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...
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...
Magnetoencephalography -- Technique.; Magnetic susceptibility.
The measurement of human brain function is the goal of many noninvasive medical imaging modalities. Two sources of physiological contrast are commonly targeted to achieve this goal. The most direct approach to measuring neuronal activity is with...
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...
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,...
Magnetic fields at all scales are prevalent in our universe. However, current cosmological models predict that initially the universe was bereft of large-scale fields. Standard magnetohydrodynamics (MHD) does not permit magnetogenesis; in the MHD...
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...
Bayesian nonparametric methods have become increasingly popular in machine learning for their ability to allow the data to determine model complexity. In particular, Bayesian nonparametric versions of common latent variable models can learn as...
The purpose of this thesis is to describe methods for detecting hidden crevasses on glaciers in Polar regions. Crevasses form in ice sheets as a result of forces imposed upon the brittle ice. The crevasses are hidden from view by bridges of soft...
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...
We prove the existence of nontrivial multiparameter isospectral deformations of metrics on the classical compact simple Lie groups SO (n) (n = 9, n â‰¥11), Spin(n) (n = 9, n â‰¥11), SU (n) (n â‰¥7), and Sp (n) (n â‰¥5). The proof breaks into three...
During an immune reaction to an invading pathogen, a population of lymphocytes with receptors that specifically recognize the pathogen are activated and become memory cells. Characteristically, memory lymphocytes persist for long periods of time...
How the genome is shaped directly influences how it is expressed. In fact, the genome is organized at many different levels, each imparting specific regulation over transcription. Fundamental principles regulating genome organization are poorly...
Given graded C *-algebras A and B , we define the notion of an admissible pair ([straight phi], D ) for A and B . Associated to an admissible pair ([straight phi], D ) is an equivalence class of asymptotic morphisms from A to B . Under certain...
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...
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...
There is a growing demand for power-constrained sensors in many areas, particularly in emerging healthcare and next-generation biomedical applications. Such sensors have very limited power budget, among which interface circuits, including analog...
Computer security has come a long way since the days of the first Internet worm. With the spreading and commercialization of the Internet, the stakes have gotten higher. Viruses existed and spread before most computers were online, but as global...
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...