Applied Mathematics Commons^™

Multiplicative Noise Removal With A Sparsity-Aware Optimization Model, Jian Lu, Lixin Shen, Chen Xu, Yuesheng Xu

Mathematics & Statistics Faculty Publications

Restoration of images contaminated by multiplicative noise (also known as speckle noise) is a key issue in coherent image processing. Notice that images under consideration are often highly compressible in certain suitably chosen transform domains. By exploring this intrinsic feature embedded in images, this paper introduces a variational restoration model for multiplicative noise reduction that consists of a term reflecting the observed image and multiplicative noise, a quadratic term measuring the closeness of the underlying image in a transform domain to a sparse vector, and a sparse regularizer for removing multiplicative noise. Being different from popular existing models which focus …

Computational Fluid Dynamics In A Terminal Alveolated Bronchiole Duct With Expanding Walls: Proof-Of-Concept In Openfoam, Jeremy Myers

Theses and Dissertations

Mathematical Biology has found recent success applying Computational Fluid Dynamics (CFD) to model airflow in the human lung. Detailed modeling of flow patterns in the alveoli, where the oxygen-carbon dioxide gas exchange occurs, has provided data that is useful in treating illnesses and designing drug-delivery systems. Unfortunately, many CFD software packages have high licensing fees that are out of reach for independent researchers. This thesis uses three open-source software packages, Gmsh, OpenFOAM, and ParaView, to design a mesh, create a simulation, and visualize the results of an idealized terminal alveolar sac model. This model successfully demonstrates that OpenFOAM can be …

Network Analytics For The Mirna Regulome And Mirna-Disease Interactions, Joseph Jayakar Nalluri

Theses and Dissertations

miRNAs are non-coding RNAs of approx. 22 nucleotides in length that inhibit gene expression at the post-transcriptional level. By virtue of this gene regulation mechanism, miRNAs play a critical role in several biological processes and patho-physiological conditions, including cancers. miRNA behavior is a result of a multi-level complex interaction network involving miRNA-mRNA, TF-miRNA-gene, and miRNA-chemical interactions; hence the precise patterns through which a miRNA regulates a certain disease(s) are still elusive. Herein, I have developed an integrative genomics methods/pipeline to (i) build a miRNA regulomics and data analytics repository, (ii) create/model these interactions into networks and use optimization techniques, motif …

A New Formulation Of Time Boundary Integral Equation For Acoustic Wave Scattering In The Presence Of A 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 constant uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation, in both the time domain and the frequency domain. Compared with solving partial differential equations, numerical methods based on the boundary integral equation have the advantage of a reduced spatial dimension and, hence, requiring only a surface mesh. However, the constant uniform 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 uniform mean flow. In …

Moduli Spaces Of Flat Gsp-Bundles, Neal David Livesay

LSU Doctoral Dissertations

A classical problem in the theory of differential equations is the classification of first-order singular differential operators up to gauge equivalence. A related algebro-geometric problem involves the construction of moduli spaces of meromorphic connections. In 2001, P. Boalch constructed well-behaved moduli spaces in the case that each of the singularities are diagonalizable. In a recent series of papers, C. Bremer and D. Sage developed a new approach to the study of the local behavior of meromorphic connections using a geometric variant of fundamental strata, a tool originally introduced by C. Bushnell for the study of p-adic representation theory. Not only …

Manifestations Of Symmetry In Polynomial Link Invariants, Kyle Istvan

LSU Doctoral Dissertations

The use and detection of symmetry is ubiquitous throughout modern mathematics. In the realm of low-dimensional topology, symmetry plays an increasingly significant role due to the fact that many of the modern invariants being developed are computationally expensive to calculate. If information is known about the symmetries of a link, this can be incorporated to greatly reduce the computation time. This manuscript will consider graphical techniques that are amenable to such methods. First, we discuss an obstruction to links being periodic, developed jointly with Dr. Khaled Qazaqzeh at Kuwait University, using a model developed by Caprau and Tipton. We will …

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.

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 …

An Introduction To The Lebesgue Integral, Ikhlas Adi

All Student Theses and Dissertations

The Riemann integral is the simplest integral to define, and it allows one to integrate every continuous function. It is really important to have a definition of the integral that allows a wider class of functions to be integrated. However, there are many other types of integrals, the most important of which is the Lebesgue integral. The Lebesgue integral allows one to integrate unbounded or discontinuous functions whose Riemann integral does not exist, and it has mathematical properties that the Riemann integral does not. The definition of the Lebesgue integral requires the use of measure theory since picking out a …

Fitting A Linear Regression Model And Forecasting In R In The Presence Of Heteroskedascity With Particular Reference To Advanced Regression Technique Dataset On Kaggle.Com., Samuel Mbah Nde

All Student Theses and Dissertations

Since ancient times, men have built and sold houses. But just how much is a house worth? The challenge is to be able to use information about a house such as its location, and the area on which it is built to predict its price. Such predicted prices can be of great importance to any participant in the real estate business be it an agent, a buyer, seller or a bank to make intelligent decisions and the profit that come with such decisions. Since every company’s success depends on its ability to accurately predict financial outcomes, its profitability will depend …

