In this thesis, we study the dynamics of magnetic flows on compact nilmanifolds. Magnetic flows are generalizations of geodesic flows. They model the motion of a particle of unit mass and unit charge in a smooth manifold M in the presence of a...
Optical tomography. ; Near infrared spectroscopy. ; Image analysis -- Mathematical models. ; Imaging systems -- Image quality -- Mathematical models. ; Image reconstruction -- Mathematical models. ; Least squares. Breast -- Tomography.
Diffuse optical tomography (DOT) has the potential to become a non-invasive and non-ionizing diagnostic imaging technique for breast cancer imaging. DOT uses near-infrared (NIR) light to illuminate the breast, generally through the use of fiber...
Brain tissue mechanics are an important biomarker for neurological disorders, yet methods to obtain tissue information yield inconsistent conclusions. These techniques can be invasive or require excised tissue, where tissue function is altered from...
This project focuses on the development of research tools and methods that are used to study the relationship between neural activity and subsequent hemodynamic responses in the human brain. This relationship, referred to as neurovascular coupling,...
For many scientific applications, the data set cannot entirely fit in main memory. The data must reside out-of-core, i.e., on parallel disks. For many basic data-movement operations such as permuting, if the programmer does not design efficient...
Breast -- Cancer -- Tomography. ; Breast -- Cancer -- Imaging. ; Microwave imaging in medicine. ; Breast -- Electric properties. ; Breast Neoplasms -- diagnosis. ; Diagnostic Imaging -- methods.
Coherent states. Quantum field theory. Nonlinear theories.
In this thesis we study the properties of time-dependent, nontopological configurations and their effect on the macroscopic properties of a system described by a nonlinear field theory. These structures seem to be ubiquitous in relativistic field...
Prostate cancer (PCa) recurrences are often predicted by assessing the status of surgical margins (SM) â€“ positive surgical margins (PSM) increase the chances of biochemical recurrence by 2-4 times which may lead to PCa recurrence. At present,...
While plant-plant interactions define community patterns in alpine tundra around the world, topography and elevation and the resulting physical changes that occur when moving down-slope play a greater role in community formation and maintenance in...
Phase transitions occur in such diverse and important systems as ferromagnets, liquid crystals and the early Universe. The dynamics of phase transitions such as these have been studied for decades, but the analytical models still need a great deal...
Protein kinase C activators and microtubule damaging drugs stimulate BCL2 phosphorylation, which has been associated with either enhancement or inhibition of cell viability. In a Burkitt lymphoma cell line, both types of agents likewise stimulated...
We associate, to each positive integer n , a Cayley graph to the group PSL(2.Î–[subscript n]). We then consider the isoperimetric numbers of these graphs. In chapter three we determine upper bounds for the isoperimetric number by a detailed...
In the late 1960s, Ihara began work that led to the Ihara zeta function, a zeta function which is defined on a finite graph. This function is an interesting graph invariant which gives information on expansion properties of the graph. It also...
Motivated by the goal of investigating the dynamics of the electroweak phase transition in the early Universe, a study of dynamical aspects of nonlinear field-theoretical systems is performed. Symmetric and asymmetric double-well potentials in the...
For a local field K, we study the affine buildings Îž n and Î” n naturally associated to SL n ( K ) and Sp n ( K ), respectively. Since Sp n ( K ) is a subgroup of SL 2 n ( K ), we investigate properties of a natural embedding of Î” n in Îž 2 n ....
Magnetic Resonance Elastography (MRE) has emerged as a noninvasive, quantitative physical examination of the elastic properties of soft biological tissues including breast, liver, prostate, and brain. Implementation of constitutive relations that...
Quantum dots. Heterostructures. Metal oxide semiconductors -- Design and construction. Silicon oxide. Electron gas. Ohmic contacts. Microelectronics -- Technological innovations.
Solid-state approaches to quantum computing include quantum dot qubit implementations based on the Loss-DiVincenzo proposal. Prior work in GaAs two-dimensional electron gas (2DEG) materials serves as a proving ground for device designs that can be...
Manifolds (Mathematics) Geodesics (Mathematics) Space and time.
We investigate weak and strong refocusing of light rays in a space-time and related concepts. A strongly causal space-time ( X^ n +1 , g ) is emphstrongly refocusing at x âˆˆ X if there is a point y â‰ x such that all null-geodesics through y pass...
Ovaries -- Cancer -- Photochemotherapy.
Ovaries -- Cancer -- Treatment -- Evaluation.
Ovaries -- Cancer -- Treatment -- Mathematical models.
The translational potential of new therapeutic strategies for cancer is limited, in part, by a lack of biological models that capture important aspects of tumor growth and treatment response. It is also becoming increasingly evident that no single...
Microwave imaging (MI) is based on recovering dielectric properties (permittivity and conductivity) of materials. Over the last two decades, MI has attracted increasing interests in biomedical applications, in particular, for breast cancer...
In this thesis, the dynamics of long-lived, time-dependent, coherent field configurations, known as oscillons, are investigated in the presence of an expanding background. In a (1+1)-dimensional expanding spacetime, scalar-field oscillon lifetimes...
Investigations into alternative breast cancer (BC) imaging techniques have become increasingly popular based on the limitations of traditional imaging modalities: X-ray mammography uses ionizing radiation, has limited intrinsic contrast and is...
The goal of this work was to improve the computational tools for near-infrared light modeling for clinical applications in photodynamic therapy (PDT) analysis and eventual treatment planning. The tools to facilitate this modeling were developed in...
Strong evidence exists showing that stellar evolution models are unable to accurately predict the fundamental properties of low-mass stars. Observations of low-mass stars in detached eclipsing binaries (DEBs) indicate that stellar models...
In an undercooled environment any protuberance or bump on a planar solid/liquid interface that extends into the melt enhances its growth since the surrounding temperature gradient is greater than that about the planar surface. Consequently, the...
The focus of this thesis is the study of nuclearity and exactness for groupoid crossed product C*-algebras. In particular, we present generalizations of two well-known facts from group dynamical systems and crossed products to the groupoid setting....
This thesis centers around a generalization of the classical discrete Fourier transform. We first present a general diagrammatic approach to the construction of efficient algorithms for computing the Fourier transform of a function on a finite...
Metal ions confer structural stability and reactivity to a large number of proteins that use the amino acids histidine (His) and cysteine (Cys) to form stable metal-ligand complexes. The stability of metal-His and metal-Cys interactions and their...
Prostacyclin (PGI 2 ) is a major product of COX-2 catalyzed metabolism of arachidonic acid in the endothelium and has been shown to be atheroprotective. PGI 2 signals though its G-coupled protein receptor (GPCR) the human Prostacyclin receptor...
The essential QSR1 gene in Saccharomyces cerevisiae is a member of a highly conserved family of genes found in eukaryotic and archaebacterial cells. QSR1 was discovered by its synthetic lethal relationship with QCR6, the nuclear encoded gene for...