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Full-Text Articles in Physical Sciences and Mathematics
Computing The Rank Of Braids, Justin Meiners
Computing The Rank Of Braids, Justin Meiners
Theses and Dissertations
We describe a method for computing rank (and determining quasipositivity) in the free group using dynamic programming. The algorithm is adapted to computing upper bounds on the rank for braids. We test our method on a table of knots by identifying quasipositive knots and calculating the ribbon genus. We consider the possibility that rank is not theoretically computable and prove some partial results that would classify its computational complexity. We then present a method for effectively brute force searching band presentations of small rank and conjugate length.
Qwasi: The Quantum Walk Simulator, Warren V. Wilson
Qwasi: The Quantum Walk Simulator, Warren V. Wilson
Theses and Dissertations
As quantum computing continues to evolve, the ability to design and analyze novel quantum algorithms becomes a necessary focus for research. In many instances, the virtues of quantum algorithms only become evident when compared to their classical counterparts, so a study of the former often begins with a consideration of the latter. This is very much the case with quantum walk algorithms, as the success of random walks and their many, varied applications have inspired much interest in quantum correlates. Unfortunately, finding purely algebraic solutions for quantum walks is an elusive endeavor. At best, and when solvable, they require simple …
A Robust And Automated Deconvolution Algorithm Of Peaks In Spectroscopic Data, William Johan Burke Iv
A Robust And Automated Deconvolution Algorithm Of Peaks In Spectroscopic Data, William Johan Burke Iv
Theses and Dissertations
The huge amount of spectroscopic data in use in metabolomic experiments requires an algorithm that can process the data in an autonomous fashion while providing quality of analysis comparable to manual methods. Scientists need an algorithm that effectively deconvolutes spectroscopic peaks automatically and is resilient to the presence of noise in the data. The algorithm must also provide a simple measure of quality of the deconvolution. The deconvolution algorithm presented in this thesis consists of preprocessing steps, noise removal, peak detection, and function fitting. Both a Fourier Transform and Continuous Wavelet Transform (CWT) method of noise removal were investigated. The …
An Examination Of Kinetic Monte Carlo Methods With Application To A Model Of Epitaxial Growth, Dylana Ashton Wilhelm
An Examination Of Kinetic Monte Carlo Methods With Application To A Model Of Epitaxial Growth, Dylana Ashton Wilhelm
Theses and Dissertations
Through the assembly of procedural information about physical processes, the kinetic Monte Carlo method offers a simple and efficient stochastic approach to model the temporal evolution of a system. While suitable for a variety of systems, the approach has found widespread use in the simulation of epitaxial growth. Motivated by chem- ically reacting systems, we discuss the developments and elaborations of the kinetic Monte Carlo method, highlighting the computational cost associated with realizing a given algorithm. We then formulate a solid-on-solid bond counting model of epitax- ial growth which permits surface atoms to advance the state of the system through …
Effects Of Dynamic Goals On Agent Performance, Nathan R. Ball
Effects Of Dynamic Goals On Agent Performance, Nathan R. Ball
Theses and Dissertations
Autonomous systems are increasingly being used for complex tasks in dynamic environments. Robust automation needs to be able to establish its current goal and determine when the goal has changed. In human-machine teams autonomous goal detection is an important component of maintaining shared situational awareness between both parties. This research investigates how different categories of goals affect autonomous change detection in a dynamic environment. In order to accomplish this goal, a set of autonomous agents were developed to perform within an environment with multiple possible goals. The agents perform the environmental task while monitoring for goal changes. The experiment tests …
Increasing The Computational Efficiency Of Combinatoric Searches, Wiley Spencer Morgan
Increasing The Computational Efficiency Of Combinatoric Searches, Wiley Spencer Morgan
Theses and Dissertations
A new algorithm for the enumeration of derivative superstructures of a crystal is presented. The algorithm will help increase the efficiency of computational material design methods such as cluster expansion by increasing the size and diversity of the types of systems that can be modeled. Modeling potential alloys requires the exploration of all possible configurations of atoms. Additionally, modeling the thermal properties of materials requires knowledge of the possible ways of displacing the atoms. One solution to finding all symmetrically unique configurations and displacements is to generate the complete list of possible configurations and remove those that are symmetrically equivalent. …
Algorithmic And Combinatorial Results On Fence Patrolling, Polygon Cutting And Geometric Spanners, Anirban Ghosh
Algorithmic And Combinatorial Results On Fence Patrolling, Polygon Cutting And Geometric Spanners, Anirban Ghosh
