Applied Mathematics Commons^™

Bootstrapping Tsmars Models, Liangzhong Chen

Theses

We investigate bootstrap inference methods for nonlinear time series models obtained using Multivariate Adaptive Regression Splines for Time Series (TSMARS), for which theoretical properties are not currently known. We use two different methods of bootstrapping to obtain confidence intervals for the underlying nonlinear function and prediction intervals for future values, based on estimated TSMARS models for the bootstrapped data. We also explore the method of Bootstrap AGGregatING (Bagging), due to Breiman (1996), to investigate whether the residual and prediction mean squared errors from a fitted TSMARS model can be reduced by averaging across the values obtained from each of the …

Stability And Reconstruction For An Inverse Problem For The Heat Equations, Kurt M. Bryan, Lester Caudill

Mathematical Sciences Technical Reports (MSTR)

We examine the inverse problem of determining the shape of some unknown portion of the boundary of a region W from measurements of the Cauchy data for solutions to the heat equation on W. By suitably linearizing the inverse problem we obtain uniqueness and continuous dependence results. We propose an algorithm for recovering estimates of the unknown portion of the surface and use the insight gained from a detailed analysis of the inverse problem to regularize the inversion. Several computational examples are presented.

(A Note On)(2) The Shape Of The Erythrocyte, J. A. Adam

Mathematics & Statistics Faculty Publications

A note on the shape of the red blood cell is revisited, utilizing variational calculus to to find an extremum for the surface area of such a cell, using the volume as a constraint. A fairly significant error in the value of the volume is corrected, and the note concludes with a discussion of measures of cell shape (such as the sphericity index) which are more appropriate than the dimensional surface area to volume ratio.

Onset Of Superconductivity In Decreasing Fields For General Domains, Andrew J. Bernoff, Peter Sternberg

All HMC Faculty Publications and Research

Ginzburg–Landau theory has provided an effective method for understanding the onset of superconductivity in the presence of an external magnetic field. In this paper we examine the instability of the normal state to superconductivity with decreasing magnetic field for a closed smooth cylindrical region of arbitrary cross-section subject to a vertical magnetic field. We examine the problem asymptotically in the boundary layer limit (i.e., when the Ginzburg–Landau parameter, k, is large). We demonstrate that instability first occurs in a region exponentially localized near the point of maximum curvature on the boundary. The transition occurs at a value of the …

Calibrated Probabilistic Quantitative Precipitation Forecasts Based On The Mrf Ensemble, Frederick Anthony Eckel

Theses and Dissertations

Probabilistic quantitative precipitation forecasts (PQPF) based on the medium range forecast (MRF) ensemble are currently in operational use below their full potential quality (i.e., accuracy and reliability). This unfulfilled potential is due to the MRF ensemble being adversely affected by systematic errors which arise from an imperfect model and less than ideal ensemble initial perturbations. This thesis sought to construct a calibration to account for these systematic errors and thus produce higher quality PQPF. Systematic errors were explored with the use of the verification rank histogram, which tracks the performance of the ensemble. The information in these histograms was then …

Improved Mathematical Modeling For Gps Based Navigation, Salvatore Nardi

Theses and Dissertations

This thesis is concerned with the development of new closed form GPS position determination algorithms that work in the presence of pseudorange measurement noise. The mathematical derivation of two closed form algorithms, based on stochastic modeling and estimation techniques, is presented. The algorithms provide an estimate of the GPS solution parameters (viz., the user position and the user clock bias) as well as the estimation error covariance. The experimental results are analyzed by comparison to the baseline results from the conventional Iterative Least Squares (ILS) algorithm. In typical GPS scenarios, the closed form algorithms are extremely sensitive to noise, making …

Neural Network Modeling Of The Head-Related Transfer Function, Damion Reinhardt

Theses and Dissertations

Battlefield synthesis of 3-D audio may require the interpolation and compression of head-related transfer function (HRTF) data. This thesis is an implementation of a functional model of the HRTF using artificial neural networks (ANNs), the model provides both compression and interpolation.

