Physical Sciences and Mathematics Commons^™

Incorporating Death Into Health-Related Variables In Longitudinal Studies, Paula Diehr, Laura Lee Johnson, Donald L. Patrick, Bruce Psaty

UW Biostatistics Working Paper Series

Background: The aging process can be described as the change in health-related variables over time. Unfortunately, simple graphs of available data may be misleading if some people die, since they may confuse patterns of mortality with patterns of change in health. Methods have been proposed to incorporate death into self-rated health (excellent to poor) and the SF-36 profile scores, but not for other variables.

Objectives: (1) To incorporate death into the following variables: ADLs, IADLs, mini-mental state examination, depressive symptoms, body mass index (BMI), blocks walked per week, bed days, hospitalization, systolic blood pressure, and the timed walk. (2) To …

Integral Transforms, Convolution Products, And First Variations, Bong Jin Kim, Byoung Soo Kim, David Skough

Department of Mathematics: Faculty Publications

We establish the various relationships that exist among the integral transform F_α,βF, the convolution product (F∗G)α, and the first variation δF for a class of functionals defined on K[0,T], the space of complex-valued continuous functions on [0,T] which vanish at zero.

Discrete Approximations And Necessary Optimality Conditions For Functional-Differential Inclusions Of Neutral Type, Boris S. Mordukhovich, Lianwen Wang

Mathematics Research Reports

This paper deals with necessary optimality conditions for optimal control systems governed by constrained functional-differential inclusions of neutral type. While some results are available for smooth control systems governed by neutral functional-differential equations, we are not familiar with any results for neutral functional-differential inclusions, even with smooth cost functionals in the absence of endpoint constraints. Developing the method of discrete approximations and employing advanced tools of generalized differentiation, we conduct a variational analysis of neutral functional-differential inclusions and obtain new necessary optimality conditions of both Euler-Lagrange and Hamiltonian types.

A Computational Model For Martensitic Thin Films With Compositional Fluctuation, Pavel Bělík, Mitchell Luskin

Faculty Authored Articles

We develop a computational model for the martensitic first-order structural phase transformation in a single crystal thin film, and we use this model to study the effect of spatial compositional fluctuation, spatial temporal noise, and the loss of stability of the metastable phase at temperatures sufficiently far from the transformation temperature.

Computational Modeling Of Softening In A Structural Phase Transformation, Pavel Bělík, Mithcell Luskin

Faculty Authored Articles

We develop a free energy density to model a structural first-order phase transformation from a high-temperature cubic phase to a low-temperature tetragonal phase. The free energy density models the softening of the elastic modulus controlling the low-energy path from the cubic to the tetragonal lattice, the loss of stability of the tetragonal phase at high temperatures and the loss of stability of the cubic phase at low temperatures, and the effect of compositional fluctuation on the transformation temperature.

Numerical experiments are given for the quasi-static cooling and heating of a single crystal thin film through the transformation. Tweed-like oscillations are …

Diel Activity Patterns Of The Louisiana Pine Snakes (Pituophis Ruthveni) In Eastern Texas, Marc J. Ealy, Robert R. Fleet, D. Craig Rudolph

Faculty Publications

This study examined the diel activity patterns of six Louisiana pine snakes in eastern Texas using radio-telemetry. snakes were monitored for 44 days on two study areas from May to October 1996. Louisana pine snakes were primarily diurnal with moderate crepuscular activity, spending the night within pocket gopher burrows or inactive on the surface. During daylight hours, snakes spent approximately 59% of their time underground within gopher burrows, burned out/rotten stumps, or nine-branded armadillo (Dasypus novemcinctus) burrows. Remaining time was spent on the surface either close to subteranean refuge, or in long distance movements that generally terminet at …

Bioconductor: Open Software Development For Computational Biology And Bioinformatics, Robert C. Gentleman, Vincent J. Carey, Douglas J. Bates, Benjamin M. Bolstad, Marcel Dettling, Sandrine Dudoit, Byron Ellis, Laurent Gautier, Yongchao Ge, Jeff Gentry, Kurt Hornik, Torsten Hothorn, Wolfgang Huber, Stefano Iacus, Rafael Irizarry, Friedrich Leisch, Cheng Li, Martin Maechler, Anthony J. Rossini, Guenther Sawitzki, Colin Smith, Gordon K. Smyth, Luke Tierney, Yee Hwa Yang, Jianhua Zhang

