Applied Mathematics Commons^™

Using Domination To Analyze Rna Structures., Travis Reves Coake

Electronic Theses and Dissertations

Understanding RNA molecules is important to genomics research. Recently researchers at the Courant Institute of Mathematical Sciences used graph theory to model RNA molecules and provided a database of trees representing possible secondary RNA structures. In this thesis we use domination parameters to predict which trees are more likely to exist in nature as RNA structures. This approach appears to have promise in graph theory applications in genomics research.

Fréchet Subdifferential Calculus And Optimality Conditions In Nondifferentiable Programming, Boris S. Mordukhovich, Nguyen Mau Nam, N. D. Yen

Mathematics Research Reports

We develop various (exact) calculus rules for Frechet lower and upper subgradients of extended-realvalued functions in general Banach spaces. Then we apply this calculus to derive new necessary optimality conditions for some remarkable classes of problems in constrained optimization including minimization problems for difference-type functions under geometric and operator constraints as well as subdifferential optimality conditions for the so-called weak sharp minima.

Introduction (2005), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2005

Fifteenth Conference of the Association of Christians in the Mathematical Sciences

Disease Outbreaks In Coupled Populations : An Application To Measles Spread In Cameroon, Kirsten Maggie Viz

Theses, Dissertations and Culminating Projects

Many childhood diseases can be modeled mathematically using a system of differential equations that group the overall population into compartments. Much research has been done to understand and control the spread of these diseases within a single population and between coupled populations with constant parameters. In this thesis, we are concerned with how a disease is spread through and between coupled populations using models with time-varying parameters and asymmetric coupling.

Measles outbreaks in the West African country of Cameroon present a good example of disease spread with seasonality. By dividing Cameroon into two subpopulations and using parameters that reflect recent …

Lower Bounds For Simplicial Covers And Triangulations Of Cubes, Adam Bliss '03, Francis E. Su

All HMC Faculty Publications and Research

We show that the size of a minimal simplicial cover of a polytope P is a lower bound for the size of a minimal triangulation of P, including ones with extra vertices. We then use this fact to study minimal triangulations of cubes, and we improve lower bounds for covers and triangulations in dimensions 4 through at least 12 (and possibly more dimensions as well). Important ingredients are an analysis of the number of exterior faces that a simplex in the cube can have of a specified dimension and volume, and a characterization of corner simplices in terms of their …

A Mathematical Model For Treatment-Resistant Mutations Of Hiv, Helen Moore, Weiqing Gu

All HMC Faculty Publications and Research

In this paper, we propose and analyze a mathematical model, in the form of a system of ordinary differential equations, governing mutated strains of human immunodeficiency virus (HIV) and their interactions with the immune system and treatments. Our model incorporates two types of resistant mutations: strains that are not responsive to protease inhibitors, and strains that are not responsive to reverse transcriptase inhibitors. It also includes strains that do not have either of these two types of resistance (wild-type virus) and strains that have both types. We perform our analysis by changing the system of ordinary differential equations (ODEs) to …

Structure Preserving Algorithms For Computing The Symplectic Singular Value Decom Position, Archara Chaiyakarn

Dissertations

In this thesis we develop two types of structure preserving Jacobi algorithms for com puting the symplectic singular value decomposition of real symplectic matrices and complex symplectic matrices. Unlike general purpose algorithms, these algorithms produce symplectic structure in all factors of the singular value decomposition.

Our first algorithm uses the relation between the singular value decomposition and the polar decomposition to reduce the problem of finding the symplectic singular value decomposition to th a t of calculating the structured spectral decomposition of a doubly structured m atrix. A Jacobi-like m ethod is developed to compute this doubly structured spectral decomposition. …

Stratification And Domination In Graphs And Digraphs, Ralucca M. Gera

Dissertations

In this thesis we combine the idea of stratification with the one of domination in graphs and digraphs, respectively.

