Applied Mathematics Commons^™

Extremal Problems For Independent Set Enumeration, Jonathan Cutler, A. J. Radcliffe

Department of Mathematics: Faculty Publications

The study of the number of independent sets in a graph has a rich history. Recently, Kahn proved that disjoint unions of Kr,r’s have the maximum number of independent sets amongst r-regular bipartite graphs. Zhao extended this to all r-regular graphs. If we instead restrict the class of graphs to those on a fixed number of vertices and edges, then the Kruskal-Katona theorem implies that the graph with the maximum number of independent sets is the lex graph, where edges form an initial segment of the lexicographic ordering. In this paper, we study three related questions. Firstly, we …

An Entropy Proof Of The Kahn-Lovasz Theorem, Jonathan Cutler, A. J. Radcliffe

Department of Mathematics: Faculty Publications

Bregman [2], gave a best possible upper bound for the number of perfect matchings in a balanced bipartite graph in terms of its degree sequence. Recently Kahn and Lovasz [8] extended Bregman’s theorem to general graphs. In this paper, we use entropy methods to give a new proof of the Kahn-Lovasz theorem. Our methods build on Radhakrishnan’s [9] use of entropy to prove Bregman’s theorem.

Specification Of Structural Viewer And Analytical Tool (Jecp/Svat), Xingzhong Li

Nebraska Center for Materials and Nanoscience: Faculty Publications

Java Electron Crystallography Package (JECP) is a collection of programs for crystallography and electron diffraction analysis. The package is designed and written by Dr. X.Z. Li. The software can be used as a research tool as well as a teaching aid. The need of a structural viewer/an analytical tool, using the same input data format as the JECP and proJECT software, becomes obvious with the growth of the JECP and proJECT programs and users. There exist many programs for structural design and/or display in various levels developed by individual, research group or software company. Some of them are expensive software …

A Dynamic System Model Of Biogeography-Based Optimization, Daniel J. Simon

Electrical and Computer Engineering Faculty Publications

We derive a dynamic system model for biogeography-based optimization (BBO) that is asymptotically exact as the population size approaches infinity. The states of the dynamic system are equal to the proportion of each individual in the population; therefore, the dimension of the dynamic system is equal to the search space cardinality of the optimization problem. The dynamic system model allows us to derive the proportion of each individual in the population for a given optimization problem using theory rather than simulation. The results of the dynamic system model are more precise than simulation, especially for individuals that are very unlikely …

Symmetric Nonconforming Mixed Finite Elements For Linear Elasticity, Jay Gopalakrishnan, Johnny Guzmán

Mathematics and Statistics Faculty Publications and Presentations

We present a family of mixed methods for linear elasticity that yield exactly symmetric, but only weakly conforming, stress approximations. The method is presented in both two and three dimensions (on triangular and tetrahedral meshes). The method is efficiently implementable by hybridization. The degrees of freedom of the Lagrange multipliers, which approximate the displacements at the faces, solve a symmetric positive-definite system. The design and analysis of this method is motivated by a new set of unisolvent degrees of freedom for symmetric polynomial matrices. These new degrees of freedom are also used to give a new simple calculation of the …

Solving The Partial Differential Equation Of Vibrations With Interval Parameters Using The Interval Finite Difference Method, Brenda G. Medina

Open Access Theses & Dissertations

Accuracy and efficiency are among the main factors that drive today's innovative disciplines. As technology rapidly advances, efficiency takes on new meanings but what about accuracy? How accurate is accurate? Human error, uncertainties in measurement, and rounding errors are just some causes of inaccuracy. Interval Computations is an area that allows for such issues to be taken into account; for each measurement attained (for example), an interval can be built by considering the error associated with the measurement, and such an interval can be utilized in the mathematical computations of interest.

