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The phenomenal growth of social media, web forums, and online reviews has spurred a growing interest in automated analysis of user-generated text. At the same time, a proliferation of voice recordings and efforts to archive culture heritage documents are fueling demand for effective automatic speech recognition (ASR) and optical character recognition (OCR). These sources of text all have two qualities in common: they are high in volume, and they frequently diverge from standard language in their surface forms, making them difficult to analyze using conventional methods. To address these challenges, we either need to update our analysis methods to be robust to noisy text, or we need to design a technique to convert such text into a predetermined standard form, or "normalize" it. This document introduces an instance of the latter approach. Many techniques have been proposed to normalize ASR, OCR, and Twitter data, but they have always been treated as separate tasks despite having much in common. To our knowledge, the work presented here is the first to unite these tasks under a single umbrella task of generalized lexical normalization and develop an approach to this task based on deep learning. We introduce two architectures for this purpose. The first uses a simple feed-forward neural network to perform Twitter normalization. This approach is context-insensitive and achieved third place in the Lexical Normalization of English Tweets Challenge conducted with the ACL Workshop on Noisy User Text at the 2015 Annual Meeting of the Association for Computational Linguistics. Our second architecture is an extension of the first that, using concepts from neural machine translation, adds a gated bidirectional recurrent neural network to use the context in which a word appears as well as the characters in the word itself to normalize both Twitter and other sources of noisy text. We evaluate this second architecture on optical character recognition post-processing, automatic speech recognition post-processing, and Twitter text normalization. In comparison with specialized tools for OCR postprocessing and Twitter normalization, we find that our model performs comparably on each of these tasks to the competing model specialized for it and significantly outperforms the model specialized for the other task. This indicates the ability for our model to learn to normalize different types of noise from data, and suggests that it could similarly learn to be effective on other unseen types of noise without the need for expensive feature engineering. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

In addition to the display application, Liquid Crystals (LC) can be very useful in other applications such as beam steering, tunable lenses, etc. Electro-optical LC tunable lenses have been considered as an alternative to conventional glass lenses because of their ability to change their focal length with the application of a control voltage, as well as small size and weight and low power consumption, fast speed, etc. They have a great potential in many applications such as: imaging systems of compact cameras, eye correction, and 3D display systems. So far, while many LC lens designs have been published, high quality performance has been only mentioned in very few papers; also, the level of details in those work is less than what is required to have an accurate evaluation of the performance as well as how it could be improved. Therefore, the main goal of the work in this dissertation is designing high quality or near diffraction limited LC tunable lenses. We will not only introduce our design concepts and considerations, but also demonstrate fine details about the fabrication and evaluations. More importantly, we will use both simulation and experimental approaches for fully understanding the fundamental limiting factors affecting LC lenses. Consequently, we will introduce how they could be optimized and demonstrate the improved performance. In addition, there will be work addressing the concerns about speed, optical power, and off-axis performance. The outline of the dissertation is given as follows, and each chapter has its own focus: In chapter 2, we will review the background of tunable LC lenses, introduce our design, and evaluate its performance in details; in chapter 3, we will investigate the physical limitations and fundamental factors affecting LC lens performance with both simulation and experimental results; in chapter 4, we will introduce the optimized design and demonstrate the improved performance; in chapter 5, we will introduce a multi-cell approach to improve its off-axis imaging performance and achieve a higher optical power, while keeping the fast switching speed; in chapter 6, we will discuss the phase reset methods to achieve higher optical power and fast response; finally in the last chapter, we will make the conclusion and summary. Also, there are four appendices in which we show the detailed LC lens fabrication process, complete optical characterization methods, simulation methods used in this dissertation work and the core Matlab codes, respectively. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