Bioconductor Project Working Papers

The Bioconductor project is an initiative for the collaborative creation of extensible software for computational biology and bioinformatics. We detail some of the design decisions, software paradigms and operational strategies that have allowed a small number of researchers to provide a wide variety of innovative, extensible, software solutions in a relatively short time. The use of an object oriented programming paradigm, the adoption and development of a software package system, designing by contract, distributed development and collaboration with other projects are elements of this project's success. Individually, each of these concepts are useful and important but when combined they have …

Swarming Patterns In A Two-Dimensional Kinematic Model For Biological Groups, Chad M. Topaz, Andrea L. Bertozzi

Chad M. Topaz

We construct a continuum model for the motion of biological organisms experiencing social interactions and study its pattern-forming behavior. The model takes the form of a conservation law in two spatial dimensions. The social interactions are modeled in the velocity term, which is nonlocal in the population density and includes a parameter that controls the interaction length scale. The dynamics of the resulting partial integrodifferential equation may be uniquely decomposed into incompressible motion and potential motion. For the purely incompressible case, the model resembles one for fluid dynamical vortex patches. There exist solutions which have constant population density and compact …

Multifrequency Control Of Faraday Wave Patterns, Chad M. Topaz, Jeff Porter, Mary Silber

Chad M. Topaz

We show how pattern formation in Faraday waves may be manipulated by varying the harmonic content of the periodic forcing function. Our approach relies on the crucial influence of resonant triad interactions coupling pairs of critical standing wave modes with damped, spatiotemporally resonant modes. Under the assumption of weak damping and forcing, we perform a symmetry-based analysis that reveals the damped modes most relevant for pattern selection, and how the strength of the corresponding triad interactions depends on the forcing frequencies, amplitudes, and phases. In many cases, the further assumption of Hamiltonian structure in the inviscid limit determines whether the …

Pattern Control Via Multi-Frequency Parametric Forcing, Jeff Porter, Chad M. Topaz, Mary Silber

Chad M. Topaz

We use symmetry considerations to investigate control of a class of resonant three-wave interactions relevant to pattern formation in weakly damped, parametrically forced systems near onset. We classify and tabulate the most important damped, resonant modes and determine how the corresponding resonant triad interactions depend on the forcing parameters. The relative phase of the forcing terms may be used to enhance or suppress the nonlinear interactions. We compare our symmetry-based predictions with numerical and experimental results for Faraday waves. Our results suggest how to design multifrequency forcing functions that favor chosen patterns in the lab.

Uniqueness Theorems In Bioluminescence Tomography, Ge Wang, Yi Li, Ming Jiang

Yi Li

Motivated by bioluminescent imaging needs for studies on gene therapy and other applications in the mouse models, a bioluminescence tomography (BLT) system is being developed in the University of Iowa. While the forward imaging model is described by the well-known diffusion equation, the inverse problem is to recover an internal bioluminescent source distribution subject to Cauchy data. Our primary goal in this paper is to establish the solution uniqueness for BLT under practical constraints despite the ill-posedness of the inverse problem in the general case. After a review on the inverse source literature, we demonstrate that in the general case …

Uniqueness Theorems In Bioluminescence Tomography, Ge Wang, Yi Li, Ming Jiang

Mathematics and Statistics Faculty Publications

Motivated by bioluminescent imaging needs for studies on gene therapy and other applications in the mouse models, a bioluminescence tomography (BLT) system is being developed in the University of Iowa. While the forward imaging model is described by the well-known diffusion equation, the inverse problem is to recover an internal bioluminescent source distribution subject to Cauchy data. Our primary goal in this paper is to establish the solution uniqueness for BLT under practical constraints despite the ill-posedness of the inverse problem in the general case. After a review on the inverse source literature, we demonstrate that in the general case …

The Dual Spectral Set Conjecture, Steen Pedersen

Mathematics and Statistics Faculty Publications

Suppose that Λ = (aZ + b) ∪ (cZ + d) where a, b, c, d are real numbers such that a ≠ 0 and c ≠ 0. The union is not assumed to be disjoint. It is shown that the translates Ω + λ, λ is an element of Λ, tile the real line for some bounded measurable set Ω if and only if the exponentials e_λ(x) = e^i2πλx, λ is an element of Λ, form an orthogonal basis for some bounded measurable set Ω'.

