<p>In the first part of this thesis we present a C++ implementation of an improved O(n log n) algorithm to compute runs, number of primitively rooted distinct squares, and maximal repetitions, based on Crochemore's partitioning algorithm. This is a joint work with Mei Jiang and extends her work on the problem. In the second part we present a C++ implementation of a linear algorithm to compute runs based on the Main's, and Kolpakov and Kucherov's algorithms following the strategy:</p> <p>1. Compute suffix array and LCP array in linear time;</p> <p>2. Using the suffix array and LCP array, compute Lempel-Ziv factorization in linear time;</p> <p>3. Using the Lempel-Ziv factorization, compute in linear time some of the runs that include all the leftmost runs following Main's algorithm;</p> <p>4. Using Kolpakov and Kucherov's approach, compute in linear time the rest of all the runs.</p> <p>For our linear time implementation, we partially relied on Jonathan Fischer's Java implementation.</p> / Master of Science (MSc)

Extended piano techniques, which mainly involve playing directly on the internal components of the piano, emerged early in the twentieth century, mainly in the United States. Henry Cowell (1897-1965) explored some of these techniques in short piano pieces such as The Tides of Manaunaun (1917; clusters) The Banshee (1925; glissando, pizzicato) and Sinister Resonance (1930; mute, harmonic). Several contemporary composers followed this path. Notably, George Crumb's (b. 1929) mature works combine conventional techniques with an unprecedented variety of extended techniques, including vocal and percussive effects. Although extended techniques are no longer a novelty, most pianists are still unfamiliar with them. Extended piano works are rarely performed or taught. This situation is regrettable considering the quality of these compositions, and the great potential of extended techniques to expand the piano's coloristic resources. A Pedagogical Guide to Extended Piano Techniques is designed to help pianists learn this idiom and achieve fluency. Teachers may also find it useful in planning courses at the undergraduate college level. Chapters 1 and 2 provide general information such as the development and classification of unconventional techniques, and the construction of the grand piano. Chapters 3, 4 and 5 form the core of the monograph. They contain practical exercises, composed by the author, presented in a progressive order and accompanied by detailed instructions explaining how to execute and practice each technique. From a technical point of view, natural string piano techniques--pizzicatos, glissandos, mutes and harmonics--are the basis upon which most other extended techniques are founded. Therefore, this document focuses mainly on mastering these string techniques through the acquisition of two important skills: visual techniques and aural-motor coordination. The following topics are also discussed: use of foreign objects inside the piano, percussive technique, vocal effects, and strategies to integrate various techniques into a unified musical context. Prepared piano techniques are excluded because they do not require the acquisition of performance skills, which form the essence of this monograph. Chapter 6 provides a suggested course schedule to organize the pianist's study and practice time, and offers practical advice for the preparation of performances involving extended piano techniques. It is hoped that this document will play a positive role in helping pianists gain the knowledge, ability, confidence and enthusiasm to explore and perform extended piano repertoire. / Music Performance