A graph is 2-stratified if its vertex set is partitioned into two classes, where the vertices in one class are colored red and those in the other class are colored blue. Let F be a 2-stratified graph rooted at some blue vertex v . An F -coloring of a graph G is a red-blue coloring of the vertices of G in which every blue vertexu belongs to a copy of F rooted at u . The F -domination number γ …

Global Optimality Conditions In Mathematical Programming And Optimal Control, Pariwat Pacheenburawana

Dissertations

We derive new first-order necessary and sufficient optimality conditions characterizing global minimizers in mathematical programming and optimal controlproblems. These conditions are based on level sets of an objective functional and they do not assume special structure of a problem (convexity, linearity, etc.). For a mathematical programming problem of minimization of a smooth functional on some compact convex set with equality nonlinear constraints, we derive first-order optimality conditions in the form of a generalized Lagrange multiplier rule. This rule should hold for any point from the level set of the objective functional corresponding to a global minimizer. We demonstrate that these …

A Sampling And Transformation Approach To Solving Random Differential Equations, Roger A. Erich

Theses and Dissertations

This research explores an innovative sampling method used to conduct uncertainty analysis on a system with one random input. Given the distribution of the random input, X, we seek to find the distribution of the output random variable Y. When the functional form of the transformation Y=g(X) is not explicitly known, complicated procedures, such as stochastic projection or Monte Carlo simulation must be employed. The main focus of this research is determining the distribution of the random variable Y=g(X) where g(X) is the solution to an ordinary differential equation and X is a random parameter. Here, y=g(X) is approximated by …

Steady State Stress In A Coated Infinite Half-Space Subjected To A Moving Load, Jason M. Cruthirds

Theses and Dissertations

This research investigates the use of coatings to mitigate the stress distribution into an infinite half-space. High energy impact phenomenon at velocities exceeding the speed of sound is an important area of interest to the Air Force Research Laboratory. Holloman Air Force Base's High Speed Test Track sustains significant damage due to this phenomenon. In this thesis, the track system and coating are modeled analytically with equations of motion in terms of linear displacements. Coating thickness and material properties of epoxy or polymer laminates are investigated to understand their affect of stress distribution in the rail. An analytic solution is …

Error Analysis Of Variable Degree Mixed Methods For Elliptic Problems Via Hybridization, Bernardo Cockburn, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

A new approach to error analysis of hybridized mixed methods is proposed and applied to study a new hybridized variable degree Raviart-Thomas method for second order elliptic problems. The approach gives error estimates for the Lagrange multipliers without using error estimates for the other variables. Error estimates for the primal and flux variables then follow from those for the Lagrange multipliers. In contrast, traditional error analyses obtain error estimates for the flux and primal variables first and then use it to get error estimates for the Lagrange multipliers. The new approach not only gives new error estimates for the new …

Environmental Acoustic Transfer Functions And Filtering Acoustic Signals, Brandon P. Dias

Theses and Dissertations

Signal processing is the method of taking a given signal and extracting useful information, usually by a means of a transformation of some kind. Acoustic signals are functions of time in which the output is a pressure or a velocity potential response. An acoustic signal is affected by the environment in which it propagates, so one can attempt to remove the environmental effects to extract the useful information, in this case the original signal. This thesis will derive, in a mathematical framework, the process of filtering extraneous signals in a way that yields the original signal, and will then apply …

Noise Estimation In The Presence Of Bpsk Digital Burst Transmissions, Susan E. Bettison

Theses and Dissertations

This research explores noise estimation techniques in an attempt to improve upon a previously developed digital burst transmission Binary Phase Shift Keyed (BPSK) demodulator. The demodulator success is dependent on the accuracy of the estimate of Power Spectral Density (PSD) of the unknown noise. Given a discrete time signal transformed into the frequency domain, the research seeks to determine if it is possible to effectively estimate the PSD of the unknown noise. The demodulator was developed using a new signal model for digital burst transmissions based on linear spectral subspace theory. Using this model and the redundancy properties of BPSK …

Reconstruction Of An Unknown Boundary Portion From Cauchy Data In N- Dimensions, Kurt Bryan, Lester Caudill

Department of Math & Statistics Faculty Publications

We consider the inverse problem of determining the shape of some inaccessible portion of the boundary of a region in n dimensions from Cauchy data for the heat equation on an accessible portion of the boundary. The inverse problem is quite ill-posed, and nonlinear. We develop a Newton-like algorithm for solving the problem, with a simple and efficient means for computing the required derivatives, develop methods for regularizing the process, and provide computational examples.

