Applied Mathematics Commons^™

Paley-Wiener Theorems With Respect To The Spectral Parameter, Susanna Dann

LSU Doctoral Dissertations

One of the important questions related to any integral transform on a manifold M or on a homogeneous space G/K is the description of the image of a given space of functions. If M=G/K, where (G,K) is a Gelfand pair, then harmonic analysis on M is closely related to the representations of G and the direct integral decomposition of L^2(M) into irreducible representations of G. R^n can be realized as the quotient R^n=E(n)/SO(n), where E(n) is the orientation preserving Euclidean motion group. The pair (E(n), SO(n)) is a Gelfand pair. Hence this realization of R^n comes with its own natural …

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, …

Shock-Associated Noise Generation In Curved Coanda Turbulent Wall Jets, Caroline P. Lubert, Richard J. Shafer

Department of Mathematics and Statistics - Faculty Scholarship

Curved three-dimensional turbulent Coanda wall jets are present in a multitude of natural and engineering applications. The mechanism by which they form a shock-cell structure is poorly understood, as is the accompanying shock-associated noise (SAN) generation. This paper discusses these phenomena from both a modeling and experimental perspective. The Method of Characteristics is used to rewrite the governing hyperbolic partial differential equations as ordinary differential equations, which are then solved numerically using the Euler predictor-corrector method. The effects of complicating factors -- such as radial expansion and streamline curvature -- on the prediction of shock-cell location are then discussed. This …

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 …

Cooper’S Hawk Nest Site Characteristics In The Pineywoods Region, Richard R. Schaefer, D. Craig Rudolph, Josh B. Pierce, Jesse F. Fagan

Faculty Publications

Early accounts describe the Cooper’s Hawk (Accipiter cooperi) as a species in decline in much of North America during the early twentieth century (Bent 1937), particularly when in close proximity to humans (Eaton 1914). This decreasing population trend continued to be recognized later in the century in both Texas (Oberholser 1974) and Louisiana (Lowery 1974). Shooting and trapping during the first half of the 1900s, and pesticide use (especially DDT) after World War II are suggested as primary causes of the decline (Henny and Wight 1972, Bednarz et al. 1990). The Migratory Bird Treaty Act of 1972 and the ban …

A Time Series Approach To Electric Load Modelling, Matthias Benjamin Noller

Masters Theses

"With resources becoming more and more scarse [sic] as well as increasing competition caused by the liberalisation of the energy markets electric load modelling becomes ever more important for proper resource allocation.

This work tries to bridge the gap between long-term modelling done mainly via econometric approaches and short-term modelling in which time series models are more commonplace by focussing [sic] on pure time series modelling [sic] and exploring its limits in the process. Due to various seasonalities present in the data the approach chosen starts with a subdivision of the time axis in different time frames: A model for …

Dea With A Perfect Object: Analytical Solutions, Alexander Vaninsky

Publications and Research

For the main DEA models, adding a Perfect Object—that is, a virtual object that has the smallest inputs and greatest outputs—to a collection of actual objects permits obtaining solutions analytically. The paper derives formulas for the solutions and demonstrates that computations with them comprise simple operations with ratios of inputs and outputs while avoiding the use of linear programming (LP) algorithms. A numerical example illustrates the utility of the approach.

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 …

On Constrained Optimization Schemes For Joint Inversion Of Geophysical Datasets, Uram Anibal Sosa Aguirre

Open Access Theses & Dissertations

In the area of geological sciences, there exist several experimental techniques used to advance in the understanding of the Earth. We implement a joint inversion least-squares (LSQ) algorithm to characterize one dimensional Earth's structure by using seismic shear wave velocities as a model parameter. We use two geophysical datasets sensitive to shear velocities, namely Receiver Function and Surface Wave dispersion velocity observations, with a choice of an optimization method: Truncated Singular Value Decomposition (TSVD) or Primal-Dual Interior-Point (PDIP). The TSVD and the PDIP methods solve a regularized unconstrained and a constrained minimization problem, respectively. Both techniques include bounds into the …

Nonlinear Behaviour Of Sea Surface Waves Based On Low-Gradient Phase-Only Scattering Effects, Jonathan Blackledge, Eugene Coyle, Derek Kearney

Conference papers

Nonlinear sea waves generated by the wind, including freak waves, are considered to be phenomena that can be modelled using the nonlinear (cubic) Schrodinger equation, for example. However, there is a problem with this approach which is that sea surface waves, driven by wind speeds of varying strength, must be considered to be composed of two distinct types, namely, linear waves and nonlinear waves. In this paper, we consider a different approach to modelling ‘nonlinear’ waves that is based on a solution to the linear wave equation under a low-gradient, phase-only condition. This approach is entirely compatible with the fluid …

