Applied Mathematics Commons^™

Cyclic Codes And Cyclic Lattices, Scott Maislin

CMC Senior Theses

In this thesis, we review basic properties of linear codes and lattices with a certain focus on their interplay. In particular, we focus on the analogous con- structions of cyclic codes and cyclic lattices. We start out with a brief overview of the basic theory and properties of linear codes. We then demonstrate the construction of cyclic codes and emphasize their importance in error-correcting coding theory. Next we survey properties of lattices, focusing on algorithmic lattice problems, exhibit the construction of cyclic lattices and discuss their applications in cryptography. We emphasize the similarity and common prop- erties of the two …

Daily Traffic Flow Pattern Recognition By Spectral Clustering, Matthew Aven

CMC Senior Theses

This paper explores the potential applications of existing spectral clustering algorithms to real life problems through experiments on existing road traffic data. The analysis begins with an overview of previous unsupervised machine learning techniques and constructs an effective spectral clustering algorithm that demonstrates the analytical power of the method. The paper focuses on the spectral embedding method’s ability to project non-linearly separable, high dimensional data into a more manageable space that allows for accurate clustering. The key step in this method involves solving a normalized eigenvector problem in order to construct an optimal representation of the original data.

While this …

Hamiltonian Model For Coupled Surface And Internal Waves In The Presence Of Currents, Rossen Ivanov

Articles

We examine a two dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface. The two media are separated by a free common interface. The gravity driven surface and internal water waves (at the common interface between the media) in the presence of a depth-dependent current are studied under certain physical assumptions. Both media are considered incompressible and with prescribed vorticities. Using the Hamiltonian approach the Hamiltonian of the system is constructed in terms of ’wave’ variables and the equations of motion are calculated. The resultant equations of motion …

Family-Based Association Studies Of Autism In Boys Via Facial-Feature Clusters, Luke Andrew Settles

Masters Theses

"Autism spectrum disorder (ASD) refers to a set of developmental disorders with varied attributes. Due to its substantial heterogeneity in terms of behavioral and clinical phenotypes, it is challenging to discern the genetic biomarkers behind ASD, even though the disease is known to be genetic in nature. This serves as a motivation to detect relationships between single nucleotide polymorphisms (SNPs) and a causal autism disease susceptibility locus (DSL) within more homogeneous subgroups. Recently, clinically meaningful subclassifications of ASD have been discovered utilizing facial features of prepubescent boys. Therefore, through the employment of data from 44 prepubertal Caucasian boys with ASD …

Paving The Randomized Gauss-Seidel, Wei Wu

Scripps Senior Theses

The Randomized Gauss-Seidel Method (RGS) is an iterative algorithm that solves overdetermined systems of linear equations Ax = b. This paper studies an update on the RGS method, the Randomized Block Gauss-Seidel Method. At each step, the algorithm greedily minimizes the objective function L(x) = kAx bk2 with respect to a subset of coordinates. This paper describes a Randomized Block Gauss-Seidel Method (RBGS) which uses a randomized control method to choose a subset at each step. This algorithm is the first block RGS method with an expected linear convergence rate which can be described by the properties of the matrix …

End-To-End Molecular Communication Channels In Cell Metabolism: An Information Theoretic Study, Zahmeeth Sayed Sakkaff, Jennie L. Catlett, Mikaela Cashman, Massimiliano Pierobon, Nicole R. Buan, Myra B. Cohen, Christine A. Kelley

Department of Biochemistry: Faculty Publications

The opportunity to control and fine-tune the behavior of biological cells is a fascinating possibility for many diverse disciplines, ranging from medicine and ecology, to chemical industry and space exploration. While synthetic biology is providing novel tools to reprogram cell behavior from their genetic code, many challenges need to be solved before it can become a true engineering discipline, such as reliability, safety assurance, reproducibility and stability. This paper aims to understand the limits in the controllability of the behavior of a natural (non-engineered) biological cell. In particular, the focus is on cell metabolism, and its natural regulation mechanisms, and …