Discrete-Time Approximations Of Stochastic Delay Equations: The Milstein Scheme, Yaozhong Hu, Salah-Eldin A. Mohammed, Feng Yan

Articles and Preprints

In this paper, we develop a strong Milstein approximation scheme for solving stochastic delay differential equations (SDDE's). The scheme has convergence order 1. In order to establish the scheme, we prove an infinite-dimensional Itô formula for "tame" functions acting on the segment process of the solution of an SDDE. It is interesting to note that the presence of the memory in the SDDE requires the use of the Malliavin calculus and the anticipating stochastic analysis of Nualart and Pardoux. Given the non-anticipating nature of the SDDE, the use of anticipating calculus methods appears to be novel.

A Survey Of Results Involving Transforms And Convolutions In Function Space, David Skough, David Storvick

Department of Mathematics: Faculty Publications

In this paper we survey various results involving Fourier-Wiener transforms, Fourier-Feynman transforms, integral transforms and convolution products of functionals over function space that have been established since Cameron and Martin first introduced Fourier-Wiener transforms in 1945.

Which Mean Do You Mean?: An Exposition On Means, Mabrouck K. Faradj

LSU Master's Theses

The objective of this thesis is to give a brief exposition on the theory of means. In Greek mathematics, means are intermediate values between two extremes, while in modern mathematics, a mean is a measure of the central tendency for a set of numbers. We begin by exploring the origin of the antique means and list the classical means. Next, we present an overview of the theories of binary means and n-ary means. We include a general discussion on axiomatic systems for means and present theorems on properties that characterize the most common types of means.

Semilinear Equations With Discrete Spectrum, Alfonso Castro

All HMC Faculty Publications and Research

This is an overview of the solvability of semilinear equations where the linear part has discrete spectrum. Semilinear elliptic and hyperbolic equations, as well as Hammerstein integral equations, are used as motivating examples. The presentation is intended to be accessible to non experts.

An Existence Result For A Class Of Sublinear Semipositone Systems, Alfonso Castro, C. Maya, Ratnasingham Shivaji

All HMC Faculty Publications and Research

We consider the existence of positive solutions for the system

-Δu_i = λ[f_i(u₁,u₂,...,u_m) - h_i]; Ω

u_i = 0; ∂Ω

where λ > 0 is a parameter, Δ is the Laplacian operator, Ω is a bounded domain in Rⁿ; n ≥ 1 with a smooth boundary ∂Ω, f_i are C¹ functions satisfying f₁(0,0,...,0) = 0, lim z→∞ f_i(z,z,...,z) = ∞ and lim z→∞ f_i(z,z,...,z)/z = 0, and h_i are nonnegative continuous functions in Ω for i = 1,2,...,m. …

Examples Of Cayley 4-Manifolds, Weiqing Gu, Christopher Pries '03

All HMC Faculty Publications and Research

We determine several families of so-called Cayley 4-dimensional manifolds in the real Euclidean 8-space. Such manifolds are of interest because Cayley 4-manifolds are supersymmetric cycles that are candidates for representations of fundamental particles in String Theory. Moreover, some of the examples of Cayley manifolds discovered in this paper may be modified to construct explicit examples in our current search for new holomorphic invariants for Calabi-Yau 4-folds and for the further development of mirror symmetry.

We apply the classic results of Harvey and Lawson to find Cayley manifolds which are graphs of functions from the set of quaternions to itself. We …

A Partial Differential Equation To Model The Tacoma Narrows Bridge Failure, James Paul Swatzel

Theses Digitization Project

The purpose of this thesis was to examine a partial differential equation to model the Tacoma Narrows bridge failure. This thesis will examine the equation developed by Lazer and McKenna to model a suspension bridge in no wind.