A New Sequential Goodness Of Fit Test For The Three-Parameter Weibull Distribution With Known Shape Based On Skewness And Kurtosis, Jonathan C. Clough

Theses and Dissertations

The Weibull distribution finds wide applicability across a broad spectrum of disciplines and is very prevalent in reliability theory. Consequently, numerous statistical tests have been developed to determine whether sample data can be adequately modeled with this distribution. Unfortunately, the majority of these goodness-of-fit tests involve a substantial degree of computational complexity. The study presented here develops and evaluates a new sequential goodness-of-fit test for the three-parameter Weibull distribution with a known shape that delivers power comparable to popular procedures while dramatically reducing computational requirements. The new procedure consists of two distinct tests, using only the sample skewness and sample …

Flight Test And Handling Qualities Analysis Of A Longitudinal Flight Control System Using Multiobjective Techniques, John R. Anderson

Theses and Dissertations

This thesis addresses the application of optimal, multiobjective control theory control theory to flight control design for the approach and landing phase of flight. Five flight control systems were designed using classical, H2, H infinity, and Mixed H2/H infinity methods. The MATLAB™ MUTOOLS™ and AFIT MXTOOLS toolboxes were used to produce the optimal, multiobjective designs. These designs were implemented for flight test on the Calspan VSS I Learjet, simulating the unstable longitudinal dynamics of an F-16 type aircraft. A limited handling qualities investigation was performed. Model following was used in the design phase to meet handling qualities specifications. The designs …

Solving Geometric Knapsack Problems Using Tabu Search Heuristics, Christopher A. Chocolaad

Theses and Dissertations

An instance of the geometric knapsack problem occurs in air lift loading where a set of cargo must be chosen to pack in a given fleet of aircraft. This paper demonstrates a new heuristic to solve this problem in a reasonable amount of time with a higher quality solution then previously reported in literature. We also report a new tabu search heuristic to solve geometric knapsack problems.

The Set Of Hemispheres Containing A Closed Curve On The Sphere, Mary Kate Boggiano, Mark Desantis

Department of Math & Statistics Technical Report Series

Suppose you get in your car and take a drive on the sphere of radius R, so that when you return to your starting point the odometer indicates you've traveled less than 2πR. Does your path, γ, have to lie in some hemisphere?

This question was presented to us by Dr. Robert Foote of Wabash College. Previous authors chose two points, A and B, on γ such that these points divided γ into two arcs of equal length. Then they took the midpoint of the great circle arc joining A and B to be the North Pole and showed that …

Dynamical Systems: Predictability And Chaos, Blane Hollingsworth

Honors Capstone Projects and Theses

No abstract provided.

Positive Solutions For A Concave Semipositone Dirichlet Problem, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

No abstract provided for this article

Orthogonal Harmonic Analysis Of Fractal Measures, Palle Jorgensen, Steen Pedersen

Mathematics and Statistics Faculty Publications

We show that certain iteration systems lead to fractal measures admitting an exact orthogonal harmonic analysis.

On Intensities Of Modulated Cox Measures, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

In this paper we introduce and study functionals of the intensities of random measures modulated by a stochastic process ξ, which occur in applications to stochastic models and telecommunications. Modulation of a random measure by ξ is specified for marked Cox measures. Particular cases of modulation by ξ as semi-Markov and semiregenerative processes enabled us to obtain explicit formulas for the named intensities. Examples in queueing (systems with state dependent parameters, Little's and Campbell's formulas) demonstrate the use of the results.

A Fast Parallel Algorithm To Recognize P4-Sparse Graphs, Rong Lin, Stephan Olariu

Computer Science Faculty Publications

A number of problems in mobile computing, group-based collaboration, automated theorem proving, networking, scheduling, and cluster analysis suggested the study of graphs featuring certain “local density” characteristics. Typically, the notion of local density is equated with the absence of chordless paths of length three or more. Recently, a new metric for local density has been proposed, allowing a number of such induced paths to occur. More precisely, a graphG is called P4-sparse if no set of five vertices inG induces more than one chordless path of length three. P4-sparse graphs generalize the well-known class of cographs corresponding to …

Relationships Among The First Variation, The Convolution Product, And The Fourier-Feynman Transform, Chull Park, David Skough, David Storvick

Department of Mathematics: Faculty Publications

In this paper we examine the various relationships that exist among the first variation, the Fourier- Feynman transform, and the convolution product for functionals on Wiener space that belong to a Banach algebra S.