The Effects Of Disturbance And Species Specific Interactions On Diversity In An Agent Based Forest Simulation, Matthew E. Mills

Theses and Dissertations

In ecology literature, there is much data which suggests that conspecific negative density dependence (CNDD) and abiotic disturbances increase biodiversity in forests. This thesis elucidates the notion that not only do these two forces increase diversity, but they may also interact with one another in order to achieve higher levels of biodiversity. Abiotic disturbances, like fires and hurricanes, can indirectly impact conspecific effects because when these forces remove individuals from the landscape, the role of the conspecific effects will change. The interaction of these two factors in biodiversity are explored in an agent based forest simulation through a resource surface. …

Mathematical Models Of The Inflammatory Response In The Lungs, Sarah B. Minucci

Theses and Dissertations

Inflammation in the lungs can occur for many reasons, from bacterial infections to stretch by mechanical ventilation. In this work we compare and contrast various mathematical models for lung injuries in the categories of acute infection, latent versus active infection, and particulate inhalation. We focus on systems of ordinary differential equations (ODEs), agent-based models (ABMs), and Boolean networks. Each type of model provides different insight into the immune response to damage in the lungs. This knowledge includes a better understanding of the complex dynamics of immune cells, proteins, and cytokines, recommendations for treatment with antibiotics, and a foundation for more …

Series Solutions Of Polarized Gowdy Universes, Doniray Brusaferro

Theses and Dissertations

Einstein's field equations are a system of ten partial differential equations. For a special class of spacetimes known as Gowdy spacetimes, the number of equations is reduced due to additional structure of two dimensional isometry groups with mutually orthogonal Killing vectors. In this thesis, we focus on a particular model of Gowdy spacetimes known as the polarized T³ model, and provide an explicit solution to Einstein's equations.

Region Of Smooth Functions For Positive Solutions To An Elliptic Biological Model, Joon Hyuk Kang, Timothy Robertson

Faculty Publications

The non-existence and existence of the positive solution to the generalized elliptic model ∆u+g(u v) = 0 in Ω, ∆v+h(u, v) = 0 in Ω, u=v= 0 on∂Ω, were investigated.

Multi-Scale Cardiovascular Flow Analysis By An Integrated Meshless-Lumped Parameter Model, Leonardo A. Bueno, Eduardo A. Divo, Alain J. Kassab

Publications

A computational tool that integrates a Radial basis function (RBF)-based Meshless solver with a Lumped Parameter model (LPM) is developed to analyze the multi-scale and multi-physics interaction between the cardiovascular flow hemodynamics, the cardiac function, and the peripheral circulation. The Meshless solver is based on localized RBF collocations at scattered data points which allows for automation of the model generation via CAD integration. The time-accurate incompressible flow hemodynamics are addressed via a pressure-velocity correction scheme where the ensuing Poisson equations are accurately and efficiently solved at each time step by a Dual-Reciprocity Boundary Element method (DRBEM) formulation that takes advantage …

Equators Have At Most Countable Many Singularities With Bounded Total Angle, Pilar Herreros, Mario Ponce, J.J.P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

For distinct points p and q in a two-dimensional Riemannian manifold, one defines their mediatrix Lpq as the set of equidistant points to p and q. It is known that mediatrices have a cell decomposition consisting of a finite number of branch points connected by Lipschitz curves. In the case of a topological sphere, mediatrices are called equators and it can benoticed that there are no branching points, thus an equator is a topological circle with possibly many Lipschitz singularities. This paper establishes that mediatrices have the radial …

Direct Sampling Methods For Inverse Scattering Problems, Ala Mahmood Nahar Al Zaalig

Dissertations, Master's Theses and Master's Reports

Recently, direct sampling methods became popular for solving inverse scattering problems to estimate the shape of the scattering object. They provide a simple tool to directly reconstruct the shape of the unknown scatterer. These methods are based on choosing an appropriate indicator function f on R^d, d=2 or 3, such that f(z) decides whether z lies inside or outside the scatterer. Consequently, we can determine the location and the shape of the unknown scatterer.

In this thesis, we first present some sampling methods for shape reconstruction in inverse scattering problems. These methods, which are described in Chapter 1, …

Modeling And Simulation Of The Peristaltic Flow Of Newtonian And Non-Newtonian Fluids With Application To The Human Body, Samer Alokaily

Dissertations, Master's Theses and Master's Reports

Computational models are developed to investigate peristaltic motion in the human gastro-intestinal tract. The peristaltic motion is simulated by means of traveling waves which deform the boundary of the tubes. An axisymmetric tube of uniform diameter is used to model the small intestines, and an axisymmetric conical geometry is developed to model the lower part of the human stomach. The conical geometry represents a simplification of the more complicated three-dimensional models of the human stomach that have been used in other studies. Also, they seeks to reduce computational costs and circumvent difficulties of mesh generation. The computations are performed within …

