Three-dimensional imaging in medicine -- Mathematical models. ; Stereoencephalotomy.
In the past, clinicians skilled at image-guided neurosurgery have relied solely on pre-operative scans for their navigational information. Often in the course of surgery, tissue is purposely retracted/resected or inadvertently moved resulting in a...
I consider the problem of extending certain invariants of subsets of natural numbers to their equivalents for subsets of larger cardinals. The two specific questions I will address are the extension of the off-branch number [Special characters...
This thesis contains material relating to two separate subjects. The first section determines when the C*-algebra affiliated to a directed graph has continuous trace. We use groupoid methods and the focus is on producing conditions on a graph that...
Evolutionary Computation (EC) is one of the most advanced computational techniques. It has been frequently and successfully used to find good solutions to many complicated optimization problems with limited computational resources. EC is the...
Understanding mercury (Hg) and lead (Pb) accumulation and retention in forest soils is needed to reduce their negative impacts on human and wildlife health. In addition, mercury and lead can be used to characterize the role of soil in terrestrial...
We present a number of findings concerning groupoid dynamical systems and groupoid crossed products. The primary result is an identification of the spectrum of the groupoid crossed product when the groupoid has continuously varying abelian...
There are no Vassiliev invariants of degree one for classical knots. A. Henrich proved the existence of a sequence of three Vassiliev invariants of degree one for virtual knots. The invariants get stronger and stronger, and the final invariant is...
Boundary integral methods have long been used to solve boundary value problems for elliptic partial differential equations with piecewise constant coefficients, since they have several numerical advantages over conventional volume discretization....
Topological graph theory. Aperiodicity. Paths and cycles (Graph theory)
The condition ""every cycle has an entry"" first appeared in the literature in Kumjian, Pask, and Raeburn's paper on Cuntz-Krieger algebras of directed graphs, where it was called Condition (L). It provides a necessary condition for simplicity of...
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...
This thesis approaches the problem of locating zero-day exploits used in network attacks. The hypothesis is that the advent of high-performance virtualization presents a unique opportunity to both discover these events and increase the attacker's...
'Orthogonal modular forms are algebraic modular forms arising from lattices in quadratic spaces. In this thesis, we define orthogonal modular forms, establish their basic properties, and then apply them to a case of ternary quadratic spaces to...
Goldman and Turaev constructed a Lie bialgebra structure on the free Z-module generated by free homotopy classes of loops on an oriented surface. Turaev conjectured that the cobracket of A is zero if and only if A is a power of a simple class. Chas...
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...
This thesis investigates the embedding theory of orders in central simple algebras, placing a particular emphasis on the role that the phenomenon known as selectivity plays in the theory. Although the notion of selectivity is completely algebraic,...
This thesis constitutes the first steps in the author's program to investigate the question of when a homotopy of 2-cocycles Ï‰ = {Ï‰[subscript t]}[subscript tâˆŠ[0,1]] on a locally compact Hausdorff groupoid Æ“ induces an isomorphism of the...
In this thesis, we consider several problems relating to cyclic subgroups of the group [mathematical equation]. Each element of [mathematical equation] has a unique representative in one of the two intervals [mathematical equation] and...
Loss processes greatly impact the dynamics of the Earth's radiation belts. In 1996, a balloon-borne germanium detector flown over Kiruna, Sweden detected the first terrestrial X-rays with energies on the order of 1 MeV. The spectrum for these...
Objectives: This dissertation comprises three essays on geographic variations in healthcare, and the association between utilization and health outcomes. I first explore associations between outpatient visits and Medicare beneficiaries'...
A metric structure on a set gives a concept of distance between any two elements of that set, and it induces a topology. In this thesis, we provide several ways to put a metric structure on the collection of CW complexes. We accomplish this by...
Structural control (Engineering). ; Smart structures -- Vibration. ; Strains and stresses -- Computer simulation. ; Automatic control -- Sensitivity. ; Feedback control systems.
This thesis investigates vibration-based damage identification problems in smart structures. Vibration-based damage metrics suffer from small sensitivity of modal properties to damage, thus making it difficult to detect, locate, and determine the...
Three-dimensional imaging in medicine -- Mathematical models. Intraoperative monitoring. Cerebral cortex -- Imaging. Computer vision. Space perception.
Brain deformation models have proven to be a powerful tool in compensating for soft tissue deformation during image-guided neurosurgery. The accuracy of these models can be improved by incorporating intraoperative measurements of brain motion. We...
Metal powders -- Extrusion. Metal powders -- Microstructure. Shear flow.
The manufacture of bulk parts from metastable powder materials requires new approaches to cold consolidation. One potential technique is equal-channel angular extrusion (ECAE), a simple shear process. This thesis describes an investigation into the...
This thesis explores practical and theoretical aspects of several privacy-providing technologies, including tools for anonymous web-browsing, verifiable electronic voting schemes, and private information retrieval from databases. State-of-art...
This dissertation examines the behavioral and physiological adaptations employed by modern humans to subsist in tropical rainforests. I employ various theoretical and methodological approaches to test hypotheses using empirical data from African...