Theses and Dissertations
The purpose of this dissertation is to study problems that lie at the intersection of geometry and computer science. We have studied and obtained several results from three different areas, namely–geometric spanners, polygon cutting, and fence patrolling. Specifically, we have designed and analyzed algorithms along with various combinatorial results in these three areas. For geometric spanners, we have obtained combinatorial results regarding lower bounds on worst case dilation of plane spanners. We also have studied low degree plane lattice spanners, both square and hexagonal, of low dilation. Next, for polygon cutting, we have designed and analyzed algorithms for cutting out …
Effects Of Visualization On Algorithm Comprehension, Matthew Mulvey
Effects Of Visualization On Algorithm Comprehension, Matthew Mulvey
Theses and Dissertations
Computer science students are expected to learn and apply a variety of core algorithms which are an essential part of the field. Any one of these algorithms by itself is not necessarily extremely complex, but remembering the large variety of algorithms and the differences between them is challenging. To address this challenge, we present a novel algorithm visualization tool designed to enhance students understanding of Dijkstra’s algorithm by allowing them to discover the rules of the algorithm for themselves. It is hoped that a deeper understanding of the algorithm will help students correctly select, adapt and apply the appropriate algorithm …
The Bioluminescence Heterozygous Genome Assembler, Jared Calvin Price
The Bioluminescence Heterozygous Genome Assembler, Jared Calvin Price
Theses and Dissertations
High-throughput DNA sequencing technologies are currently revolutionizing the fields of biology and medicine by elucidating the structure and function of the components of life. Modern DNA sequencing machines typically produce relatively short reads of DNA which are then assembled by software in an attempt to produce a representation of the entire genome. Due to the complex structure of all but the smallest genomes, especially the abundant presence of exact or almost exact repeats, all genome assemblers introduce errors into the final sequence and output a relatively large set of contigs instead of full-length chromosomes (a contig is a DNA sequence …
Improving Performance Of The Filtered-X Least Mean Square Algorithm For Active Control Of Noise Contatining Multiple Quasi-Stationary Tones, Stephan P. Lovstedt
Improving Performance Of The Filtered-X Least Mean Square Algorithm For Active Control Of Noise Contatining Multiple Quasi-Stationary Tones, Stephan P. Lovstedt
Theses and Dissertations
The Filtered-X Least-Mean-Square (FXLMS) algorithm is widely used in active noise control due to its robustness, simplicity, and ability to be implemented in real time. In a feedforward implementation of the FXLMS algorithm, a reference signal that is highly correlated with the noise to be controlled is filtered with an estimate of the transfer function of the secondary path. The convergence characteristics of the FXLMS algorithm have been well studied. A convergence parameter is used to optimize the convergence of the algorithm. However, the optimal value for the convergence parameter is frequency dependent. Thus for noise containing multiple tones at …
Simulation And Visualization Of Environments With Multidimensional Time, Luther A. Tychonievich
Simulation And Visualization Of Environments With Multidimensional Time, Luther A. Tychonievich
Theses and Dissertations
This work introduces the notion of computational hypertime, or the simulation and visualization of hypothetical environments possessing multidimensional time. An overview of hypertime is provided,including an intuitive visualization paradigm and a discussion of the failure of common simulation techniques when extended to include multidimensional time. A condition for differential equations describing hypertime motion to be amenable to standard time-iterative simulation techniques is provided,but is not satisfied by any known model of physics. An alternate simulation algorithm involving iterative refinement of entire equations of motion is presented,with an example implementation to solve elastic collisions in hypertime. An artificial intelligence algorithm for …
Limitations And Extensions Of The Wolf-Phc Algorithm, Philip R. Cook
Limitations And Extensions Of The Wolf-Phc Algorithm, Philip R. Cook
Theses and Dissertations
Policy Hill Climbing (PHC) is a reinforcement learning algorithm that extends Q-learning to learn probabilistic policies for multi-agent games. WoLF-PHC extends PHC with the "win or learn fast" principle. A proof that PHC will diverge in self-play when playing Shapley's game is given, and WoLF-PHC is shown empirically to diverge as well. Various WoLF-PHC based modifications were created, evaluated, and compared in an attempt to obtain convergence to the single shot Nash equilibrium when playing Shapley's game in self-play without using more information than WoLF-PHC uses. Partial Commitment WoLF-PHC (PCWoLF-PHC), which performs best on Shapley's game, is tested on other …
Probabilistic Methods, Joseph Kwaku Asafu-Adjei
Probabilistic Methods, Joseph Kwaku Asafu-Adjei
Theses and Dissertations