Since the advent of electronic data processing, organizations have accrued vast amounts of data contained in multiple databases with no reliable global unique identifier. These databases were developed by different departments for different purposes at different times. Organizing and analyzing these data for human services requires linking records from all sources. RL (Record Linkage) is a process that connects records that are related to the identical or a sufficiently similar entity from multiple heterogeneous databases. RL is a data and compute intensive, mission critical process. The process must be efficient enough to process big data and effective enough to provide accurate matches. We have evaluated an RL system that is currently in use by a local health and human services department. We found that they were using the typical approach that was offered by Fellegi and Sunter with tuple-by-tuple processing, using the Soundex as the primary approximate string matching method. The Soundex has been found to be unreliable both as a phonetic and as an approximate string matching method. We found that their data, in many cases, has more than one value per field, suggesting that the data were queried from a 5NF data base. Consider that if a woman has been married 3 times, she may have up to 4 last names on record. This query process produced more than one tuple per database/entity apparently generating a Cartesian product of this data. In many cases, more than a dozen tuples were observed for a single database/entity. This approach is both ineffective and inefficient. An effective RL method should handle this multi-data without redundancy and use edit-distance for approximate string matching. However, due to high computational complexity, edit-distance will not scale well with big data problems. We developed two methodologies for resolving the aforementioned issues: PSH and ALIM. PSH – The Probabilistic Signature Hash is a composite method that increases the speed of Damerau-Levenshtein edit-distance. It combines signature filtering, probabilistic hashing, length filtering and prefix pruning to increase the speed of edit-distance. It is also lossless because it does not lose any true positive matches. ALIM – Aggregate Link and Iterative Match is a graph-based record linkage methodology that uses a multi-graph to store demographic data about people. ALIM performs string matching as records are inserted into the graph. ALIM eliminates data redundancy and stores the relationships between data. We tested PSH for string comparison and found it to be approximately 6,000 times faster than DL. We tested it against the trie-join methods and found that they are up to 6.26 times faster but lose between 10 and 20 percent of true positives. We tested ALIM against a method currently in use by a local health and human services department and found ALIM to produce significantly more matches (even with more restrictive match criteria) and that ALIM ran more than twice as fast. ALIM handles the multi-data problem and PSH allows the use of edit-distance comparison in this RL model. ALIM is more efficient and effective than a currently implemented RL system. This model can also be expanded to perform social network analysis and temporal data modeling. For human services, temporal modeling can reveal how policy changes and treatments affect clients over time and social network analysis can determine the effects of these on whole families by facilitating family linkage. / Computer and Information Science

Using Monte Carlo simulations and analytic methods, we examine the dynamics of inter-species competition using the Penna bit-string model. We begin with a study of the steady state with a single species, then proceed to the dynamics of competition between two species. When the species are not evenly matched in fitness, a simple differential equation provides a satisfactory model of the behavior of the system. However, when the species are equally fit, we show that a model, originally proposed to describe population genetics [Fisher,Wright], is required. When mutations are allowed between the competing species, the dynamics becomes more interesting. The mutation rate becomes a parameter that dictates the steady state behavior. If the two species are not equally fit, the value of the mutation rate determines whether the longer-lived or faster reproducing species is favored. With two species that are equally fit, the steady state varies with mutation rate from a single peaked to a double peaked distribution. This behavior is shown to be well described by an extension to the Fisher-Wright model mentioned above. Finally, we describe the preliminary results of a few new lines of investigation, and suggest ideas for further study of the dynamics of this model. / Ph. D.

This thesis is devoted to a discussion of two-dimensional theories with (0,2) supersymmetry. Examples of two-dimensional (0,2) gauged linear sigma models (GLSMs) are constructed for various spaces including Grassmannians, complete intersections in Grassmannians, and non-complete intersections such as Pfaffians. Generalizations of (2,2) Toda dual theories to (0,2) Toda-like theories are also discussed and some examples are given, including products of projective spaces and del Pezzo surfaces. Correlation functions are computed to show the examples are the correct mirror models. / Ph. D.

