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...
Partially ordered sets and permutations are combinatorial structures having vast applications in theoretical computer science. In this thesis, we study various computational and algorithmic problems related to these structures. The first chapter of...
Functional neuroimaging has confirmed a high degree of localization of function in the cerebral cortex of man. In contrast, microstructural analysis has contributed very little to the topographical characterization of cortical areas. In this work I...
In the Firefighter Problem, a fire starts at a vertex of a graph, and in discrete time units, it spreads from burned vertices to their neighbors, unless they are protected by one of the f firefighters that are deployed every turn. Once burned or...
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...
Community health services -- United States -- Evaluation. ; Health care reform -- United States. ; Medical care -- United States -- Evaluation. ; Evidence-based medicine.
Outcome assessment (Medical care). ; Aortic valve -- Surgery -- Complications. ; Aortic valve -- Surgery -- New England. ; Cardiovascular instruments Implanted.
Aortic valve disease is a frequent and serious disorder. Although aortic valve replacement (AVR) is arguably the only effective treatment, important issues remain unresolved in the care of patients with this disease. Recent studies have focused...
Modern distributed systems scatter sensors, storage, and computation throughout the environment. Ideally these devices communicate and share resources, but there is seldom motivation for a device''s owner to yield control to another user. We...
This thesis is divided into 2 parts. In the first part of the thesis, we describe a software based approach to speeding up the Magnetic Resonance Imaging modality. In the second part of the thesis, we describe Significance Tree Quantization, which...
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...
Coding theory. Characters of groups. Error-correcting codes (Information theory). Polynomials.
We introduce vector-valued character theory, a higher dimensional generalization of character theory. We then use vector-valued characters to extend the MacWilliams equivalence theorem for linear codes to a class of additive codes, called...
Sensing light from the environment using photoreceptors is of great adaptive significance to eukaryotes. A prominent feature of the photochemistry of these receptors is the photocycle length, the time taken to decay from the initial signaling light...
Relativity (Physics). ; Anisotropy -- Mathematical models. ; Einstein field equations. ; Newtonian fluids. ; Astrophysics.
We study the effects of anisotropic pressure on the properties of spherically symmetric, gravitationally bound spheres. We consider the full general-relativistic and Newtonian treatment of this problem and obtain exact solutions for various forms...
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...
In the late 1960s, Ihara began work that led to the Ihara zeta function, a zeta function which is defined on a finite graph. This function is an interesting graph invariant which gives information on expansion properties of the graph. It also...
The performance of machine learning algorithms largely depends on data representation. As a critical step in machine learning, representation learning (feature learning) learns a transformation of training data to give a new representation that can...
Partially ordered sets. ; Convex polytopes. ; Representations of groups.
This thesis deals with geometric representations of ordered sets. In a geometric representation, each element of the ordered set is assigned a geometric object, with two elements incomparable in the ordered set if and only if the corresponding...
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...