Numerical Solutions Of The Radiosity Equation By The Galerkin Method For The Spherical Pyramid (Mars Project), Qiuyang Deng

Mathematics Theses

The Radiosity of a surface is the rate at which energy leaves that surface. It includes the energy emitted by a surface as well as the energy reflected. In this thesis, a spherical shaped interior space was designed on a spacecraft, which one day might land on Mars. The Radiosity model was used to determine the brightness inside the space. A global Galerkin method is used to solve the Radiosity Equation for several spherical shapes. This research is based on the study of the Radiosity Equation for occluded surfaces using the Collocation Method by Atkinson and Chein. The previous research …

On A Time Domain Boundary Integral Equation Formulation For Acoustic Scattering By Rigid Bodies In Uniform Mean Flow, Fang Q. Hu, Michelle E. Pizzo, Douglas M. Nark

Mathematics & Statistics Faculty Publications

It has been well-known that under the assumption of a uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation. However, the constant mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the assumed uniform flow. A customary boundary condition for rigid surfaces is that the normal acoustic velocity be zero. In this paper, a careful study of the acoustic energy conservation equation is presented that shows such a boundary condition would in fact lead to source …

Fire, Ice, Water, And Dirt: A Simple Climate Model, John Kroll

Mathematics & Statistics Faculty Publications

A simple paleoclimate model was developed as a modeling exercise. The model is a lumped parameter system consisting of an ocean (water), land (dirt), glacier, and sea ice (ice) and driven by the sun (fire). In comparison with other such models, its uniqueness lies in its relative simplicity yet yielding good results. For nominal values of parameters, the system is very sensitive to small changes in the parameters, yielding equilibrium, steady oscillations, and catastrophes such as freezing or boiling oceans. However, stable solutions can be found, especially naturally oscillating solutions. For nominally realistic conditions, natural periods of order 100kyrs are …

Triple Non-Negative Matrix Factorization Technique For Sentiment Analysis And Topic Modeling, Alexander A. Waggoner

CMC Senior Theses

Topic modeling refers to the process of algorithmically sorting documents into categories based on some common relationship between the documents. This common relationship between the documents is considered the “topic” of the documents. Sentiment analysis refers to the process of algorithmically sorting a document into a positive or negative category depending whether this document expresses a positive or negative opinion on its respective topic. In this paper, I consider the open problem of document classification into a topic category, as well as a sentiment category. This has a direct application to the retail industry where companies may want to scour …

An Application Of Time Series Methods To Investigate Eu Dairy Commodity Price Dynamics, Dennis Bergmann

Theses

Fundamental changes to the common agricultural policy (CAP) have led to greater market orientation which in turn has resulted in significantly changed price dynamics of EU dairy prices. These changed dynamics include sharply increased price variability of EU farm gate milk prices as well EU dairy commodity prices such as butter and Skimmed Milk Powder (SMP). In addition it was expected that EU dairy prices will align to Word dairy prices. This alignment of prices would also see an alignment of volatility levels which were significantly higher for World dairy prices than EU dairy prices. The aim of this thesis …

Estimates Of Life Span Of Solutions Of A Cauchy Problem, Joon Hyuk Kang

Faculty Publications

In this paper we get estimates of life span of a Cauchy problem ut(x, t) = ∆ u(x, t) +u(x, t)p, x∈Rn, t >0,u(x,0) =λφ(x), x∈Rn in terms of the positive constant parameterλ whenφ(x)∈Lq is a nonnegative bounded continuous function in Rn but not identically zero, where q is large enough. The technique we used in this paper is the Comparison Principle.

