This thesis contains some results concerning groupoid dynamical systems and crossed products. We introduce the notion of a proper groupoid dynamical system and of its generalized fixed point algebra. We show that our notion of proper groupoid...
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...
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...
In a variety of applications spanning mobile devices, performance computing, and even renewable energy and automotive, power management and power delivery are an increasing bottleneck in reducing size and cost, improving reliability, and even...
Problem Statement Patient safety in the modern hospital is supported by multiple human and technological systems, and this type of high-risk/high-complexity domain requires multiple layers of protection against harm. This fault-tolerant approach is...
For a local field K, we study the affine buildings Ξ n and Δ 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 Δ n in Ξ 2 n ....
Proteins, the basic structural and functional building blocks of cellular machinery, evolve under significant constraint. Evolutionary pressures limit the acceptable variation and covariation of amino acids in a protein. As such, these evolutionary...
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 ∈ X if there is a point y ≠ x such that all null-geodesics through y pass...
Autonomous off-road navigation in unstructured, terrain can encounter mobility difficulties even when the surface that the vehicle is driving over is level and free from obstacles. Mobility challenges result from soil characteristics that prevent...
As the visual effect and movie industries are striving for realism and high fidelity images, physically based lighting, global illumination, realistic materials, and highly tessellated geometry are gradually accepted and used in movie and game...
Thermodynamics, and the classic balance between entropy and enthalpy, provides a proverbial zoo of exotic phase behaviour that chemists can harness to create new materials out of simple liquids and polymers. The diversity of self-assembling...
A new type of analytic expansion for use in stability calculations is presented and applied to the question of the stability of laminar solutions of the Navier-Stokes equation. This leads in a natural way to a model of the transition from laminar...
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...
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,...
Opinion dynamics is a complex procedure that entails a cognitive process when it deals with how a person integrates influential opinions to form revised opinion. Early research on opinion formation and social influence can be traced back to the...
The need for social connection is a pervasive and powerful human drive. When this fundamental need is not fulfilled, people place greater emphasis on forming social bonds and are motivated to behave in ways consistent with accomplishing these...
Internet -- Security measures. Public key infrastructure (Computer security). Digital signatures. Peer-to-peer architecture (Computer networks) -- Security measures.
The Internet has become a virtual place where people not only operate in isolation but also interact with other Internet users. Collaborative systems are becoming more popular. Applications now being introduced could provide better remote education...
This thesis constitutes the first steps in the author's program to investigate the question of when a homotopy of 2-cocycles ω = {ω[subscript t]}[subscript t∊[0,1]] on a locally compact Hausdorff groupoid Ɠ induces an isomorphism of 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....
In the past few years there has been a tremendous growth in the usage of digital images. Users can now access millions of photos, a fact that poses the need of having methods that can efficiently and effectively search the visual information of...
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...
Robustness to genetic perturbations is a fundamental property of all living things. The genetic code is degenerate, RNA secondary structure is robust to sequence changes, and protein structure is robust to amino acid substitutions. Complex systems...
Through a series of case studies, signal processing and statistical tools, analyses of dynamic sea ice processes of drift, deformation, and ice pack expansion and decay are investigated for the Weddell Sea region during 1992. Cavitating fluid (CAV)...