Traffic congestion and safety has become a major issue in the modern world's commute. Congestion has been causing people to travel billions of hours more and to purchase billions of gallons of fuel extra which account to congestion cost of billions of dollars. Autonomous driving vehicles have been one solution to this problem because of their huge impact on efficiency, pollution, and human safety. Also, extensive research has been carried out on control design of vehicular platoons because a further improvement in traffic throughput while not compromising the safety is possible when the vehicles in the platoon are provided with better predictive abilities. Motion control is a key area of autonomous driving research that handles moving parts of vehicles in a deliberate and controlled manner. A widely worked on problem in motion control concerned with time parameterized reference tracking is trajectory tracking. Having an efficient and effective tracking algorithm embedded in the autonomous driving system is the key for better performance in terms of resources consumed and tracking error. Many tracking control algorithms in literature rely on an accurate model of the vehicle and often, it can be an intimidating task to come up with an accurate model taking into consideration various conditions like friction, heat effects, ageing processes etc. And typically, control algorithms rely on periodic execution of the tasks that update the control actions, but such updates might not be required, which result in unnecessary actions that waste resources. The main focus of this work is to design an intermittent model-free optimal control algorithm in order to enable autonomous vehicles to track trajectories at high-speeds. To obtain a solution which is model-free, a Q-learning setup with an actor-network to approximate the optimal intermittent controller and a critic network to approximate the optimal cost, resulting in the appropriate tuning laws is considered. / Master of Science / A risen research effort in the area of autonomous vehicles has been witnessed in the past few decades because these systems improve safety, comfort, transport time and energy consumption which are some of the main issues humans are facing in the modern world’s highway systems. Systems like emergency braking, automatic parking, blind angle vehicle detection are creating a safer driving environment in populated areas. Advanced driver assistance systems (ADAS) are what such kind of systems are known as. An extension of these partially automated ADAS are vehicles with fully automated driving abilities, which are able to drive by themselves without any human involvement. An extensively proposed approach for making traffic throughput more efficient on existing highways is to assemble autonomous vehicles into platoons. Small intervehicle spacing and many vehicles constituting each platoon formation improve the traffic throughput significantly. Lately, the advancements in computational capabilities, in terms of both algorithms and hardware, communications, and navigation and sensing devices contributed a lot to the development of autonomous systems (both single and multiagent) that operate with high reliability in uncertain/dynamic operating conditions and environments. Motion control is an important area in the autonomous vehicles research. Trajectory-tracking is a widely studied motion control scenario which is about designing control laws that force a system to follow some time-dependent reference path and it is important to have an effective and efficient trajectory-tracking control law in an autonomous vehicle to reduce the resources consumed and tracking error. The goal of this work is to design an intermittent model-free trajectory tracking control algorithm where there is no need of any mathematical model of the vehicle system being controlled and which can reduce the controller updates by allowing the system to evolve in an open loop fashion and close the loop only when an user defined triggering condition is satisfied. The approach is energy efficient in that the control updates are limited to instances when they are needed rather than unnecessary periodic updates. Q-learning which is a model-free reinforcement learning technique is used in the trajectory tracking motion control algorithm to make the vehicles track their respective reference trajectories without any requirement of their motion model, the knowledge of which is generally needed when dealing with a motion control problem. The testing of the designed algorithm in simulations and experiments is presented in this work. The study and development of a vehicle platform in order to perform the experiments is also discussed. Different motion control and sensing techniques are presented and used. The vehicle platform is shown to track a reference trajectory autonomously without any human intervention, both in simulations and experiments, proving the effectiveness of the proposed algorithm.

Slender structures in fluid flow exhibit a variety of rich behaviors. Here we study the equilibrium shapes of perfectly flexible strings that are moving with a uniform velocity and axial flow in viscous fluid. The string is acted upon by local, anisotropic, linear drag forces and a uniform body force. Generically, the configurations of the string are planar, and we provide analytical expressions for the equilibrium shapes of the string as a first order five parameter dynamical system for the tangential angle of the body ($theta$). Phase portraits in the angle-curvature ($theta,partial_s theta$) plane are generated, that can be shown to be $pi$ periodic after appropriate scaling and reflection operations. The rich parameter space allows for different kinds of phase portraits that give rise to a variety of curve geometries. Some of these solutions are unstable due to the presence of compressive stresses. Special cases of the problem include sedimenting filaments, dynamic catenaries, and towed strings. We also discuss equilibrium configurations of towed cables and other relevant problems with fixed boundary conditions. Special cases of the boundary value problem involve towing of neutrally buoyant cables and strings with pure axial flow between two fixed points. / Master of Science