Characterization Of Rectifying And Sphere Curves In R^3, Yun Myung Oh, Julie Logan

Faculty Publications

Studies of curves in 3D-space have been developed by many geometers and it is known that any regular curve in 3D space is completely determined by its curvature and torsion, up to position. Many results have been found to characterize various types of space curves in terms of conditions on the ratio of torsion to curvature. Under an extracondition on the constant curvature, Y.L. Seo and Y. M. Oh found the series solution when the ratio of torsion to curvature is a linear function. Furthermore, this solution is known to be a rectifying curve by B. Y. Chen’s work. This …

Adrc Based Control Of Nonlinear Dynamical System With Multiple Sources Of Disturbance And Multiple Inputs, Chan Mi Park

Electronic Theses and Dissertations

In this thesis, we study the stability of Active Disturbance Rejection Control (ADRC) applied to controlling the Lorenz system. The Lorenz system is a nonlinear dynamical system that we attempt to control. In fact, the system is used to model convection flow such as that found in thermosyphons, electric circuits, and lasers. We are stabilizing the Lorenz system along with a few disturbances. Thus, to stabilize this chaotic system, a robust controller is required. The ADRC system is known as as effective method to stabilize a dynamical system. With the help of the Extended State Observer (ESO), the system can …

Applications Of Flow Network Models In Finance, Angel J. Woods

Electronic Theses and Dissertations

In this thesis we explore the applications of flow networks in practical problems in finance. After introducing basic definitions and background information, we first survey some known applications of flow networks in theoretical mathematics. We also briefly comment on their potential applications in the setting of financial flow networks. We then construct networks from practical financial flows and present the construction, reasoning, and known applications. Lastly, we show a design of financial flow networks that takes time into consideration and discuss its applications.

The Bessel Function, The Hankel Transform And An Application To Differential Equations, Isaac C. Voegtle

Electronic Theses and Dissertations

In this thesis we explore the properties of Bessel functions. Of interest is how they can be applied to partial differential equations using the Hankel transform. We use an example in two dimensions to demonstrate the properties at work as well as formulate thoughts on how to take the results further.

Dynamics Of Gene Networks In Cancer Research, Paul Scott

Electronic Theses and Dissertations

Cancer prevention treatments are being researched to see if an optimized treatment schedule would decrease the likelihood of a person being diagnosed with cancer. To do this we are looking at genes involved in the cell cycle and how they interact with one another. Through each gene expression during the life of a normal cell we get an understanding of the gene interactions and test these against those of a cancerous cell. First we construct a simplified network model of the normal gene network. Once we have this model we translate it into a transition matrix and force changes on …

A Markov Decision Process Approach To Adaptive Contact Strategies, Artur Grygorian

Electronic Theses and Dissertations

In the field of survey methodology, optimizing contact strategies helps organizations increase response rates using their allocated budget. Markov Decision Processes (MDP) are widely used to model decision-making strategies in situations where the outcomes have a random component. In this research, we use MDPs and adaptive sampling techniques to construct a strategy that, based on target audience characteristics, suggests the best contact policy. The data we use comes from the First Destination Survey conducted by the Office of Career Services at Georgia Southern University. The constructed model is quite flexible and can be used by other organizations to optimize their …

Reduced Order Models For Beam-Wave Interaction In High Power Microwave Sources, Lokendra Singh Thakur

LSU Doctoral Dissertations

We apply an asymptotic analysis to show that corrugated waveguides can be represented as cylindrical waveguides with smooth metamaterial coatings when the corrugtions are subwavelength. Here the metamaterial delivers an effective anisotropic surface impedance, effective dielectric constant, and imparts novel dispersive effects on signals traveling inside the waveguide. These properties arise from the subwavelength resonances of the metamaterial. For sufficiently deep corrugations, the waveguide exhibits backward wave propagation, which can be understood in the present context as a multi-scale phenomenon resulting from local resonances inside the subwavelength geometry. Our approach is well suited to numerical computation and we provide a …

On The Skein Theory Of 0-Framed Surgery Along The Trefoil Knot, Andrew Robert Holmes

LSU Doctoral Dissertations

In this dissertation, we will give a generating set of the Kauffman bracket skein module over the field Q(A) of 0-framed surgery along the trefoil knot. This generating set is described as a certain subset of a known basis for the skein module over Z[A^±1] of the trefoil exterior.