We consider the partial differential equation (PDE) of vibrations …

Software Development For A Three-Dimensional Gravity Inversion And Application To Study Of The Border Ranges Fault System, South-Central Alaska, Rolando Cardenas

Open Access Theses & Dissertations

The Border Ranges Fault System (BRFS) bounds the Cook Inlet and Susitna Basins, an important petroleum province within south-central Alaska. A primary goal in the research is to test several plausible models of structure along the Border Ranges Fault System using a novel three-dimensional inversion utilizing gravity and magnetic data, constrained with other geophysical, borehole and surface geological information. This research involves the development of inversion modeling software using a Borland C++ compiler as part of the Rapid Application Development (RAD) Studio. The novel inversion approach directly models known geology, and "a priori" uncertainties on the geologic model to allow …

Digital Image Processing Based On Sparse Representation And Convex Programming, Carlos Andres Ramirez

Open Access Theses & Dissertations

Sparse representation models have been of central interest in recent years due to important achievements in computational harmonic analysis, such as wavelet transformations, and the most recent sampling theory, compressed sensing. Numerous applications based on sparse models have been studied in the last decade leading to promising results. These applications include areas in seismology, image processing, wireless sensor networks, computed tomography and magnetic resonance imaging just to mention a few.

In this work, we propose to extend such applications in the area of image processing, particularly for the image segmentation problem, and examine algorithms involved in sparse modeling from both …

A Sparse Representation Technique For Classification Problems, Reinaldo Sanchez Arias

Open Access Theses & Dissertations

In pattern recognition and machine learning, a classification problem refers to finding an algorithm for assigning a given input data into one of several categories. Many natural signals are sparse or compressible in the sense that they have short representations when expressed in a suitable basis. Motivated by the recent successful development of algorithms for sparse signal recovery, we apply the selective nature of sparse representation to perform classification. In order to find such sparse linear representation, we implement an l₁-minimization algorithm. This methodology overcomes the lack of robustness with respect to outliers. In contrast to other classification …

Dispersive Wave Equations For Solids With Microstructure, A. Berezovski, Juri Engelbrecht, Mihhail Berezovski

Publications

The dispersive wave motion in solids with microstructure is considered in the one-dimensional setting in order to understand better the mechanism of dispersion. It is shown that the variety of dispersive wave propagation models derived by homogenization, continualisation, and generalization of continuum mechanics can be unified in the framework of dual internal variables theory.

Parallel-Sparse Symmetrical/Unsymmetrical Finite Element Domain Decomposition Solver With Multi-Point Constraints For Structural/Acoustic Analysis, Siroj Tungkahotara, Willie R. Watson, Duc T. Nguyen, Subramaniam D. Rajan

Civil & Environmental Engineering Faculty Publications

Details of parallel-sparse Domain Decomposition (DD) with multi-point constraints (MPC) formulation are explained. Major computational components of the DD formulation are identified. Critical roles of parallel (direct) sparse and iterative solvers with MPC are discussed within the framework of DD formulation. Both symmetrical and unsymmetrical system of simultaneous linear equations (SLE) can be handled by the developed DD formulation. For symmetrical SLE, option for imposing MPC equations is also provided.

Large-scale (up to 25 million unknowns involving complex numbers) structural and acoustic Finite Element (FE) analysis are used to evaluate the parallel computational performance of the proposed DD implementation using …

Acceleration Techniques By Post-Processing Of Numerical Solutions Of The Hammerstein Equation, Khomsan Neamprem, Hideaki Kaneko

Mathematics & Statistics Faculty Publications

No abstract provided.

Modeling, Analysis, And Simulation Of Discrete-Continuum Models Of Step-Flow Epitaxy: Bunching Instabilities And Continuum Limits, Nicholas O. Kirby

University of Kentucky Doctoral Dissertations

Vicinal surfaces consist of terraces separated by atomic steps. In the step-flow regime, deposited atoms (adatoms) diffuse on terraces, eventually reaching steps where they attach to the crystal, thereby causing the steps to move. There are two main objectives of this work. First, we analyze rigorously the differences in qualitative behavior between vicinal surfaces consisting of infinitely many steps and nanowires whose top surface consists of a small number of steps bounded by a reflecting wall. Second, we derive the continuum model that describes the macroscopic behavior of vicinal surfaces from detailed microscopic models of step dynamics.

