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 comprises two separate but related studies, dealing with two strongly interacting nanoscale systems on the border between the quantum and classical domains. In Part 1, we use a Born-Markov approximated master equation approach to study...
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...
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...
We present new forensic tools that are capable of detecting traces of tampering in digital images without the use of watermarks or specialized hardware. These tools operate under the assumption that images contain natural properties from a variety...
Infrared imaging. Image reconstruction. Optical images -- Mathematical models. Breast -- Imaging. Infrared radiation in medicine.
Finite element based reconstruction algorithms for optical property profiling in biological tissues have been developed, implemented and evaluated using simulated data and laboratory measurements obtained with near infrared continuous wave (cw) and...
Medical imaging methods have become increasingly important in diagnosing diseases and assisting therapeutic treatment. In particular, early detection of breast cancer is considered as a critical factor in reducing the mortality rate of women....
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...
This research has established feasibility of surface temperature characterization using ruby fluorescence. Study was performed in pin-on-disk geometry, with balls made of different plastics sliding against the sapphire disk. Fluorescence signal was...
Riemannian manifolds. Singularities (Mathematics). Laplacian operator. Spectral theory (Mathematics). Riemann surfaces. Curves on surfaces. Geometry
Historically, inverse spectral theory has been concerned with the relationship between the geometry and the spectrum of compact Riemannian manifolds, where spectrum means the eigenvalue spectrum of the Laplace operator as it acts on smooth...
We present designs, theory and the results of fabrication and testing for a novel parallel microrobotic assembly scheme using stress-engineered MEMS microrobots. The robots are 240-280 μm × 60 μm × 7-20 μm in size, each robot consist of a...
Diagnostic imaging -- Mathematics. Expectation-maximization algorithms. Imaging systems in medicine -- Mathematics.
We have developed a general-purpose registration algorithm for medical images and volumes. The transformation between images is modeled as locally affine but globally smooth, and explicitly accounts for local and global variations in image...
Protein complexes play vital roles in cellular processes within living organisms. They are formed by interactions between either different proteins (hetero-oligomers) or identical proteins (homo-oligomers). In order to understand the functions of...
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...
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...
In Chapter 2 we look at the distribution of permutation statistics in the context of pattern-avoiding permutations. The first part of this chapter deals with a recursively defined bijection of Robertson [37] between 123- and 132-avoiding...
The experiments comprising this thesis aimed to characterize the neural and behavioral correlates of learning about and responding to the predictive information conveyed by social cues. Facial expressions are cues that convey critical information...
One of the most distinctive aspects of humans as a species is our propensity to form complex social networks made up of intense, non-reproductive bonds with non-kin. Navigating these networks presents a considerable cognitive challenge that is...
In this thesis we develop a theory of Fourier analysis and fast Fourier transforms (FFTs) for finite inverse semigroups. Our results generalize results in the theory of Fourier analysis for finite groups. There is a general method for generating...
We start by introducing avoidance coupling of Markov chains, with an overview of existing results. We then introduce and motivate a new notion, uniform coupling. We show that the only Markovian avoidance coupling on a cycle is of this type, and...
Information resources management -- Mathematical models. ; Database management -- Methodology. ; Change. ; World Wide Web.
Many modern information management tasks consist of an observer that must maintain current knowledge of a collection of changing information. The goal of this observer is to maintain acceptably accurate state estimates given limited observation...
Let K be the function field over a finite field of odd order, and let H be a definite quaternion algebra over K. If Α is an order of level M in H , we define theta series for each ideal I of Α using the reduced norm on H. Using harmonic analysis...
Spectral theory is the subfield of differential geometry which provided the solution to Kac''s famous question, "Can you hear the shape of a drum?" That is, can we use the Laplace spectrum of a manifold to draw conclusions about its geometry or...
Breast -- Magnetic resonance imaging. Breast -- Tomography. Near infrared spectroscopy. Optical tomography. Imaging systems -- Design and construction. Diagnostic imaging -- Mathematical models.