Indexing and processing strings are very important topics in database management. Strings can be database records, DNA sequences, protein sequences, or plain text. Various string operations are required for several application categories, such as bioinformatics and entity resolution. When the string count or sizes become very large, several state-of-the-art techniques for indexing and processing such strings may fail or behave very inefficiently. Modifying an existing technique to overcome these issues is not usually straightforward or even possible. A category of string operations can be facilitated by the suffix tree data structure, which basically indexes a long string to enable efficient finding of any substring of the indexed string, and can be used in other operations as well, such as approximate string matching. In this document, we introduce a novel efficient method to construct the suffix tree index for very long strings using parallel architectures, which is a major challenge in this category. Another category of string operations require clustering similar strings in order to perform application-specific processing on the resulting possibly-overlapping clusters. In this document, based on clustering similar strings, we introduce a novel efficient technique for record linkage and entity resolution, and a novel method for correcting errors in a large number of small strings (read sequences) generated by the DNA sequencing machines.

The most general AdS$_5 imes Y$ solutions of type IIB string theory that are AdS/CFT dual to superconformal field theories in four dimensions can be fruitfully described in the language of generalized geometry, a powerful hybrid of complex and symplectic geometry. We show that the cone over the compact five-manifold $Y$ is generalized Calabi-Yau and carries a generalized holomorphic Killing vector field $xi$, dual to the R-symmetry. Remarkably, this cone always admits a symplectic structure, which descends to a contact structure on $Y$, with $xi$ as Reeb vector field. Moreover, the contact volumes of $Y$, which can be computed by localization, encode essential properties of the dual CFT, such as the central charge and the conformal dimensions of BPS operators corresponding to wrapped D3-branes. We then define a notion of ``generalized Sasakian geometry'', which can be characterized by a simple differential system of three symplectic forms on a four-dimensional transverse space. The correct Reeb vector field for an AdS$_5$ solution within a given family of generalized Sasakian manifolds can be determined---without the need of the explicit metric---by a variational procedure. The relevant functional to minimize is the type IIB supergravity action restricted to the space of generalized Sasakian manifolds, which turns out to be just the contact volume. We conjecture that this contact volume is equal to the inverse of the trial central charge whose maximization determines the R-symmetry of the dual superconformal field theory. The power of this volume minimization is illustrated by the calculation of the contact volumes for a new infinite family of solutions, in perfect agreement with the results of $a$-maximization in the dual mass-deformed generalized conifold theories.

This thesis studies the cosmology of ultra-light scalar fields with masses in the range 10⁻³³ eV ? m ? 10⁻¹⁸ eV and their effects on cosmology. The existence of such fields is motivated by the theoretical framework of the "String Axiverse". All types of string theory contain multiple axion fields associated with antisymmetric tensor fields compactified on closed cycles in the compact space. Since the masses of these fields scale exponentially with the volume of the cycle, it is possible for them to be naturally light. We study the effects of these fields as a component of the dark matter and show analytically and numerically that they cause a suppression of structure formation on cosmological scales set by the inverse mass. We show that it will be possible with future galaxy redshift and weak lensing surveys to detect an ultra- light field comprising of order a percent of the total dark matter. If such a field is allowed to couple to the geometry that provided its mass via a phenomenological scalar potential for the axion and modulus, then the expansion of the universe can be altered significantly. In particular, we find that it is possible to have multiple epochs of accelerated expansion over a large region of parameter space, and to have a flat universe with a big crunch in the distant future. Finally, we address the issue of isocurvature perturbations in axion cosmologies, and demonstrate that in the ultra-light case the power spectrum is effected. This may have implications for the conclusions made about fine tuning in the axiverse in relation to a potential detection of tensor modes in the CMB that are different to the case of a standard axion.

The asymptotic behaviour of an elastically supported infinite string and an elastic isotropic half plane (in frames of specific asymptotic model) under a moving point load are studied. The main results of this work are uniform asymptotic formulae and the asymptotic profile for the string and the exact solution and uniform asymptotic formulae for a half plane. The crucial assumption for both structures is that the acceleration is sufficiently small. In order to describe asymptotically the oscillations of an infinite string auxiliary canonical functions are introduced, asymptotically analyzed and tabulated. Using these functions uniform asymptotic formulae for the string under constant accelerating and decelerating point loads are obtained. Approximate formulae for the displacement in the vicinity of the point load and the singularity area behind the shock wave using the steady speed asymptotic expansion with additional contributions from stationary points where appropriate are derived. It is shown how to generalise uniform asymptotic results to the arbitrary acceleration case. As an example these results are applied for the case of sinusoidal load speed. It is shown that the canonical functions can successfully be used in the arbitrary acceleration case as well. The graphical comparative analysis of numerical solu- tion and approximations is provided for different moving load speed intervals and values of the parameters. Vibrations of an elastic half plane are studied within the framework of the asymp- totic model suggested by J. Kaplunov et al. in 2006. Boundary conditions for the main problem are obtained as a solution for the problem of a string on the surface of a half plane subject to uniformly accelerated moving load. The exact solution over the interior of the half plane is derived with respect to boundary conditions. Steady speed and Rayleigh wave speed asymptotic expansions are obtained. In the neighborhood of the Rayleigh speed the uniform asymptotic formulae are derived. Some of their interesting properties are discovered and briefly studied. The graphical comparative analysis of the exact solution and approximations is provided for different moving load speed intervals and values of the parameters.

This study explored factors relating to participation in public school orchestra programs and the relationship and predictability of such factors in accordance with Maehr's theory of personal investment.