Subiecte Posibile Pentru Examenul De Admitere În Liceu Şi Examenul De Capacitate (In Romanian), Florentin Smarandache, Constantin Coanda, Gheorghe Duta

Branch Mathematics and Statistics Faculty and Staff Publications

Prezenta lucrare" încearcă să pună la dispoziţia elevilor şi profesorilor instrumente de evaluare a cunoştinţelor la toate capitolele din actuala programă de matematică. " În evoluţia adolescenţi/or din ţara noastră etapa admiterii în liceu mobilizează eforturi şi emoţii cu totul speciale. 'Actuala lucrare se doreşte a fi un sfljtuitor permanent În perioada fierbinte dintre e.;wmenul de capacitate şi admiterea În liceu. Testele cuprinse in această culegere au un caracter complementar faţă de multe materiale scrise În vederea sprijinirii celor ce se pregătesc pentru astfel de examene şi se referă la intreaga materie cuprinsă În programele analitice de aritmetică, algebră şi …

Steady Incompressible Magnetohydrodynamic Flow Near A Point Of Reattachment, J. M. Dorrepaal, S. Moosavizadeh

Mathematics & Statistics Faculty Publications

The oblique stagnation-point flow of an electrically conducting fluid in the presence of a magnetic field is a highly nonlinear problem whose solution is of interest even in the simplest of geometries. The problem models the flow of a viscous conducting fluid near a point where a separation vortex reattaches itself to a rigid boundary. A similarity solution exists which reduces the problem to a coupled system of four ordinary differential equations which can be integrated numerically. The problem has two independent parameters, the conductivity of the fluid and the strength of the magnetic field. Solutions are tabulated for a …

Uniform Lipschitz Continuity Of Best L(P)-Approximations By Polyhedral Sets, Martina Finzel, Wu Li

Mathematics & Statistics Faculty Publications

In this paper we prove that the metric projection Π_{k, p} onto a polyhedral subset K of ℝⁿ, endowed with the p-norm, is uniformly Lipschitz continuous with respect to p,1 , p , ∞. As a consequence the strict best approximation and the natural best approximation are Lipschitz continuous selections for the metric projections Π_k, _∞ and Π_k,1, respectively. This extends a recent analogous result in Berens et al. [J.Math. Anal. Appl. 213 1997, 183-201] on linear subspaces.

On Circulant Weighing Matrices, K. T. Arasu, Jennifer Seberry

Mathematics and Statistics Faculty Publications

Algebraic techniques are employed to obtain necessary conditions for the existence of certain circulant weighing matrices. As an application we rule out the existence of many circulant weighing matrices. We study orders n = 82 +8+1, for 10 ~ 8 ~ 25. These orders correspond to the number of points in a projective plane of order 8.

Asymptotically Tight Bounds For Performing Bmmc Permutations On Parallel Disk Systems, Thomas H. Cormen, Thomas Sundquist, Leonard F. Wisniewski

Dartmouth Scholarship

This paper presents asymptotically equal lower and upper bounds for the number of parallel I/O operations required to perform bit-matrix-multiply/complement (BMMC) permutations on the Parallel Disk Model proposed by Vitter and Shriver. A BMMC permutation maps a source index to a target index by an affine transformation over GF(2), where the source and target indices are treated as bit vectors. The class of BMMC permutations includes many common permutations, such as matrix transposition (when dimensions are powers of 2), bit-reversal permutations, vector-reversal permutations, hypercube permutations, matrix reblocking, Gray-code permutations, and inverse Gray-code permutations. The upper bound improves upon the asymptotic …

Lee Weights Of Z/4z-Codes From Elliptic Curves, José Felipe Voloch, Judy L. Walker

Department of Mathematics: Faculty Publications

In [15: J. L. Walker, Algebraic geometric codes over rings], the second author defined algebraic geometric codes over rings. This definition was motivated by two recent trends in coding theory: the study of algebraic geometric codes over finite fields, and the study of codes over rings. In that paper, many of the basic parameters of these new codes were computed. However, the Lee weight, which is very important for codes over the ring Z/4Z, was not considered. In [14: J.-F. Voloch and J. L. Walker, Euclidean weights of codes from elliptic curves over rings], this …

