The main purpose of this thesis is to define the stability of a system of linear difference equations of the form, ∇y(t) = Ay(t), and to analyze the stability theory for such a system using the eigenvalues of the corresponding matrix A in nabla discrete calculus and nabla fractional discrete calculus. Discrete exponential functions and the Putzer algorithms are studied to examine the stability theorem. This thesis consists of five chapters and is organized as follows. In the first chapter, the Gamma function and its properties are studied. Additionally, basic definitions, properties and some main theorem of discrete calculus are discussed by using particular example. In the second chapter, we focus on solving the linear difference equations by using the undetermined coefficient method and the variation of constants formula. Moreover, we establish the matrix exponential function which is the solution of the initial value problems (IVP) by the Putzer algorithm.

A stationary or temporary offset in the steering system of a vehicle can result in functions, relying on the steering wheel angle, performing poorly. Due to the wide range of different vehicle configurations at Scania CV, all sensors with relevant information regarding vehicle direction are not available on all vehicles. By using a statistical approach, including common sensors installed on the vehicle, a conceptual algorithm calibrating the Steering Wheel Angle Sensor offset in real- time has been developed. The algorithm is simple and relies on the assumption that a vehicle is driving straight ahead most of the time above a certain minimum vehicle speed, thus the most frequent steering wheel angle is the straight ahead angle. The algorithm is only active above the certain minimum vehicle speed and consists of two moving windows comprising steering wheel angle samples in which the calculations are performed. The results show that the algorithm is able to detect offsets with a short calibration time. Storage of samples is required but no vehicle specific parameters are needed.

The main results of this dissertation show evidence supporting the Successive Surface Scaffolding Conjecture. This is a new conjecture that, if true, guarantees the existence of all the wye-delta-order minimal obstructions of a surface S as subgraphs of the irreducible triangulations of the surface S with a crosscap added. A new data structure, i.e. an augmented rotation system, is presented and used to create an exponential-time algorithm for embedding graphs in any surface with a constant-time check of the change in genus when inserting an edge. A depiction is a new formal definition for representing an embedding graphically, and it is shown that more than one depiction can be given for nonplanar embeddings, and that sometimes two depictions for the same embedding can be drastically different from each other. An algorithm for finding the essential cycles of an embedding is given, and is used to confirm for the projective-plane obstructions, a theorem that shows any embedding of an obstruction must have every edge in an essential cycle. Obstructions of a general surface S that are minor-minimal and not double-wye-delta-minimal are shown to each have an embedding on the surface S with a crosscap added. Finally, open questions for further research are presented. / Graduate

Approved for public release; distribution is unlimited / Reissued 30 May 2017 with Second Reader’s non-NPS affiliation added to title page. / Online propaganda embodies a potent new form of warfare; one that extends the strategic reach of our adversaries and overwhelms analysts. Foreign organizations have effectively leveraged an online presence to influence elections and distance-recruit. The Islamic State has also shown proficiency in outsourcing violence, proving that propaganda can enable an organization to wage physical war at very little cost and without the resources traditionally required. To augment new counter foreign propaganda initiatives, this thesis presents a pipeline for defining, detecting and monitoring ideology in text. A corpus of 3,049 modern online texts was assembled and two classifiers were created: one for detecting authorship and another for detecting ideology. The classifiers demonstrated 92.70% recall and 95.84% precision in detecting authorship, and detected ideological content with 76.53% recall and 95.61% precision. Both classifiers were combined to simulate how an ideology can be detected and how its composition could be passively monitored across time. Implementation of such a system could conserve manpower in the intelligence community and add a new dimension to analysis. Although this pipeline makes presumptions about the quality and integrity of input, it is a novel contribution to the fields of Natural Language Processing and Information Warfare. / Lieutenant, United States Coast Guard

An option, a type of a financial derivative, is a contract that creates an opportunity for a market player to avoid risks involved in investing, especially in equities. An investor desires to know the accurate value of an option before entering into a contract to buy/sell the underlying asset (stock). There are various techniques that try to simulate real market conditions in order to price or evaluate an option. However, most of them achieved limited success due to high uncertainty in price behavior of the underlying asset. In this study, I propose two new Firefly variant algorithms to compute accurate worth for European and American option contracts and compare them with popular option pricing models (such as Black-Scholes-Merton, binomial lattice, Monte-Carlo, etc.) and real market data. In my study, I have first modelled the option pricing as a multi-objective optimization problem, where I introduced the pay-off and probability of achieving that pay-off as the main optimization objectives. Then, I proposed to use a latest nature-inspired algorithm that uses the bioluminescence of Fireflies to simulate the market conditions, a first attempt in the literature. For my thesis, I have proposed adaptive weighted-sum based Firefly algorithm and non-dominant sorting Firefly algorithm to find Pareto optimal solutions for the option pricing problem. Using my algorithm(s), I have successfully computed complete Pareto front of option prices for a number of option contracts from the real market (Bloomberg data). Also, I have shown that one of the points on the Pareto front represents the option value within 1-2 % error of the real data (Bloomberg). Moreover, with my experiments, I have shown that any investor may utilize the results in the Pareto fronts for deciding to get into an option contract and can evaluate the worth of a contract tuned to their risk ability. This implies that my proposed multi-objective model and Firefly algorithm could be used in real markets for pricing options at different levels of accuracy. To the best of my knowledge, modelling option pricing problem as a multi-objective optimization problem and using newly developed Firefly algorithm for solving it is unique and novel. / October 2016

