of computer games and computer generated films lies 3D content creation. A student wanting to learn how to create and edit 3D meshes can quickly find thousands of videos explaining the workflow process. These videos are a popular...
Molecular imaging of cancer features is a critical part of advancing better tools for oncology management and drug discovery, yet it is still evolving as a useful tool. Diffuse Fluorescence Tomography (FT) is one approach to molecular imaging, used...
This thesis describes the synthesis of sulfobetaines having the general structure $\rm RN\sp{+}(CH\sb3)\sb2(CH\sb2)\sb{x}SO\sb{3\sp{-}}$ as novel inhibitors of squalene synthase. Squalene synthase reductively couples two molecules of farnesyl...
Partially ordered sets. ; Convex polytopes. ; Representations of groups.
This thesis deals with geometric representations of ordered sets. In a geometric representation, each element of the ordered set is assigned a geometric object, with two elements incomparable in the ordered set if and only if the corresponding...
In order to most effectively investigate protein structure and improve protein function, it is necessary to carefully plan appropriate experiments. The combinatorial number of possible experiment plans demands effective criteria and efficient...
I investigate the kinematics and space densities of the local cataclysmic variable (CV) population. CVs are close binary star systems composed of a white dwarf that accretes matter from a less compact companion star in Roche lobe overflow....
Polynomials. Finite fields (Algebra). Algebraic functions. Number theory.
The ring of univariate polynomials over a finite field shares many foundational arithmetic properties with the ring of rational integers. This similarity makes it possible for many problems in elementary number theory to be translated 'through the...
Since its discovery in the 1930's, the Cherenkov effect has been paramount in the development of high-energy physics research. It results in light emission from charged particles traveling faster than the local speed of light in a dielectric...
Magnetic nanoparticles are promising candidates for use in biomedical applications as remote sensors of biophysical properties, thermal therapy agents, and detectors of specific biomolecules. Many approaches have been used to model magnetic...
In this thesis we look at several problems that lie in the intersection between combinatorial and multiplicative number theory. A common theme of many of these problems are estimates for and properties of the smooth numbers, those integers not...
In this thesis we study 1=k-geodesics, those closed geodesics that minimize on any subinterval of length L=k, where L is the length of the geodesic. These curves arise as critical points of the uniform energy, a function introduced in Morse theory...
The rat limbic system contains head direction (HD) cells that fire according to heading in the horizontal plane. These HD cells are thought to provide animals with an internal compass to guide navigation. Previous work has found that HD cell tuning...
Motivated by quantum mechanics and geometric optics, it is a long-standing problem whether the length spectrum of a compact Riemannian manifold can be recovered from its Laplace spectrum. One route to proving that the length spectrum depends on the...
In this thesis, we present different approaches to tying knots using robots by enforcing different types of constraints. We attack the problem from three different directions; mechanical design, motion planning with simple control strategies, and...
'The control of waves using periodic structures is crucial for modern optical, electromagnetic and acoustic devices such as diffraction gratings, filters, photonic crystals, solar cells, sensors, and absorbers. We present a high-order accurate...
All cells must organize their cytoplasm in order to carry out functions properly and survive in different environments, and the requirement for organization is increased in large, multinucleate cells. It has long been known that membrane-bound...
Space and time in language. ; Space perception. ; Figure-ground perception. ; Psycholinguistics.
Across languages, there exists a relatively small number of spatial prepositions. These terms are used to express the infinite number of possible spatial locations of an unlimited number of different entities in the environment. Previous research...
2-D and 3-D woven composites are becoming materials of choice for the forming of structural parts for an ever-increasing range of industries from infrastructure to aerospace. Research has shown that for a wide range of structural composites, in...
Acyl-coenzyme A: cholesterol acyltransferase (ACAT) plays important roles in cellular cholesterol homeostasis and in early stages of atherogenesis. ACAT has been investigated as a pharmaceutical target, yet its active site(s) remain largely...
Part I. A photoprecursor for difluorocarbene . The goal of this research was to develop a more practical and efficient photoprecursor for difluorocarbene. The first approach was concerned with the synthesis of 4,4-difluoropyrazoline-3,5-dione ( 5...