Balanced Scaling Vectors Using Linear Combinations Of Existing Scaling Vectors, Bruce Kessler

Mathematics Faculty Publications

The majority of the research done into creating balanced multiwavelets has involved establishing a series of conditions on the mask of the new scaling vector by solving a large nonlinear system. The result is a completely different new function vector solution to the dilation equation with the new matrix coefficients. The research presented here will show a way to use previously-constructed orthonormal scaling vectors to generate equivalent orthonormal scaling vectors that are balanced up to the approximation order of the previous scaling vector. The technique uses linear combinations of the integer translates of the previous-constructed scaling vector.

Cluster Analysis Of Genomic Data With Applications In R, Katherine S. Pollard, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In this paper, we provide an overview of existing partitioning and hierarchical clustering algorithms in R. We discuss statistical issues and methods in choosing the number of clusters, the choice of clustering algorithm, and the choice of dissimilarity matrix. In particular, we illustrate how the bootstrap can be employed as a statistical method in cluster analysis to establish the reproducibility of the clusters and the overall variability of the followed procedure. We also show how to visualize a clustering result by plotting ordered dissimilarity matrices in R. We present a new R package, hopach, which implements the hybrid clustering method, …

Multiple Testing Procedures And Applications To Genomics, Merrill D. Birkner, Katherine S. Pollard, Mark J. Van Der Laan, Sandrine Dudoit

U.C. Berkeley Division of Biostatistics Working Paper Series

This chapter proposes widely applicable resampling-based single-step and stepwise multiple testing procedures (MTP) for controlling a broad class of Type I error rates, in testing problems involving general data generating distributions (with arbitrary dependence structures among variables), null hypotheses, and test statistics (Dudoit and van der Laan, 2005; Dudoit et al., 2004a,b; van der Laan et al., 2004a,b; Pollard and van der Laan, 2004; Pollard et al., 2005). Procedures are provided to control Type I error rates defined as tail probabilities for arbitrary functions of the numbers of Type I errors, V_n, and rejected hypotheses, R_n. These error rates include: …

Robust Inferences For Covariate Effects On Survival Time With Censored Linear Regression Models, Larry Leon, Tianxi Cai, L. J. Wei

Harvard University Biostatistics Working Paper Series

Various inference procedures for linear regression models with censored failure times have been studied extensively. Recent developments on efficient algorithms to implement these procedures enhance the practical usage of such models in survival analysis. In this article, we present robust inferences for certain covariate effects on the failure time in the presence of "nuisance" confounders under a semiparametric, partial linear regression setting. Specifically, the estimation procedures for the regression coefficients of interest are derived from a working linear model and are valid even when the function of the confounders in the model is not correctly specified. The new proposals are …

Internal Design Of Uniform Shear Rate Dies, Thomas J. Awe, M. B. M. Eligindi, R. W. Langer, University Of Wisconsin - Eau Claire, Department Of Mathematics

Morehead Electronic Journal of Applicable Mathematics Archives

No abstract provided.

A Survey Of The Quadratic Assignment Problem, With Applications, Clayton W. Commander

Morehead Electronic Journal of Applicable Mathematics Archives

No abstract provided.

Implementing Lazy Streams In C++, David Renz, Mike Borowczak

Morehead Electronic Journal of Applicable Mathematics Archives

No abstract provided.