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This thesis consists of four papers that concern error estimates for the Born-Oppenheimer molecular dynamics, and adaptive algorithms for the Car-Parrinello and Ehrenfest molecular dynamics. In Paper I, we study error estimates for the Born-Oppenheimer molecular dynamics with nearly crossing potential surfaces. The paper first proves an error estimate showing that the difference of the values of observables for the time-independent Schrödinger equation, with matrix valued potentials, and the values of observables for the ab initio Born-Oppenheimer molecular dynamics of the ground state depends on the probability to be in the excited states and the nuclei/electron mass ratio. Then we present a numerical method to determine the probability to be in the excited states, based on the Ehrenfest molecular dynamics, and stability analysis of a perturbed eigenvalue problem. In Paper II, we present an approach, motivated by the so called Landau-Zener probability estimation, to systematically choose the artificial electron mass parameters appearing in the Car-Parrinello and Ehrenfest molecular dynamics methods to approximate the Born-Oppenheimer molecular dynamics solutions. In Paper III, we extend the work presented in Paper II for a set of more general problems with more than two electron states. A main conclusion of Paper III is that it is necessary to resolve the near avoided conical intersections between all electron eigenvalue gaps, including gaps between the occupied states. In Paper IV, we numerically compare, using simple model problems, the Ehrenfest molecular dynamics using the adaptive mass algorithm proposed in Paper II and III and the Born-Oppenheimer molecular dynamics based on the so called purification of the density matrix method concluding that the Born-Oppenheimer molecular dynamics based on purification of density matrix method performed better in terms of computational efficiency. / <p>QC 20161102</p>

A search for vector-like quarks (VLQs) decaying to a Z boson using multi-stage machine learning was compared to a search using a standard square cuts search strategy. VLQs are predicted by several new theories beyond the Standard Model. The searches used 20.3 inverse femtobarns of proton-proton collisions at a center-of-mass energy of 8 TeV collected with the ATLAS detector in 2012 at the CERN Large Hadron Collider. CLs upper limits on production cross sections of vector-like top and bottom quarks were computed for VLQs produced singly or in pairs, Tsingle, Bsingle, Tpair, and Bpair. The two stage machine learning classification search strategy did not provide any improvement over the standard square cuts strategy, but for Tpair, Bpair, and Tsingle, a third stage of machine learning regression was able to lower the upper limits of high signal masses by as much as 50%. Additionally, new test statistics were developed for use in the Neyman construction of confidence regions in order to address deficiencies in current frequentist methods, such as the generation of empty set confidence intervals. A new method for treating nuisance parameters was also developed that may provide better coverage properties than current methods used in particle searches. Finally, significance ratio functions were derived that allow a more nuanced interpretation of the evidence provided by measurements than is given by confidence intervals alone.

Objectives. The goal in radiotherapy is to deliver adequate radiation to the tumor volume while limiting damage to the surrounding healthy tissue. However, this goal is challenged by respiratory-induced motion. The objective of this work was to identify whether motion in electronic portal images can be tracked with an optical flow algorithm and whether a neural network can predict tumor motion. Methods. A multi-resolution optical flow algorithm that incorporates weighting based on the differences between image frames was used to automatically sample the vectors corresponding to the motion. The global motion was obtained by computing the average weighted mean from the set of vectors. The algorithm was evaluated using tumor trajectories taken from seven lung cancer patients, a 3D printed patient tumor and a virtual dynamic multi-leaf collimator (DMLC) system. The feasibility of detecting and tracking motion at the field edge was examined with a proof-of-concept implementation that included (1) an algorithm that detected local motion, and (2) a control algorithm that adapted the virtual MLC. To compensate for system latency, a generalized neural network, using both offline (treatment planning data) and online (during treatment delivery) learning, was implemented for tumor motion prediction. Results and Conclusions. The algorithm tracked the global motion of the target with an accuracy of around 0.5 mm. While the accuracy is similar to other methods, this approach does not require manual delineation of the target and can, therefore, provide real-time autonomous motion estimation during treatment. Motion at the treatment field edge was tracked with an accuracy of -0.4 ± 0.3 mm. This proof-of-concept simulation demonstrated that it is possible to adapt MLC leaves based on the motion detected at the field edges. Unplanned intrusions of external organs-at-risk could be shielded. A generalized network with a prediction error of 0.59 mm, and a shorter initial learning period (compared to previous studies) was achieved. This network may be used as a plug-and-play predictor in which tumor position could be predicted at the start of treatment and the need for pretreatment data and optimization for individual patients may be avoided. / February 2017

Clustering techniques are important for gene expression data analysis. However, efficient computational algorithms for clustering time-series data are still lacking. This work documents two improvements on an existing profile-based greedy algorithm for short time-series data; the first one is implementation of a scaling method on the pre-processing of the raw data to handle some extreme cases; the second improvement is modifying the strategy to generate better clusters. Simulation data and real microarray data were used to evaluate these improvements; this approach could efficiently generate more accurate clusters. A new feature-based algorithm was also developed in which steady state value; overshoot, rise time, settling time and peak time are generated by the 2nd order control system for the clustering purpose. This feature-based approach is much faster and more accurate than the existing profile-based algorithm for long time-series data.