Recently, developments in novel and high-purity materials allow for the presence of a single, solitary crystalline defect to define the electronic, magnetic, and optical functionality of a device. The discrete nature of the active dopant, whose properties are defined by a quantum mechanical description of its structure, enables radically new quantum investigations and applications in these arenas. Finally, there has been significant development in large-scale device engineering due to mature semiconductor manufacturing techniques. The diverse set of photonic device architectures offering light confinement, guiding, and extraction is a prime example. These three paradigms--solitary dopant photonics and optoelectronics (solotronics), quantum science and technology, and device engineering--merge in the development of novel quantum photonic devices for the next generation of information processing systems. We present in this thesis a series of investigations of optical nanostructures for single optically active spins in single crystal diamond. Chapter 1 introduces the Nitrogen-Vacancy (NV) color center, summarizes its applications, and motivates the need for their integration into photonic structures. Chapter 2 describes two prototype nanobeam photonic crystal cavities for generating strong light-matter interactions with NV centers. The first device consists of a silicon nitride photonic crystal nanobeam cavity with high quality factor Q ~ 10[superscript 5] and small mode volume V ~ 0.5*(?/n)[superscript 3]. The second device consists of a monolithic diamond nanobeam cavity fabricated with the focused ion beam (FIB) directly in a single crystal diamond sample. Chapter 3 presents a high-efficiency source of single photons consisting of a single NV center in a photonic diamond nanowire. Early FIB prototypes are described, as is the first successful realization of the device achieved via reactive ion etching nanowires in a single crystal diamond containing NV centers, and finally a variation of this approach based on incorporation of NV centers in pure diamond via ion implantation. In chapter 4 we consider the optimal design of photonic devices offering both collection efficiency and cavity-enhancements and extend the model of the NV center to include photonic effects. In chapter 5 we briefly introduce a novel optically active spin discovered in a diamond nanowire. Finally, in chapter 6 we conclude with several proposals to extend this research program. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

Multibeam interference lithography is investigated as a manufacturing technique for three-dimensional photonic crystal templates. In this research, optimization of the optical setup and the photoresist initiation system leads to a significant improvement of the optical quality of the crystal, as characterized by normal incidence optical spectroscopy. Theoretical spectra are calculated and demonstrate close agreement with experimental values, indicating that this fabrication process achieves excellent optical quality. X-ray microscopy provides non-destructive inspection of the fabricated crystals at nano-scale resolution. A reconstructed crystal model is generated by computed tomography which allows for comparison to a predicted structure's geometry and optical spectra. Using the polymer crystal as a template, electrodeposition is performed to completely infiltrate the crystal with Cu[subscript 2]O. After polymer removal the inverted Cu[subscript 2]O crystal exhibits a high peak reflectance at the predicted wavelength, indicating the structure is an exact inverse of the template. A conformal growth algorithm is developed for the commonly used chemical vapor deposition infiltration technique to explain growth results and verified experimentally with atomic layer deposition of oxide materials. Finally, a customized chemically amplified positive photoresist system and its processing steps are developed as a route to zero-shrinkage template material for high fidelity patterning of the designed interference patterns. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

The field of ultra-cold atoms, since the achievement of Bose-Einstein Condensation (Anderson et al., 1995; Davis et al., 1995; Bradley et al., 1995), have seen an immensely growing interest over the past decade. With the creation of optical lattices, new possibilities of studying some of the widely used models in condensed matter have opened up. In this dissertation we shall study two such problems, one with two component attractive fermions on optical lattices, and the second one with a circular array of Josephson junctions made with independent BECs. In the first part of the dissertation, we shall study fermions with an attractive interaction in an optical lattice with a single-band Hubbard model away from half-filling with on-site attraction "U" and nearest neighbor hopping "t." Our goal is to understand the crossover from BCS (Bardeen-Cooper-Schrieffer) superfluidity in the weak attraction limit to the BEC of molecules in the strong attraction limit, with particular emphasis on how this crossover in an optical lattice differs from the much better studied continuum problem. We use a large "N" theory with Sp(2"N") symmetry to study the fluctuations beyond mean field theory. At "T" = 0, we calculate across the crossover various observables, including chemical potential, gap, ground state energy, speed of sound and compressibility. The superfluid density "n[subscript s]" is found to have nontrivial "U/t" dependence in this lattice system. We show that the transition temperature "T[subscript c]" scales with the energy gap in the weak coupling limit but crosses over to a "t[superscript 2]/U" scaling in the BEC limit, where phase fluctuations controlled by "n[subscript s]" determine "T[subscript c]". We also find, quite contrary to our expectations, that in the strong coupling limit, the large-"N" theory gives qualitatively wrong trends for compressibility. A comparison with a simple Hartree shifted BCS theory, which takes into account both pairing and Hartree shifts, and correctly recovers the atomic limit and the right qualitative trend for compressibility, reveals that the large-"N" theory on the lattice, although considers a larger number of diagrams, is in fact inferior to the simpler Hartree shifted BCS theory. The failure of the large-"N" approach is explained by noting (i) the importance of Hartree shift in lattice problems, and (ii) inability of the large-"N" approach to treat particle-particle and particle-hole channels at equal footing at the saddle point level. In the second half of the dissertation, we investigate the problem of vortex trapping in cyclically coupled Bose-Josephson junctions. Starting with "N" independent BECs we couple the condensates through Josephson links and allow the system to reach a stable circulation by adding a dissipative term in our semiclassical equations of motion. The central question we address is what is the probability to trap a vortex with winding number "m." Our numerical simulations reveal that the final distribution of winding numbers is narrower than the initial distribution of total phases, indicating an increased probability for no-vortex configurations. Specifically, the final width of the distribution of winding numbers for "N" sites scales as "lambda N alpha," where "alpha" = 0.47 +/- 0.01 and lambda is less than 0.67 (value predicted for the initial distribution). The actual value of "lambda" is found to depend on the strength of dissipation. The nonlinearity of the problem also manifests itself in the result that it is possible to obtain a non-zero circulation starting with zero total phase around the loop. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