On C^1 Robust Singular Transitive Sets For Three-Dimensional Flows, Carlos Arnoldo Morales, Maria José Pacífico, Enrique Ramiro Pujals

Publications and Research

Abstract:

The main goal of this paper is to study robust invariant transitive sets containing singularities for C¹ flows on three-dimensional compact boundaryless manifolds:they are partially hyperbolic with volume expanding central direction. Moreover, they are either attractors or repellers. Robust here means that this property cannot be destroyed by small C¹-perturbations of the flow.

Résumé:

Le but de ce travail est d'étudier des ensembles invariants robustes ayant des singularités pour des flots C¹ sur des variétés tridimensionelles : ce sont des ensembles hyperboliques singuliers. << Robuste >> veut dire ici que cette propriété ne peut être détruite par des …

On The Structure Of Graphs With Few P4s, Luitpold Babel, Stephan Olariu

Computer Science Faculty Publications

We present new classes of graphs for which the isomorphism problem can be solved in polynomial time. These graphs are characterized by containing — in some local sense — only a small number of induced paths of length three. As it turns out, every such graph has a unique tree representation: the internal nodes correspond to three types of graph operations, while the leaves are basic graphs with a simple structure. The paper extends and generalizes known results about cographs, P₄-reducible graphs, and P₄-sparse graphs.

Error Correcting Codes Associated With Complex Hadamard Matrices, I. Heng, C. H. Cooke

Mathematics & Statistics Faculty Publications

For primes p > 2, the generalized Hadamard matrix H(p,pt) can be expressed as H = x^A, where the notation means h_ij = x^aij. It is shown that the row vectors of A represent a p-ary error correcting code. Depending upon the value of t, either linear or nonlinear codes emerge. Code words are equidistant and have minimum Hamming distance d = (p − 1)t. The code can be extended so as to possess N = p²t code words of length pt …

The Adjoint Alternative For Matrix Operators, C. H. Cooke

Mathematics & Statistics Faculty Publications

The following inverse problem is considered: given a matrix B of rank r, does there exist a matrix A such that

B = T(A) = adjoint (A)

where the classical adjoint operation is intended? Conditions are determined on the rank of B which decides whether or not B lies in the range of the matrix adjoint operator.

Error-Correcting Codes Associated With Generalized Hadamard Matrices Over Groups, Iem H. Heng

Mathematics & Statistics Theses & Dissertations

Classical Hadamard matrices are orthogonal matrices whose elements are ±1. It is well-known that error correcting codes having large minimum distance between codewords can be associated with these Hadamard matrices. Indeed, the success of early Mars deep-space probes was strongly dependent upon this communication technology.

The concept of Hadamard matrices with elements drawn from an Abelian group is a natural generalization of the concept. For the case in which the dimension of the matrix is q and the group consists of the p-th roots of unity, these generalized Hadamard matrices are called “Butson Hadamard Matrices BH(p, q)”, …

On Multiple Solutions Of A Nonlinear Dirichlet Problem, Alfonso Castro, Jorge Cossio, John M. Neuberger

All HMC Faculty Publications and Research

We prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. We also prove that if the region is a ball the semilinear elliptic problem has two solutions that change sign and are nonradial.

The Fate And Transport Of Airborne Jp-4 And Jp-8 Aerosol During Cold Startup, Bradford Eugene Buckman

Theses and Dissertations

During cold startup (engine warm-up) procedures at northern tier bases, fuel aerosol (JP-4 and JP-8) is emitted before complete combustion of the fuel occurs. The time necessary for complete combustion to occur may be as long as 10 minutes. Hence, during these first few minutes, aerosol is emitted at relatively high concentrations. This research investigates the principle behavior of the emitted aerosol: advection, dispersion, evaporation, and settling. Using previous work in fuel jettisoning and evaporation as a foundation, this thesis investigates the physical factors affecting the airborne concentration of fuel aerosol at different times, the amount of fuel aerosol reaching …