We use the …

A Generalized Nonlinear Model For The Evolution Of Low Frequency Freak Waves, Jonathan Blackledge

Articles

This paper presents a generalized model for simulating wave fields associated with the sea surface. This includes the case when `freak waves' may occur through an effect compounded in the nonlinear (cubic) Schrodinger equation. After providing brief introductions to linear sea wave models, `freak waves' and the linear and nonlinear Schrodinger equations, we present a unified model that provides for a piecewise continuous transition from a linear to a nonlinear state. This is based on introducing a fractional time derivative to develop a fractional nonlinear partial differential equation with a stochastic source function. In order to explore the characteristics of …

Cryptography Using Steganography: New Algorithms And Applications, Jonathan Blackledge

Articles

Developing methods for ensuring the secure exchange of information is one of the oldest occupations in history. With the revolution in Information Technology, the need for securing information and the variety of methods that have been developed to do it has expanded rapidly. Much of the technology that forms the basis for many of the techniques used today was originally conceived for use in military communications and has since found a place in a wide range of industrial and commercial sectors. This has led to the development of certain industry standards that are compounded in specific data processing algorithms together …

Riordan Arrays Associated With Laurent Series And Generalized Sheffer-Type Groups, Tian-Xiao He

Scholarship

A relationship between a pair of Laurent series and Riordan arrays is formulated. In addition, a type of generalized Sheffer groups is defined using Riordan arrays with respect to power series with non-zero coefficients. The isomorphism between a generalized Sheffer group and the group of the Riordan arrays associated with Laurent series is established. Furthermore, Appell, associated, Bell, and hitting-time subgroups of the groups are defined and discussed. A relationship between the generalized Sheffer groups with respect to different power series is presented. The equivalence of the defined Riordan array pairs and generalized Stirling number pairs is given. A type …

Currency Trading Using The Fractal Market Hypothesis, Jonathan Blackledge, Kieran Murphy

Articles

We report on a research and development programme in financial modelling and economic security undertaken in the Information and Communications Security Research Group (ICSRG, 2011) which has led to the launch of a new company - Currency Traders Ireland Limited - funded by Enterprise Ireland. Currency Traders Ireland Limited (CTI, 2011) has a fifty year exclusive license to develop a new set of indicators for analysing currency exchange rates (Forex trading). We consider the background to the approach taken and present examples of the results obtained to date.

Estimating The Efficacy Of Mild Heating Processes Taking Into Account Microbial Non-Linearities: A Case Study On The Thermisation Of A Food Simulant, Vasilis Valdramidis, Brijesh Tiwari, Patrick J. Cullen, Alain Kondjoyan, Jan Van Impe

Articles

Traditional and novel approaches for the calculation of the heat treatment efficiency are compared in this work. The Mild Heat value (MH-value), an alternative approach to the commonly used sterilisation, pasteurisation and cook value (F, P, C–value), is calculated to estimate the efficiency of a mild heat process. MH-value is the time needed to achieve a predefined microbial reduction at a reference temperature and a known thermal resistant constant, z, for log-linear or specific types of non log-linear microbial inactivation kinetics. An illustrative example is given in which microbial inactivation data of Listeria innocua CLIP 20-595 are used for estimating …

Plurigaussian Simulation Of Rocktypes Using Data From A Gold Mine In Western Australia, Robin Dunn

Theses: Doctorates and Masters

Stochastic simulation of rocktypes, or the geometry of the geology, is a major area of continuing research as earth scientists seek a better understanding of an orebody as a precursor to the assignment of continuous rock properties, allowing more economically appropriate decisions regarding mine planning. This thesis analyses the suitability of particular geostatistical rock type modelling algorithms when applied to the five rocktypes evident in drill hole data from the Big Bell gold mine near Cue, Western Australia. The background of the geostatistical theory is considered, in particular the concept of the random function model and the link between the …

Twisted Frobenius-Schur Indicators For Hopf Algebras, Maria Vega

LSU Doctoral Dissertations

The classical Frobenius--Schur indicators for finite groups are character sums defined for any representation and any integer $m\ge 2$. In the familiar case $m=2$, the Frobenius--Schur indicator partitions the irreducible representations over the complex numbers into real, complex, and quaternionic representations. In recent years, several generalizations of these invariants have been introduced. Bump and Ginzburg in 2004, building on earlier work of Mackey from 1958, have defined versions of these indicators which are twisted by an automorphism of the group. In another direction, Linchenko and Montgomery in 2000 defined Frobenius--Schur indicators for finite dimensional semisimple Hopf algebras. In this dissertation, …