Artificially engineered metamaterials have emerged with properties and functionalities previously unattainable in natural materials. The scientific breakthroughs made in this new class of electromagnetic materials are closely linked with progress in developing physics-driven design, novel fabrication and characterization methods. The intricate behavior of these novel metamaterials is interesting from both fundamental and practical point of view, New frontiers are being explored as intrinsic limitations challenge the scaling of microwave metamaterial designs to optical frequencies. These materials promise an entire new generation of miniaturized passive and active optical elements. In this study, I demonstrate an on-fiber integrated "fishnet" metamaterial modulator for telecommunication applications. This metamaterial shows remarkable coupling to fiber guided modes (3.5dB) and a photoswitchable tuning range of more than 1.8dB. The design offers extremely small footprint (-10 wavelengths) and complete elimination of bulk optical components to realize low-cost, potential high-speed optical switching and modulation. Unique characterization techniques need to be developed as conventional optical microscopy runs out of steam to resolve the fine features of optical metamaterials. To address this challenge, I have investigated cathodoluminescence imaging and spectroscopy technique. This scanning electron beam based technique allows optical image acquisition and spectroscopy with high spectral and spatial resolution. Monochromatic photon maps (spectral bandwidth -5nm) show strong variation of localized plasmon modes on length scales as small as 25nm. Numerical simulations performed to model the eigenmodes excited by electron beam show strong agreement with experiments. I also demonstrate progress made in "superlensing", a phenomenon associated with plasmonic metamaterials, leading to subdiffraction resolution with optical imaging. Fabricating a smooth silver superlens (0.6nm root mean square roughness) with 15nm thickness, I demonstrate 30nm imaging resolution or 1/12th of the illumination wavelength (near-ultraviolet), far below the diffraction-limit. Moreover. I have extended subdiffraction imaging to far-field at infrared wavelengths. Utilizing a two-dimensional array of silver nanorods that provides near-field enhancement, I numerically show that subwavelength features can be resolved in far-field in the form of Moire features. Development of this unique far-field superlensing phenomenon at infrared wavelengths is of significant importance to chemical and biomedical imaging. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