In this thesis, we apply the methods of numerical differential geometry to several different problems in heterotic Calabi-Yau compactification. We review algorithms for computing both the Ricci-flat metric on Calabi-Yau manifolds and Hermitian Yang-Mills connections on poly-stable holomorphic vector bundles over those spaces. We apply the numerical techniques for obtaining Ricci-flat metrics to study hierarchies of curvature scales over Calabi-Yau manifolds as a function of their complex structure moduli. The work we present successfully finds known large curvature regions on these manifolds, and provides useful information about curvature variation at general points in moduli space. This research is important in determining the validity of the low energy effective theories used in the description of Calabi-Yau compactifications. The numerical techniques for obtaining Hermitian Yang-Mills connections are applied in two different fashions in this thesis. First, we demonstrate that they can be successfully used to numerically determine the stability of vector bundles with qualitatively different features to those that have appeared in the literature to date. Second, we use these methods to further develop some calculations of holomorphic Chern-Simons invariant contributions to the heterotic superpotential that have recently appeared in the literature. A complete understanding of these quantities requires explicit knowledge of the Hermitian Yang-Mills connections involved. This feature makes such investigations prohibitively hard to pursue analytically, and a natural target for numerical techniques. / Doctor of Philosophy / String theory is one of the most promising attempts to unify gravity with the other three fundamental interactions (electromagnetic, weak and strong) of nature. It is believed to give a self-consistent theory of quantum gravity, which, at low energy, could contain all of the physics that we known, from the Standard Model of particle physics to cosmology. String theories are often defined in nine spatial dimensions. To obtain a theory with three spatial dimensions one needs to hide, or ``compactify," six of the dimensions on a compact space which is small enough to have remained unobserved by our experiments. Unfortunately, the geometries of these spaces, called Calabi-Yau manifolds, and additional structures associated to them, called holomorphic vector bundles, turns out to be extremely complex. The equations determining the exact solutions of string theory for these quantities are highly non-linear partial differential equations (PDE's) which are simply impossible to solve analytically with currently known techniques. Nevertheless, knowledge of these solutions is critical in understanding much of the detailed physics that these theories imply. For example, to compute how the particles seen in three dimensions would interact with each other in a string theoretic model, the explicit form of these solutions would be required. Fortunately, numerical methods do exist for finding approximate solutions to the PDE's of interest. In this thesis we implement these algorithmic techniques and use them to study a variety of physical questions associated to the attempt to link string theory to the physics observed in our experiments.

