Thesis (Ph. D.)--University of Texas at Austin, 2003. / Vita. Includes bibliographical references. Available also from UMI Company.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

Thesis (M.S.), Eastern Illinois University, 2003. / Includes bibliographical references (leaves 52-57).

Thesis--Ph. D., University of Hong Kong, 1986.

We present a novel concept to design apertureless plasmonic probes for near-field scanning optical microscopy (NSOM) with enhanced optical power throughput and near-field confinement. Specifically, we combine unidirectional surface plasmon polariton (SPP) generation along the tip lateral walls with nanofocusing of SPPs through adiabatic propagation towards an apertureless tip. Three probe designs are introduced with different light coupling mechanisms. Optimal design parameters are obtained with 2D analysis and realistic probe geometries with patterned plasmonic surfaces are proposed using the optimized designs. The electromagnetic properties of the designed probes are characterized in the near-field and compared to those of a conventional single-aperture probe with same pyramidal shape. The optimized probes feature enhanced light localization in near-field of tip apex and improved optical throughput. Our ideas effectively combine the resolution of apertureless probes with throughput levels much larger than those available even in aperture-based devices. / text

Graphical model, the marriage between graph theory and probability theory, has been drawing increasing attention because of its many attractive features. In this paper, we consider the problem of learning the structure of graphical model based on observed data through a greedy forward-backward algorithm and with the use of learned model to classify the data into different categories. We establish the graphical model associated with a binary Ising Markov random field. And model selection is implemented by adding and deleting edges between nodes. Our experiments show that: compared with previous methods, the proposed algorithm has better performance in terms of correctness rate and model selection. / text

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This dissertation gives a general account of the properties of unitarily inequivalent representations (UIRs) in both canonical quantum field theory and algebraic quantum field theory. A simple model is constructed and then used to show how to build a broad spectrum of UIRs including a version of Haag’s theorem. Haag and Kastler,P, two of the founding fathers of algebraic quantum field theory, argue that the problems posed by UIRs are solved by adopting a notion of equivalence that is weaker than unitary equivalence, which they refer to as physical equivalence. In the dissertation, it is shown that their notion does not provide a suitable classificatory schema. Some of the most important physical representations fail to satisfy the mathematical conditions of their notion. However, Haag and Kastler's notion has an unexpected connection with classical observables. A theorem is proven in which two representations make the same predictions with respect to all classical observables if and only if they satisfy their notion of physical equivalence. Following Haag and Kastler's lead, it was claimed by most proponents of algebraic quantum field theory that all physical content resides in a specific class of observables. It is shown in the dissertation that such claims are exaggerated and misleading. UIRs are used to elucidate the nature of quantum field theory by showing that UIRs have different expectation values for some classical observables of the system, such as temperature and chemical potential, which are not in Haag and Kastler’s specific class. It is shown how UIRs may be used to construct classical observables. To capture the physical content of quantum field theory it is shown that a much larger algebra than that of Haag and Kastler is necessary. Finally, the arguments that UIRs are incommensurable theories are shown to be flawed. The lesson of UIRs is that the mathematical structures in both canonical quantum field theory and Haag and Kastler’s version of algebraic quantum field theory are not sufficient to capture all of the physical content that UIRs represent. A suitable algebraic structure for quantum field theory is provided in the dissertation. / text