Intercellular signaling is vital to communication within neuronal circuits. The suprachiasmatic nucleus (SCN), the master circadian clock of mammals, contains a dense collection of neurons that align their intrinsic rhythmicity with environmental stimulus and physiological state. While peptide physiology has been demonstrated as a contributor to SCN signal processing, the tools to explore and directly implicate peptides in SCN cell-to-cell signaling have not been utilized. By combining mass spectrometry and physiology, this thesis used novel peptidomics methodologies to discover new peptides and evaluate their functions in circadian clock phasing of the rat SCN. Coupling various peptide sampling techniques to MS analytical approaches enables detection with high spatial resolution. Electrical optic nerve (ON) stimulation in a horizontal SCN slice model is effective in shifting SCN clock phase. Effective stimulation parameters are time-of-day-specific; effective late night parameters are ineffective in generating early night phase shifts and vice-versa. Moreover, these phase shifting stimuli elicit peptide release from the SCN. Suites of released peptides correspond with time-of-day- and stimulus-specific phase shifting. Peptide release is not evoked by ON stimulation parameters that are ineffective in phase resetting. One previously unreported SCN peptide, little SAAS, was selected for further characterization. Sterological analysis confirms that little SAAS-positive cells comprise the third most abundant subpopulation of peptidergic neurons in the rat SCN. Little SAAS immunohistochemistry reveals localization to the retinorecipient ventrolateral SCN core. Up-regulation of immediate-early gene product c-Fos occurs in approximately 50% of little SAAS neurons following "in vivo" exposure to a light pulse at early night, implicating these neurons in light-responsiveness. Exogenous little SAAS is capable of shifting the phase of rhythmic firing rates of SCN brain slices in a dose- and time-of-day-dependent manner. Glutamate-induced phase shifting is blocked by exogenous treatment of the SCN slice with little SAAS antiserum, while little SAAS peptide-induced phase shifting is not blocked by NMDA receptor antagonist APV. Gastrin-releasing peptide (GRP) and vasoactive intestinal polypeptide (VIP) are involved in relay and processing of light signal information in the SCN. Little SAAS phase shifting persists in the presence of selective GRP and VIP receptor antagonists. These studies position little SAAS downstream of NMDA receptor activation and parallel to the known intra-SCN communication signals, GRP and VIP. This thesis justifies functional peptidomics as a useful approach to understanding intercellular signaling mechanisms regulating SCN clock phase. Directly detecting dynamic release properties of peptides from the SCN brain slice provides new insights on a complex phenomenon phenomenon. The identification and characterization of little SAAS serves as an example of the facets of SCN physiology left to be discovered. Utilization of peptidomics strategies will significantly advance understanding of timing homeostatic mechanisms. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]

It has been more than two decades since the copper-oxide high temperature superconductors were discovered. However, building a satisfactory theoretical framework to study these compounds still remains one of the major challenges in condensed matter physics. In addition to the mechanism of superconductivity, understanding the properties of the normal state is a major puzzle in itself. As these materials are doped Mott insulators, the interaction between electrons is particularly strong. The strong electron correlations are responsible for the breakdown of Fermi-liquid behavior in the normal state. A variety of experimental probes reveal anomalous features in these materials. Such anomalies are reflected in the photoemission spectra as well as transport coefficients such as resistivity, optical conductivity, Hall coefficient, thermoelectric power etc. The objective of this dissertation is to understand the anomalous features as universal features of doped Mott insulators arising entirely as a consequence of strong electron correlations, using the two-dimensional square lattice Hubbard model as the model Hamiltonian. This dissertation is organized into eight chapters. Chapter 1 is an introductory chapter that discusses some key issues. A brief introduction to the superconducting cuprates and their anomalous physical properties is given. Also included is an outline on Mott insulators and the concept of Mottness. Chapter 2 contains a discussion on Cluster Dynamical Mean Field Theory (CDMFT), the principal numerical technique to be implemented in this dissertation. Chapter 3 describes the exact low-energy theory of doped Mott insulators, which largely provides a theoretical framework to this dissertation. In Chapter 4, we compute the spectral function of the two-dimensional Hubbard model using CDMFT and study the origin of the kink feature observed in the electron dispersion measured by ARPES (Angle Resolved Photoemission Spectroscopy). In Chapter 5, the origin of the mid-IR band seen in optics experiments is studied. In Chapter 6, we study the universal sign change of the thermopower in the vicinity of optimal doping in the cuprates. Chapter 7 uses experimental data from Hall measurements to establish a connection between the pseudogap state and the charge-2e boson which emerges naturally in the exact low-energy theory of Mott systems. Chapter 8 is the concluding chapter which attempts to present all of our findings within the context of the central unifying theme of Mottness. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]