The Probabilistic Method was primarily used in Combinatorics and pioneered by Erdös Pai, better known to Westerners as Paul Erdos in the 1950s. The probabilistic method is a powerful tool for solving many problems in discrete mathematics, combinatorics and also in graph .theory. It is also very useful to solve problems in number theory, combinatorial geometry, linear algebra and real analysis. More recently, it has been applied in the development of efficient algorithms and in the study of various computational problems.Broadly, the probabilistic method is somewhat opposite of the extremal graph theory. Instead of considering how a graph can behave …
Integer Programming With Groebner Basis, Isabella Brooke Ginn
Integer Programming With Groebner Basis, Isabella Brooke Ginn
Theses and Dissertations
Integer Programming problems are difficult to solve. The goal is to find an optimal solution that minimizes cost. With the help of Groebner based algorithms the optimal solution can be found if it exists. The application of the Groebner based algorithm and how it works is the topic of research. The Algorithms are The Conti-Traverso Algorithm and the Original Conti-Traverso Algorithm. Examples are given as well as proofs that correspond to the algorithms. The latter algorithm is more efficient as well as user friendly. The algorithms are not necessarily the best way to solve and integer programming problem, but they …
Grobner Bases And Ideals Of Points, Eun R. Chang
Grobner Bases And Ideals Of Points, Eun R. Chang
Theses and Dissertations
The main point of this thesis is an introduction to the theory of Grobner bases. The concept of Grobner basis and construction of the Grobner basis by Buchberger's Algorithm, in which the notion of S-polynomials is introduced, and a few modified or improved versions of Grobner basis algorithm are reviewed in this paper. In Chapter 1, we have a review of ideals, the definitions and types of monomial ordering, the multivariate polynomial division algorithm and its examples. After ascertaining the monomial ordering on multivariate polynomials, we establish a leading term of a polynomial.In Chapter 2, after defining Grobner bases, we …
A Comparison For Longitudinal Data Missing Due To Truncation, Rong Liu
A Comparison For Longitudinal Data Missing Due To Truncation, Rong Liu
Theses and Dissertations
Many longitudinal clinical studies suffer from patient dropout. Often the dropout is nonignorable and the missing mechanism needs to be incorporated in the analysis. The methods handling missing data make various assumptions about the missing mechanism, and their utility in practice depends on whether these assumptions apply in a specific application. Ramakrishnan and Wang (2005) proposed a method (MDT) to handle nonignorable missing data, where missing is due to the observations exceeding an unobserved threshold. Assuming that the observations arise from a truncated normal distribution, they suggested an EM algorithm to simplify the estimation.In this dissertation the EM algorithm is …
Quantifying The Effects Of Correlated Covariates On Variable Importance Estimates From Random Forests, Ryan Vincent Kimes
Quantifying The Effects Of Correlated Covariates On Variable Importance Estimates From Random Forests, Ryan Vincent Kimes
Theses and Dissertations
Recent advances in computing technology have lead to the development of algorithmic modeling techniques. These methods can be used to analyze data which are difficult to analyze using traditional statistical models. This study examined the effectiveness of variable importance estimates from the random forest algorithm in identifying the true predictor among a large number of candidate predictors. A simulation study was conducted using twenty different levels of association among the independent variables and seven different levels of association between the true predictor and the response. We conclude that the random forest method is an effective classification tool when the goals …
An Exposition Of The Deterministic Polynomial-Time Primality Testing Algorithm Of Agrawal-Kayal-Saxena, Robert Lawrence Anderson
An Exposition Of The Deterministic Polynomial-Time Primality Testing Algorithm Of Agrawal-Kayal-Saxena, Robert Lawrence Anderson
Theses and Dissertations
I present a thorough examination of the unconditional deterministic polynomial-time algorithm for determining whether an input number is prime or composite proposed by Agrawal, Kayal and Saxena in their paper [1]. All proofs cited have been reworked with full details for the sake of completeness and readability.
Integration Of Vmc++ Into A Commercial Treatment Planning System, Joseph Kingsley Gardner
Integration Of Vmc++ Into A Commercial Treatment Planning System, Joseph Kingsley Gardner
Theses and Dissertations
Recently, there has been interest to integrate VMC++ into the commercial treatment planning system at VCU as another Monte Carlo code option, since it has been shown to increase efficiency dramatically without introducing a significant amount of systematic error. Also, independent validation of VMC++ for photon beams is of interest since this has not been performed previously in literature. This study included several tests required to integrate VMC++. Output factor normalization was performed and found to agree with experiment to within 1% for all field sizes except 1x1 cm2. Geometric validation was successful. Dosimetric validation was performed with respect to …