Analytical And Experimental Investigations Of Ships Impact Interaction With One-Sided Barrier, Ihab M. Grace

Wayne State University Dissertations

This study deals with impact interaction of ships with one-sided ice barrier during roll dynamics. An analytical model of ship roll motion interacting with ice is developed based on Zhuravlev and Ivanov non-smooth coordinate transformations. These transformations have the advantage of converting the vibro-impact oscillator into an oscillator without barriers such that the corresponding equation of motion does not contain any impact term. Such approaches, however, account for the energy loss at impact times in different ways. The present work, in particular, brings to the attention the fact that the impact dynamics may have qualitatively different response characteristics to different …

Uniform L1 Behavior Of A Time Discretization Method For A Volterra Integrodifferential Equation With Convex Kernel; Stability, Charles B. Harris, Richard D. Noren

Mathematics & Statistics Faculty Publications

We study stability of a numerical method in which the backward Euler method is combined with order one convolution quadrature for approximating the integral term of the linear Volterra integrodifferential equation u'(t) + ∫0 β (t - s)Au(s) ds = 0, t ≥ 0, u(0) = u0, which arises in the theory of linear viscoelasticity. Here A is a positive self-adjoint densely defined linear operator in a real Hilbert space, and β (t) is locally integrable, nonnegative, nonincreasing, convex, and -β'(t) is convex. We establish stability of the method under these hypotheses on β(t). Thus, …

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 …

Neural Spike Renormalization. Part Ii — Multiversal Chaos, Bo Deng

Department of Mathematics: Faculty Publications

Reported here for the first time is a chaotic infinite-dimensional system which contains infinitely many copies of every deterministic and stochastic dynamical system of all finite dimensions. The system is the renormalizing operator of spike maps that was used in a previous paper to show that the first natural number 1 is a universal constant in the generation of metastable and plastic spike-bursts of a class of circuit models of neurons.

Short-Term Facilitation May Stabilize Parametric Working Memory Trace, Vladimir Itskov, David Hansel, Misha Tsodyks

Department of Mathematics: Faculty Publications

Networks with continuous set of attractors are considered to be a paradigmatic model for parametric working memory (WM), but require fine tuning of connections and are thus structurally unstable. Here we analyzed the network with ring attractor, where connections are not perfectly tuned and the activity state therefore drifts in the absence of the stabilizing stimulus. We derive an analytical expression for the drift dynamics and conclude that the network cannot function as WM for a period of several seconds, a typical delay time in monkey memory experiments. We propose that short-term synaptic facilitation in recurrent connections significantly improves the …

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 …

On Greenberg's Question: An Algebraic And Computational Approach, David H. Chapman

LSU Doctoral Dissertations

Greenberg asked whether arithmetically equivalent number fields share the same Iwasawa invariants. In this dissertation it is shown that the problem naturally breaks up into four cases, depending on properties of Galois groups. This analysis is then used to give a positive answer to Greenberg’s question in some nontrivial examples.

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 …

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.

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 …

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.

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 …

A Second Elasticity Element Using The Matrix Bubble, Jay Gopalakrishnan, Johnny Guzmán

Mathematics and Statistics Faculty Publications and Presentations

We presented a family of finite elements that use a polynomial space augmented by certain matrix bubbles in Cockburn et al. (2010) A new elasticity element made for enforcing weak stress symmetry. Math. Comput., 79, 1331–1349 . In this sequel we exhibit a second family of elements that use the same matrix bubble. This second element uses a stress space smaller than the first while maintaining the same space for rotations (which are the Lagrange multipliers corresponding to a weak symmetry constraint). The space of displacements is of one degree less than the first method. The analysis, while similar to …

Analysis Of The Dpg Method For The Poisson Equation, Leszek Demkowicz, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

We give an error analysis of the recently developed DPG method applied to solve the Poisson equation and a convection-dffusion problem. We prove that the method is quasioptimal. Error estimates in terms of both the mesh size h and the polynomial degree p (for various element shapes) can be derived from our results. Results of extensive numerical experiments are also presented.

Variables Affecting Crime Rate, Jaime Zeigler

Honors Program Theses

The Federal Bureau of Investigation releases data about crime statistics. They publish the raw data and provide factors that influence the crime rate. They provide the general public with a few variables that they deemed most influential, but do not provide the statistical analysis to support. After performing a statistical analysis, I support or disprove their claims. Another way to question the validity of regression is comparing the current regression to a previous regression performed two years ago by myself with the same variables from the same source. An additional aspect that this paper explores the history of factors affecting …

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 …