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Signal Amplification by Reversible Exchange (SABRE) is a hyperpolarization technique that utilizes parahydrogen for the NMR signal enhancement of nuclear spins. SABRE is related to Parahydrogen Induced Polarization (PHIP), another means of hyperpolarization using parahydrogen; PHIP achieves hyperpolarization via chemical reduction. Although PHIP and SABRE share many similarities in experimentation, PHIP ultimately requires the presence of an unsaturated chemical bond as well as pairwise-addition of parahydrogen. No permanent chemical change occurs during SABRE, and instead may be considered as a merely physical exchange between molecules with sites on a catalyst. PHIP and SABRE may be compared to Dynamic Nuclear Polarization (DNP), arguably the most well-known and researched method for hyperpolarization; despite all that has been achieved with DNP, PHIP and SABRE offer vastly more-rapid, less-expensive, and more-simplified approaches for achieving hyperpolarization. The focus of this work is experimentation with SABRE processes and methods designed to overcome certain experimental challenges associated with this technique.

My research lies in the general area of functional analysis. I am particularly interested in C*-algebras and related dynamical systems. From the very beginning of the theory of operator algebras, in the works of Murray and von Neumann dating from the mid 1930's, dynamical systems and operator algebras have led a symbiotic existence. Murray and von Neumann's work grew from a few esoteric, but clearly original and prescient papers, to a ma jor river of contemporary mathematics. My work lies at the confluence of two important tributaries to this river. On the one hand, the operator algebras that I study are C*-algebras that are built from graphs. On the other, the dynamical systems on which I focus are symbolic dynamical systems of various types. My goal is to use dynamical systems theory to construct new and interesting C*-algebras and to use the algebraic invariants of these algebras to reveal properties of the dynamics. My work has two fairly distinct strands: One deals with C*-algebras built from irreversible dynamical systems. The other deals with group actions on graph C*-algebras and their generalizations.

Single-walled carbon nanotubes (SWNTs) are a new class of materials that have recently attracted a great deal of interest because of their unique structural, mechanical, and electronic properties. Also, SWNTs have a high potential for a number of technological applications, including molecular electronics, emissive devices, and photovoltaic devices. To fully utilize their unique properties, control of the solubility, processibility, and functionality of SWNTs is required. Therefore chemical functionalization of SWNTs using a variety of methods, in either covalent or noncovalent manner, has been developed to produce soluble nanotube composites coupled with various chemical moieties. To explore the possibility of making potential soluble nanotube-based materials for solar cells, SWNTs were functionalized with organic chromophore-labeled polymers via a radical coupling process. The organic chromophore was used to absorb light to produce photo-induced electrons, while the polymer chains were used for improving the solubility of SWNTs. These novel chromophore-labeled polymers were made by stable free radical polymerization (SFRP), either using a synthetic chromophore-functionalized styrenic monomer or by derivatizing well-defined polystyrenes. Specifically, the chromophores employed in this investigation were commercially available 7-hydroxycoumarin and coumarin-343. In order to carry out fluorescence studies of SWNT-coumarin composites systematically, various factors were probed by (1) altering polystyrene lengths between the SWNT and the coumarin; (2) changing the distribution of coumarins along the polymer chain, in the form of either a block or random copolymer; (3) placing single coumarins on the surface of SWNTs. All of these resulting polymer functionalized SWNTs were found to be soluble in certain organic solvents such as CHCl3. Different absorption behaviors have been observed for SWNTs functionalized with 7-hydroxycoumarin containing copolymers. Fluorescence was still observable for all of these composites, and the pi-pi interactions between coumarins and nanotubes were believed to be responsible for the broadening of emission bands of the resulting composites. / Thesis / Master of Science (MS)

BACKGROUND:A multi-labeled tree, or MUL-tree, is a phylogenetic tree where two or more leaves share a label, e.g., a species name. A MUL-tree can imply multiple conflicting phylogenetic relationships for the same set of taxa, but can also contain conflict-free information that is of interest and yet is not obvious.RESULTS:We define the information content of a MUL-tree T as the set of all conflict-free quartet topologies implied by T, and define the maximal reduced form of T as the smallest tree that can be obtained from T by pruning leaves and contracting edges while retaining the same information content. We show that any two MUL-trees with the same information content exhibit the same reduced form. This introduces an equivalence relation among MUL-trees with potential applications to comparing MUL-trees. We present an efficient algorithm to reduce a MUL-tree to its maximally reduced form and evaluate its performance on empirical datasets in terms of both quality of the reduced tree and the degree of data reduction achieved.CONCLUSIONS:Our measure of conflict-free information content based on quartets is simple and topologically appealing. In the experiments, the maximally reduced form is often much smaller than the original tree, yet retains most of the taxa. The reduction algorithm is quadratic in the number of leaves and its complexity is unaffected by the multiplicity of leaf labels or the degree of the nodes.

As the availability of unstructured data on the web continues to increase, it is becoming increasingly necessary to develop machine learning methods that rely less on human annotated training data. In this thesis, we present methods for learning from weakly labeled data. We present a unifying framework to understand weakly labeled data in terms of bias and noise and identify methods that are well suited to learning from certain types of weak labels. To compensate for the tremendous sizes of weakly labeled datasets, we leverage computationally efficient and statistically consistent spectral methods. Using these methods, we present results from four diverse, real-world applications coupled with a unifying simulation environment. This allows us to make general observations that would not be apparent when examining any one application on its own. These contributions allow us to significantly improve prediction when labeled data is available, and they also make learning tractable when the cost of acquiring annotated data is prohibitively high.

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In vitro, G-rich sequences form highly stable secondary structures known as G-Quadruplexes. These structures have been characterized by circular dichroism nuclear magnetic resonance and X-ray crystallography; although their detection in vivo has remained elusive. Due to the biological implication of a transisent and polymorphic secondary structure forming within the hypothetical G-Quadruplex forming regions, there is growing interest to understand their in vivo molecular dynamics. / text

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We discuss results dealing with universal cycles (ucycles) and s-overlap cycles, and contribute to the body of those results by proving existence of universal cycles of naturally labeled posets (NL posets), s-overlap cycles of words of weight k, and juggling patterns. The result on posets is, to the best of our knowledge, the first demonstration of the existence of a ucycle whose length is unknown.