Physical Sciences and Mathematics Commons^™

A Multi-Objective Approach To A Bipartite Assignment Matching Problem Using Weighted Values From Multiple Contraints, Greg S. Jeong

Theses and Dissertations

US Air Force recruiters routinely assign new recruits to available jobs every month. The goal is to find the best assignments in an efficient manner. Although this problem is modeled as a bipartite assignment matching problem, it is not new to the field of Operations Research. This research presents a new approach to solve assignment matching problems given multiple side constraints. Using two multi-criteria optimization techniques, lexicographic optimization and the elastic constraint method, the assignment matching algorithm efficiently produces an optimal solution in a fraction of the time currently spent. This approach is demonstrated in assigning new USAF recruits to …

Screening And Sufficiency In Multiobjective Decision Problems With Large Alternative Sets, Michael D. Cote

Theses and Dissertations

Portfolio selection problems with combinatorially-large alternative sets can be impossible to evaluate precisely on a reasonable timescale. When portfolios require complex modeling for performance assessment, prohibitive computational processing times can result. Eliminating a small number of alternatives through an intelligent screening process can greatly reduce the number of alternative combinations, thereby decreasing a problem's evaluation time and cost. A methodology was developed for the class of hierarchical portfolio selection problems in which multiple objectives are all judged on the same sub-objectives. First, a novel capability-based alternative screening process was devised to identify and remove poor alternatives, thereby reducing the number …

An Algorithm For Wavelet–Based Elemental Spectrum Analysis, Bruce Kessler

Mathematics Faculty Publications

At the previous Approximation Theory XII meeting, I discussed some preliminary work with the Applied Physics Institute at Western Kentucky University in using multiwavelets to provide an objective analysis of gamma-ray spectrum generated from fast neutron bombardment of objects, for the purpose of identifying the elemental composition of the object. The method discussed at the time worked moderately well with the limited amount of data provided, but subsequent use with data sets of different compounds and with different detectors brought to light serious flaws with its implementation.

This talk will illustrate those issues and will address how they have been …

Comments Submitted To The Us Patent Office On Enhancing The Quality Of Examination, Ron D. Katznelson

Ron D. Katznelson

No abstract provided.

On Simulating Univariate And Multivariate Burr Type Iii And Type Xii Distributions, Todd C. Headrick, Mohan D. Pant, Yanyan Sheng

Mohan Dev Pant

This paper describes a method for simulating univariate and multivariate Burr Type III and Type XII distributions with specified correlation matrices. The methodology is based on the derivation of the parametric forms of a pdf and cdf for this family of distributions. The paper shows how shape parameters can be computed for specified values of skew and kurtosis. It is also demonstrated how to compute percentage points and other measures of central tendency such as the mode, median, and trimmed mean. Examples are provided to demonstrate how this Burr family can be used in the context of distribution fitting using …

Computing Prime Harmonic Sums, Eric Bach, Dominic Klyve, Jonathan P. Sorenson

Jonathan P. Sorenson

We discuss a method for computing Σ �≤� 1/�, using time about �2/3 and space about �1/3. It is based on the Meissel-Lehmer algorithm for computing the prime-counting function �(�), which was adapted and improved by Lagarias, Miller, and Odlyzko. We used this algorithm to determine the first point at which the prime harmonic sum first crosses.

Computing Prime Harmonic Sums, Eric Bach, Dominic Klyve, Jonathan P. Sorenson

Jonathan P. Sorenson

We discuss a method for computing Σ �≤� 1/�, using time about �2/3 and space about �1/3. It is based on the Meissel-Lehmer algorithm for computing the prime-counting function �(�), which was adapted and improved by Lagarias, Miller, and Odlyzko. We used this algorithm to determine the first point at which the prime harmonic sum first crosses.

First-Order And Second-Order Optimality Conditions For Nonsmooth Constrained Problems Via Convolution Smoothing, Andrew C. Eberhard, Boris S. Mordukhovich

Mathematics Research Reports

This paper mainly concerns deriving first-order and second-order necessary (and partly sufficient) optimality conditions for a general class of constrained optimization problems via smoothing regularization procedures based on infimal-like convolutions/envelopes. In this way we obtain first-order optimality conditions of both lower subdifferential and upper subdifferential types and then second-order conditions of three kinds involving, respectively, generalized second-order directional derivatives, graphical derivatives of first-order subdifferentials, and secondorder subdifferentials defined via coderivatives of first-order constructions.