Domenico Gabrielli's seven trumpet sonatas are among seventeenth-century trumpet repertoire predominant in the instrumental tradition of the basilica San Petronio, which flourished roughly from the election of Maurizio Cazzati as maestro di cappella in 1657 until the dissolution of the orchestra of the church in 1695. Fostered by numerous occasions for performance, the Bolognese trumpet works tend to exhibit a uniform musical style imposed by musical academies. After a discussion of the probable cause of the termination of the instrumental tradition and of the role of musical academies, this paper will be primarily concerned with formal aspects of fast movements of Gabrielli's sonatas. Despite the fact that the predominant organizing principle of the fast movements appears to be textural, a step toward ritornello form is taken in some of the movements, in which tutti and solo sections are independently developed. In particular, the recurrence of identical material in tutti confirming different keys, the thematic relation between tutti and solo, and the symmetrical and balanced tonal plan are unmistakable seeds of full ritornello form. The text is followed by critical notes and transcriptions of the seven sonatas.

Efforts to improve diesel fuel sprays have led to a significant increase in fuel injection pressures and a reduction in nozzle-hole diameters. Under these conditions, the likelihood for the internal nozzle flow to cavitate is increased, which potentially affects spray breakup and atomisation, but also increases the risk of causing cavitation damage to the injector. This thesis describes the study of cavitating flow phenomena in various single and multi-hole optical nozzle geometries. It includes the design and development of a high-pressure optical fuel injector test facility with which the cavitating flows were observed. Experiments were undertaken using real-scale optical diesel injector nozzles at fuel injection pressures up to 2050 bar, observing for the first time the characteristics of the internal nozzle-flow under realistic fuel injection conditions. High-speed video and high resolution photography, using laser illumination sources, were used to capture the cavitating flow in the nozzle-holes and sac volume of the optical nozzles, which contained holes ranging in size from 110 micrometers to 300 micrometers. Geometric cavitation in the nozzle-holes and string cavitation formation in the nozzle-holes and sac volume were both observed using transient and steady-state injection conditions; injecting into gaseous and liquid back pressures up to 150 bar. Results obtained have shown that cavitation strings observed at realistic fuel injection pressures exhibit the same physical characteristics as those observed at lower pressures. The formation of string cavitation was observed in the 300 micrometers multi-hole nozzle geometries, exhibiting a mutual dependence on nozzle flow-rate and the geometry of the nozzle-holes. Pressure changes, caused by localised turbulent perturbations in the sac volume and transient fuel injection characteristics, independently affected the geometric and string cavitation formation in each of the holes. String cavitation formation of was shown to occur when free-stream vapour was entrained into the low pressure core of a sufficiently intense coherent vortex. Hole diameters less than or equal to 160 micrometers were found to suppress string cavitation formation, with this effect a result of the reduced nozzle flow rate and vortex intensity. Using different hole spacing geometries, it was demonstrated that the formation of cavitation strings in a particular geometry became independent of fuel injection and back pressure once a threshold pressure drop across the nozzle had been reached.

This thesis is concerned with the Schrödinger representation of quantum field theory. We describe techniques for solving the Schrödinger equation which supplement the standard techniques of field theory. Our aim is to develop these to the point where they can readily be used to address problems of current interest. To this end, we study realistic models such as gauge theories coupled to dynamical fermions. For maximal generality we consider particles of all physical spins, in various dimensions, and eventually, curved spacetimes. We begin by considering Gaussian fields, and proceed to a detailed study of the Schwinger model, which is, amongst other things, a useful model for (3+1) dimensional gauge theory. One of the most important developments of recent years is a conjecture by Mal-dacena which relates supergravity and string/M-theory on anti-de-Sitter spacetimes to conformal field theories on their boundaries. This correspondence has a natural interpretation in the Schrödinger representation, so we solve the Schrödinger equation for fields of arbitrary spin in anti-de-Sitter spacetimes, and use this to investigate the conjectured correspondence. Our main result is to calculate the Weyl anomalies arising from supergravity fields, which, summed over the supermultiplets of type JIB supergravity compactified on AdS(_s) x S(^5) correctly matches the anomaly calculated in the conjecturally dual N = 4 SU{N) super-Yang-Mills theory. This is one of the few existing pieces of evidence for Maldacena's conjecture beyond leading order in TV.

In [GH09] M. Goresky and N. Hingston described and investigated various properties of a product on the cohomology of the free loop space of a closed, oriented manifold M relative to the constant loops. In this thesis we will give Morse and Floer theoretic descriptions of the product. There is a theorem due to J. Jones in [JJ87] which describes an isomorphism between cohomology of the free loop space and Hochschild homology of the singular cochain algebra of M with rational coefficients. We will use the theorem of J. Jones to find an algebraic model for the Goresky-Hingston product. We then use the algebraic model to explore further properties and applications of the Goresky Hingston product. In particular we use it to compute the ring structure for the n-spheres.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, 2016. / The AdS/CFT correspondence is a conjectured exact duality between type IIB string theory on the AdS5 S5 background and N = 4 Super Yang-Mills theory, a conformal eld theory (CFT), on the boundary of the AdS space. A speci c observable of the CFT, which can be read from the two point correlation function, is the anomalous dimension. In this dissertation we will compute spectra of anomalous dimensions of excited giant gravitons up to two loops in a speci c limit. We are interested in the anomalous dimensions because the AdS/CFT correspondence associates them with energies of states in quantum gravity. We study operators constructed using n Z elds and m Y elds with n << m: In this case m n is a small parameter. At the leading order in m n and at large N, the problem of determining the anomalous dimensions can be mapped into the dynamics of m non-interacting magnons. The subleading terms at two loops, computed for the rst time in this dissertation, induce interactions between the magnons. Even after including this new correction, we nd the BPS operators remain BPS. / MT2016