Asymptotic Laplace Transforms, Claudiu Mihai

LSU Doctoral Dissertations

In this work we discuss certain aspects of the classical Laplace theory that are relevant for an entirely analytic approach to justify Heaviside's operational calculus methods. The approach explored here suggests an interpretation of the Heaviside operator ${cdot}$ based on the "Asymptotic Laplace Transform." The asymptotic approach presented here is based on recent work by G. Lumer and F. Neubrander on the subject. In particular, we investigate the two competing definitions of the asymptotic Laplace transform used in their works, and add a third one which we suggest is more natural and convenient than the earlier ones given. We compute …

Response Of Dark-Adapted Retinal Rod Photoreceptors, H. Khanal, V. Alexiades, E. Dibenedetto

Publications

The process of phototransduction, whereby light is converted into an electrical response, in rod and cone photoreceptors in the retina, involves as a key setp, the diffusion of the cytoplasmic, signaling molecules cGMP (cyclic guanosime monophosphate) and Ca²+ diffuse in the cytoplasm (the fluid surrounding the discs). the complex geometry of the rod creates computational difficulties. We present spatio-temporal compuational models for interacctions and diffusion of cGMP and Ca²+ in the cytoplasm of vertebrate rod photoreceptors, as well as numerical simulations fo the response to light of dark-adapted Salamander rods.

Attractors From One Dimensional Lorenz-Like Maps, Youngna Choi

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

In this paper we study the properties of expanding maps with a single discontinuity on a closed interval and the resultant dynamics. For such a map, there exists a compact invariant subset which shares a lot of common properties with classical attractors such as the topological transitivity of the restricted map and the density of the periodic points. The invariant set, with more conditions on the boundary, can be shown to have an isolating neighborhood, hence is a chaotic attractor in the strong sense. Not all such maps derive trapping regions, yet by perturbation, those non-attractors can be made to …

Controlling Wound Healing Through Debridement, M. A. Jones, Baojun Song, D. M. Thomas

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

The formation of slough (dead tissue) on a wound is widely accepted as an inhibitor to natural wound healing. In this article, a system of differential equations that models slough/wound interaction is developed. We prove a threshold theorem that provides conditions on the amount of slough to guarantee wound healing. As a state-dependent time scale, debridement (the periodic removal of slough) is used as a control. We show that closure of the wound can be reached in infinite time by debriding.

Estimation Of Standardized Mortality Ratio In Geographic Epidemiology, Anna Kettermann

Electronic Theses and Dissertations

The analysis of geographic variation of disease and its representation on a map form an important topic of research in epidemiology and in public health in general. Identification of spatial heterogeneity of relative risk using morbidity and mortality data is required. The usual technique of disease atlas generation consists of data collection (observed number of disease cases). These data are collected during a continuous period of time (5 to 10 years). The second aspect of atlas creation relates to the analysis of these data. A traditional measure of the spatial variation is usually taken as a ratio of the number …

Calculating The Unrestricted Partition Function Towards An Investigation Of Its Arithmetic Properties, Robert Jacobson

Capstone Research Projects

No abstract provided.

Query Of Image Content Using Wavelets And Gibbs-Markov Random Fields, Imtiaz Hossain

LSU Master's Theses

The central theme of this thesis is the application of Wavelets and Random Processes to content-based image query (on texture patterns, in particular). Given a query image, a content-based search extracts a certain representative measure (or signature) from the query image and likewise for all the target images in the search archive. A good representative measure is one that provides us with the ability to differentiate easily between different patterns. A distance measure is computed between the query properties and the properties of each of the target images. The lowest distance measure gives us the best target match for the …

Cox Regression Model, Lindsay Sarah Smith

LSU Master's Theses

Cox, in 1972, came up with the Cox Regression Model to deal handle failure time data. This work presents background information leading up to the Cox's regression model for censored survival data. The marginal and partial likelihood approaches to estimate the parameters in this model are presented in detail. The estimation techniques of the hazard and survivor functions are explained. All of these ideas are illustrated using data from the Veteran’s Administration lung cancer study.

The Radon-Gauss Transform, Vochita Mihai

LSU Doctoral Dissertations

Gaussian measure is constructed for any given hyperplane in an infinite dimensional Hilbert space, and this is used to define a generalization of the Radon transform to the infinite dimensional setting, using Gauss measure instead of Lebesgue measure. An inversion formula is obtained and a support theorem proved.

Quasioptimality Of Some Spectral Mixed Methods, Jay Gopalakrishnan, Leszek Demkowicz

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we construct a sequence of projectors into certain polynomial spaces satisfying a commuting diagram property with norm bounds independent of the polynomial degree. Using the projectors, we obtain quasioptimality of some spectralmixed methods, including the Raviart–Thomas method and mixed formulations of Maxwell equations. We also prove some discrete Friedrichs type inequalities involving curl.