Time Is Not A Vector: Corrections To The Article “Vectorial Relativity Versus Special Or General Relativity?”, Jorge A. Franco

Jorge A Franco

In this work the main conceptual errors that sequentially were introduced in the development of the Special Theory of Relativity (SR) are explained. A simple presentation of the Lorentz Transformations (LT) is given, within where it is emphasized that, by using an incomplete configuration, repeated by more than one hundred years, it leads to a first error of a chain of them, when it is assumed that the cross sectional components, in the movable inertial reference system, are invariant or not affected by its relative movement respect a fixed inertial system, on the basis of a presumed “postulate of isotropy“ …

Software Internationalization: A Framework Validated Against Industry Requirements For Computer Science And Software Engineering Programs, John Huân Vũ

Master's Theses

View John Huân Vũ's thesis presentation at http://youtu.be/y3bzNmkTr-c.

In 2001, the ACM and IEEE Computing Curriculum stated that it was necessary to address "the need to develop implementation models that are international in scope and could be practiced in universities around the world." With increasing connectivity through the internet, the move towards a global economy and growing use of technology places software internationalization as a more important concern for developers. However, there has been a "clear shortage in terms of numbers of trained persons applying for entry-level positions" in this area. Eric Brechner, Director of Microsoft Development Training, suggested …

Patent Examination Policy And The Social Costs Of Examiner Allowance And Rejection Errors, Ron D. Katznelson

Ron D. Katznelson

No abstract provided.

Modular Exponentiation Via The Explicit Chinese Remainder Theorem, Daniel J. Bernstein, Jonathan P. Sorenson

Jonathan P. Sorenson

In this paper we consider the problem of computing xe mod m for large integers x, e, and m. This is the bottleneck in Rabin’s algorithm for testing primality, the Diffie-Hellman algorithm for exchanging cryptographic keys, and many other common algorithms.

Modular Exponentiation Via The Explicit Chinese Remainder Theorem, Daniel J. Bernstein, Jonathan P. Sorenson

Jonathan P. Sorenson

In this paper we consider the problem of computing xe mod m for large integers x, e, and m. This is the bottleneck in Rabin’s algorithm for testing primality, the Diffie-Hellman algorithm for exchanging cryptographic keys, and many other common algorithms.

Selective Recursive Kernel Learning For Online Identification Of Nonlinear Systems With Narx Form, Yi Liu, Haiqing Wang, Jiang Yu, Ping Li

Dr. Yi Liu

Online identification of nonlinear systems is still an important while difficult task in practice. A general and simple online identification method, namely Selective Recursive Kernel Learning (SRKL), is proposed for multi-input–multi-output (MIMO) systems with the nonlinear autoregressive with exogenous input form. A two-stage RKL online identification framework is first formulated, where the information contained by a sample (i.e., the new arriving or old useless one) can be introduced into and/or deleted from the model, recursively. Then, a sparsification strategy to restrict the model complexity is developed to guarantee all the output channels of the MIMO model accurate simultaneously. Specially, a …

Phenotypic Variance Predicts Symbiont Population Densities In Corals: A Modeling Approach, Robert Van Woesik, Kazuyo Shiroma, Semen Koksal

Ocean Engineering and Marine Sciences Faculty Publications

We test whether the phenotypic variance of symbionts (Symbiodinium) in corals is closely related with the capacity of corals to acclimatize to increasing seawater temperatures. Moreover, we assess whether more specialist symbionts will increase within coral hosts under ocean warming. The present study is only applicable to those corals that naturally have the capacity to support more than one type of Symbiodinium within the lifetime of a colony; for example, Montastraea annularis and Montastraea faveolata. Methodology/Principal Findings: The population dynamics of competing Symbiodinium symbiont populations were projected through time in coral hosts using a novel, discrete time optimal-resource model. Models …

An Analytical And Numerical Treatment Of The Carter Constant For Inclined Elliptical Orbits About A Massive Kerr Black Hole, Peter Komorowski, Sree Ram Valluri, Martin Houde

WORLDiscoveries Research Showcase

In an extreme binary black hole system, an orbit will increase its angle of inclination (i) as it evolves in Kerr spacetime. We focus our attention on the behaviour of the Carter constant (Q) for near-polar orbits. The value of Q for bound orbits is non-negative; and an increase in Q corresponds to an increase in i. For a Schwarzschild black hole, the polar orbit represents the boundary between the prograde and retrograde orbits at which Q is at its maximum value. The introduction of spin (S = |J|/M2) to the massive black hole causes this boundary, or Abutment, to …

Fast Protein Structure Alignment, Yosi Shibberu, Allen Holder, Kyla Lutz

Mathematical Sciences Technical Reports (MSTR)

We address the problem of aligning the 3D structures of two proteins. Our pairwise comparisons are based on a new optimization model that is succinctly expressed in terms of linear transformations and highlights the problem’s intrinsic geometry. The optimization problem is approximately solved with a new polynomial time algorithm. The worst case analysis of the algorithm shows that the solution is bounded by a constant depending only on the data of the problem.