In this work, we extend the well-known spectral cover construction first developed by Friedman, Morgan, and Witten to describe more general vector bundles on elliptically fibered Calabi-Yau geometries. In particular, we consider the case in which the Calabi-Yau fibration is not in Weierstrass form but can rather contain fibral divisors or multiple sections (i.e., a higher rank Mordell-Weil group). In these cases, general vector bundles defined over such Calabi-Yau manifolds cannot be described by ordinary spectral data. To accomplish this, we employ well-established tools from the mathematics literature of Fourier-Mukai functors. We also generalize existing tools for explicitly computing Fourier-Mukai transforms of stable bundles on elliptic Calabi-Yau manifolds. As an example of these new tools, we produce novel examples of chirality changing small instanton transitions. Next, we provide a geometric formalism that can substantially increase the understood regimes of heterotic/F-theory duality. We consider heterotic target space dual (0,2) GLSMs on elliptically fibered Calabi-Yau manifolds. In this context, each half of the ``dual" heterotic theories must, in turn, have an F-theory dual. Moreover, the apparent relationship between two heterotic compactifications seen in (0,2) heterotic target space dual pairs should, in principle, induce some putative correspondence between the dual F-theory geometries. It has previously been conjectured in the literature that (0,2) target space duality might manifest in F-theory as multiple $K3$-fibrations of the same elliptically fibered Calabi-Yau manifold. We investigate this conjecture in the context of both 6-dimensional and 4-dimensional effective theories and demonstrate that in general, (0,2) target space duality cannot be explained by such a simple phenomenon alone. In all cases, we provide evidence that non-geometric data in F-theory must play at least some role in the induced F-theory correspondence while leaving the full determination of the putative new F-theory duality to the future work. Finally, we consider F-theory over elliptically fibered manifolds, with a general conic base. Such manifolds are quite standard in F-theory sense, but our goal is to explore the extent of the heterotic/F-theory duality over such manifolds. We consider heterotic target space dual (0,2) GLSMs on elliptically fibered Calabi-Yau manifolds. In this context, each half of the ``dual" heterotic theories must, in turn, have an F-theory dual. Moreover, the apparent relationship between two heterotic compactifications seen in (0,2) heterotic target space dual pairs should, in principle, induce some putative correspondence between the dual F-theory geometries. It has previously been conjectured in the literature that (0,2) target space duality might manifest in F-theory as multiple $K3$-fibrations of the same elliptically fibered Calabi-Yau manifold. We investigate this conjecture in the context of both 6-dimensional and 4-dimensional effective theories and demonstrate that in general, (0,2) target space duality cannot be explained by such a simple phenomenon alone. In all cases, we provide evidence that non-geometric data in F-theory must play at least some role in the induced F-theory correspondence while leaving the full determination of the putative new F-theory duality to the future work. Finally, we consider F-theory over elliptically fibered manifolds, with a general conic base. Such manifolds are quite standard in F-theory sense, but our goal is to explore the extent of the heterotic/F-theory duality over such manifolds. / Doctor of Philosophy / String theory is the only physical theory that can lead to self-consistent, effective quantum gravity theories. However, quantum mechanics restricts the dimension of the effective spacetime to ten (and eleven) dimensions. Hence, to study the consequences of string theory in four dimensions, one needs to assume the extra six dimensions are curled into small compact dimensions. Upon this ``compactification," it has been shown (mainly in the 1990s) that different classes of string theories can have equivalent four-dimensional physics. Such classes are called dual. The advantage of these dualities is that often they can map perturbative and non-perturbative limits of these theories. The goal of this dissertation is to explore and extend the geometric limitations of the duality between heterotic string theory and F-theory. One of the main tools in this particular duality is the Fourier-Mukai transformation. In particular, we consider Fourier-Mukai transformations over non-standard geometries. As an application, we study the F-theory dual of a heterotic/heterotic duality known as target space duality. As another side application, we derive new types of small instanton transitions in heterotic strings. In the end, we consider F-theory compactified over particular manifolds that if we consider them as a geometry dual to a heterotic string, can lead to unexpected consequences.

A wide range of physical systems are modeled as axially moving strings; such examples are belts, tapes, wires and fibers with applied electromagnetic fields. In this study, we propose a model that describes the motion of a current-carrying conductive string in a lateral magnetic field, while it is being pulled axially. This model is a generalization of past studies that have neglected one or more properties featured in our system. It is assumed that the string is moving with a constant velocity between two rings that are a finite distance apart. Directions of the magnetic field and the motion of the string coincide. The problem is first considered in a static setting. Stability critical values of the magnetic field, pulling speed, and current are shown to exist when the uniform motion (along a string line) of the string buckles into spiral forms. In the dynamic setting, conditions for stability of certain solutions are presented and discussed. It is shown that there is a divergence between the critical values in the linear dynamic and static cases. Furthermore, traveling wave solutions are examined for certain cases of our general system. We develop an approximate solution for a nonlinear moving string when a periodic nonstationary current flows through the string. Domains of parameters are defined when the string falls into a pre-chaotic state, i.e., the frequency of vibrations is doubled. / MS / The modeling and analysis of elastic conductors has applications in areas ranging from manufacturing to particle physics. In this study, we model the motion of a conductive string being pulled (between two rings) while a magnetic field is applied in the lateral direction. This system’s stability is categorized through certain parameters such as the applied magnetic field, speed of pulling, and current flowing through the string. The equilibrium states are also analyzed. When the string has a periodic current, approximate solutions (string shape/orientation) are computed. In this case, we find domains of parameters that give rise to chaos. Wave speeds of traveling wave solutions are also found for certain cases.