Numerical Simulation Of Viscoelastic Multiphase Flows Using An Improved Two-Phase Flow Solver, Olabanji Shonibare

Dissertations, Master's Theses and Master's Reports

The production of uniformly-sized droplets has numerous applications in various fields including the biotechnology and chemical industries. For example, in the separation of mixtures based on their relative absorbency, an optimal arrangement of monodispersed droplets in columns is desired for an effective separation. However, very few numerical studies on the formation of viscoelastic droplets via cross-flow shear are available, none of which have considered the case when the flow of the continuous phase is Couette. In this work, a new solver capable of automatic mesh refinement is developed for the OpenFOAM CFD toolbox to solve viscoelastic two-phase flow problems. The …

Extraction Of Displacement Fields In Heterogeneous Media Using Optimal Local Basis Functions, Paul Derek Sinz

LSU Doctoral Dissertations

The Multiscale Spectral Generalized Finite Element Method (MS-GFEM) was developed in recent work by Babuska and Lipton. The method uses optimal local shape functions, optimal in the sense of the Kolmogorov n-width, to approximate solutions to a second order linear elliptic partial differential equation with L-infinity coefficients. In this dissertation an implementation of MS-GFEM over a two subdomain partition of unity is outlined and several numerical experiments are presented. The method is applied to compute local fields inside high contrast particle suspensions. The method's performance is evaluated for various examples with different contrasts between reinforcement particles and matrix material. The …

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 …

Disease Models With Immigration, Reem Almarashi

Theses and Dissertations (Comprehensive)

In this thesis we focus first on studying the susceptible, exposed, and infected ($SEI$) disease model without immigration. We determine the basic reproduction number $\mathcal{R}_0$, which can be interpreted as the expected number of new cases that can be produced by a single infection in a completely susceptible population. Further, by using the Jacobian matrix, we determine the local stability of the disease model. Then we have the result that when $\mathcal{R}_0<1$ the DFE point is locally asymptotically stable(L.A.S). In contrast, when $\mathcal{R}_0>1$ we find that the endemic equilibrium is L.A.S. After that, we analyze the $SEI$ model with immigration of infected individuals.

Furthermore, we investigate the direction that the …

Mechanistic Plug-And-Play Models For Understanding The Impact Of Control And Climate On Seasonal Dengue Dynamics In Iquitos, Peru, Nathan Levick

Mathematics & Statistics ETDs

Dengue virus is a mosquito-borne multi-serotype disease whose dynamics are not precisely understood despite half of the world’s human population being at risk of infection. A recent dataset of dengue case reports from an isolated Amazonian city— Iquitos, Peru—provides a unique opportunity to assess dengue dynamics in a simpli- fied setting. Ten years of clinical surveillance data reveal a specific pattern: two novel serotypes, in turn, invaded and exclusively dominated incidence over several seasonal cycles, despite limited intra-annual variation in climate conditions. Together with mechanistic mathematical models, these data can provide an improved understand- ing of the nonlinear interactions between …

Introduction To Random Processes Mth 453, Joanna Burkhardt

Library Impact Statements

No abstract provided.

Applied Calculus Mth 103, Joanna Burkhardt

Library Impact Statements

No abstract provided.

On The Convergence Of Two-Dimensional Fuzzy Volterra-Fredholm Integral Equations By Using Picard Method, Ali Ebadian, Foroozan Farahrooz, Amirahmad Khajehnasiri

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we prove convergence of the method of successive approximations used to approximate the solution of nonlinear two-dimensional Volterra-Fredholm integral equations and define the notion of numerical stability of the algorithm with respect to the choice of the first iteration. Also we present an iterative procedure to solve such equations. Finally, the method is illustrated by solving some examples.

A Numerical Scheme For Generalized Fractional Optimal Control Problems, N. Singha, C. Nahak

Applications and Applied Mathematics: An International Journal (AAM)

This paper introduces a generalization of the Fractional Optimal Control Problem (GFOCP). Proposed generalizations differ in terms of explaining the constraint involved in the dynamical system of the control problem. We assume the constraint as an arbitrary function of fractional derivatives and fractional integrals. By this assumption the restriction on constraint, to be of some prescribed function of fractional operators, is removed. Deduction of necessary optimality conditions followed by particular cases and examples has been provided. Additionally, we construct a solution scheme for the suggested class of (GFOCP)’s. The formulation of this scheme is done by implementing the Adomian decomposition …

On The Slow Growth And Approximation Of Entire Function Solutions Of Second-Order Elliptic Partial Differential Equations On Caratheodory Domains, Devendra Kumar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we consider the regular, real-valued solutions of the second-order elliptic partial differential equation. The characterization of generalized growth parameters for entire function solutions for slow growth in terms of approximation errors on more generalized domains, i.e., Caratheodory domains, has been obtained. Moreover, we studied some inequalities concerning the growth parameters of entire function solutions of above equation for slow growth which have not been studied so far.