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...
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....
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...
A fiber can transmit around 25 Tbit/s, but electronic signal processing today is performed at much slower speeds, usually 1-10 Gbit/s. To avoid this "bottleneck" in optical fiber communication systems, all signal processing will have to be done...
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...
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...
The problem of moving rigid bodies efficiently is of particular interest in robotics because the simplest model of a mobile robot or of a manipulated object is often a rigid body. Path planning, controller design and robot design may all benefit...
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,...
We describe a set of natural image statistics that are built upon two multi-scale image decompositions, the quadrature mirror filter pyramid decomposition and the local angular harmonic decomposition. These image statistics consist of first- and...
This thesis focuses on the emergence of universal dynamical scaling in quantum critical spin systems driven out of equilibrium, with emphasis on quench dynamics which involves isolated standard critical points, multi-critical points, and...
Brain mapping via EEG activation is a useful tool of basic neuroscience, and has wide clinical applications as well. The mapping is achieved by means of Event Related Potentials (ERPs), task-related changes in EEG time series. The methodology of...
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...
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...