Erratum: “Uniqueness Theorems In Bioluminescence Tomography” [Med. Phys. 31, 2289–2299 (2004)], Ge Wang, Yi Li, Ming Jiang

Mathematics and Statistics Faculty Publications

In this Erratum, we present a correction to our proof of Theorem D.4 in Ref. 1.

Penalty Approximation And Analytical Characterization Of The Problem Of Super-Replication Under Portfolio Constraints, Alain Bensoussan, Nizar Touzi, José Luis Menaldi

Mathematics Faculty Research Publications

In this paper, we consider the problem of super-replication under portfolio constraints in a Markov framework. More specifically, we assume that the portfolio is restricted to lie in a convex subset, and we show that the super-replication value is the smallest function which lies above the Black-Scholes price function and which is stable for the so-called face lifting operator. A natural approach to this problem is the penalty approximation, which not only provides a constructive smooth approximation, but also a way to proceed analytically.

Impulsive Systems, Stanislav Zabic

LSU Doctoral Dissertations

Impulsive systems arise when dynamics produce discontinuous trajectories. Discontinuties occur when movements of states happen over a small interval that resembles a point-mass measure. We adopt the formalism in which the controlled dynamic inclusion is the sum of a slow and a fast time velocities belonging to two distinct vector fields. Fast time velocities are controlled by a vector valued Borel measure. The trajectory of impulsive systems is a function of bounded variation. To give a definition of solutions, a notion of graph completion of the control measure is needed. In the nonimpulsive case, a solution can be defined as …

Zeta Functions Of Finite Graphs, Debra Czarneski

LSU Doctoral Dissertations

Ihara introduced the zeta function of a finite graph in 1966 in the context of p-adic matrix groups. The idea was generalized to all finite graphs in 1989 by Hashimoto. We will introduce the zeta function from both perspectives and show the equivalence of both forms. We will discuss several properties of finite graphs that are determined by the zeta function and show by counterexample several properties of finite graphs that are not determined by the zeta function. We will also discuss the relationship between the zeta function of a finite graph and the spectrum of a finite graph.

An Introduction To Sdr's And Latin Squares, Jordan Bell, Carleton University, School Of Mathematics And Statistics

Morehead Electronic Journal of Applicable Mathematics Archives

No abstract provided.

Conformal Properties And Baecklund Transform For The Associated Camassa-Holm Equation, Rossen Ivanov

Articles

Integrable equations exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants. The most basic and important example is the KdV equation and the corresponding Schwarz-KdV equation. Other examples, including the Camassa-Holm equation and the associated Camassa-Holm equation are investigated in this paper. It is shown that the B¨acklund transform is related to the conformal properties of these equations. Some particular solutions of the Associated Camassa-Holm Equation are discussed also.

Feedback Classification Of Multi-Input Nonlinear Control Systems, Issa Amadou Tall

Articles and Preprints

We study the feedback group action on multi-input nonlinear control systems with uncontrollable mode. We follow slightly an approach proposed in Kang and Krener [W. Kang and A. J. Krener, SIAM J. Control. Optim., 30 (1992), pp. 1319–1337] which consists of analyzing the system and the feedback group step by step. We construct a normal form which generalizes, on one hand, the results obtained in the single-input case and, on the other hand, those recently obtained by the same author in the controllable case. We illustrate our results by studying the Caltech Multi-Vehicle Wireless Testbed (MVWT) and the prototype …

A Symbolic Operator Approach To Several Summation Formulas For Power Series, Tian-Xiao He, Leetsch Hsu, Peter Shiue, D. Torney

Scholarship

This paper deals with the summation problem of power series of the form Sba (f; x) = ∑a ≤ k ≤ b f(k) xk, where 0≤ a < b ≤ ∞, and {f(k)} is a given sequence of numbers with k Є [a, b) or f(t) is a differentiable function defined on [a, b). We present a symbolic summation operator with its various expansions, and construct several summation formulas with estimable remainders for Sba (f; x), by the aid of some classical interpolation series due to Newton, Gauss and Everett, respectively.