Enhanced Metric Regularity And Lipschitzian Properties Of Variational Systems, Francisco J. Aragón Artacho, Boris S. Mordukhovich

Mathematics Research Reports

This paper mainly concerns the study of a large class of variational systems governed by parametric generalized equations, which encompass variational and hemivariational inequalities, complementarity problems, first-order necessary optimality conditions, and other optimization-related models important for optimization theory and applications. An efficient approach to these issues has been developed in our preceding work [1] establishing qualitative and quantitative relationships between conventional metric regularity jsubregularity and Lipschitzian/calmness properties in the framework of parametric generalized equations in arbitrary Banach spaces. This paper provides, on one hand, significant extensions of the major results in [1] to new partial metric regularity and hemiregularity properties. …

Improved Automated Monitoring And New Analysis Algorithm For Circadean Phototaxis Rhythms In Chlamydomonas, Christa Gaskill, Jennifer Forbes-Stovall, Bruce Kessler, Mike Young, Claire A. Rinehart, Sigrid Jacobshagen

Bruce Kessler

Automated monitoring of circadian rhythms is an efficient way of gaining insight into oscillation parameters like period and phase for the underlying pacemaker of the circadian clock. Measurement of the circadian rhythm of phototaxis (swimming towards light) exhibited by the green alga Chlamydomonas reinhardtii has been automated by directing a narrow and dim light beam through a culture at regular intervals and determining the decrease in light transmittance due to the accumulation of cells in the beam. In this study, the monitoring process was optimized by constructing a new computercontrolled measuring machine that limits the test beam to wavelengths reported …

Integer Functions On The Cycle Space And Edges Of A Graph, Dan Slilaty

Mathematics and Statistics Faculty Publications

A directed graph has a natural Z-module homomorphism from the underlying graph’s cycle space to Z where the image of an oriented cycle is the number of forward edges minus the number of backward edges. Such a homomorphism preserves the parity of the length of a cycle and the image of a cycle is bounded by the length of that cycle. Pretzel and Youngs (SIAM J. Discrete Math. 3(4):544–553, 1990) showed that any Z-module homomorphism of a graph’s cycle space to Z that satisfies these two properties for all cycles must be such a map induced from an edge direction …

A Majorization Algorithm For Constrained Correlation Matrix Approximation, Daniel J. Simon, Jeff Abell

Electrical and Computer Engineering Faculty Publications

We desire to find a correlation matrix of a given rank that is as close as possible to an input matrix R, subject to the constraint that specified elements in must be zero. Our optimality criterion is the weighted Frobenius norm of the approximation error, and we use a constrained majorization algorithm to solve the problem. Although many correlation matrix approximation approaches have been proposed, this specific problem, with the rank specification and the constraints, has not been studied until now. We discuss solution feasibility, convergence, and computational effort. We also present several examples.

Improved Automated Monitoring And New Analysis Algorithm For Circadean Phototaxis Rhythms In Chlamydomonas, Christa Gaskill, Jennifer Forbes-Stovall, Bruce Kessler, Mike Young, Claire A. Rinehart, Sigrid Jacobshagen

Mathematics Faculty Publications

Automated monitoring of circadian rhythms is an efficient way of gaining insight into oscillation parameters like period and phase for the underlying pacemaker of the circadian clock. Measurement of the circadian rhythm of phototaxis (swimming towards light) exhibited by the green alga Chlamydomonas reinhardtii has been automated by directing a narrow and dim light beam through a culture at regular intervals and determining the decrease in light transmittance due to the accumulation of cells in the beam. In this study, the monitoring process was optimized by constructing a new computercontrolled measuring machine that limits the test beam to wavelengths reported …

Higher Homotopy Operations And Cohomology, David Blanc, Mark W. Johnson, James M. Turner

University Faculty Publications and Creative Works

We explain how higher homotopy operations, defined topologically, may be identified under mild assumptions with (the last of) the Dwyer-Kan-Smith cohomological obstructions to rectifying homotopy-commutative diagrams. © 2010 ISOPP.

The Camassa-Holm Hierarchy And Soliton Perturbations, Georgi Grahovski, Rossen Ivanov

Conference papers

The theory of soliton perturbations is considered. The focus is on the usefulness of the so-called Generalised Fourier Transform (GFT). This is a method that involves expansions over the complete basis of “squared solutions” of the spectral problem, associated to the soliton equation. The Inverse Scattering Transform for the corresponding hierarchy of soliton equations can be viewed as a GFT where the expansions of the solutions have generalised Fourier coefficients given by the scattering data. The GFT provides a natural setting for the analysis of small perturbations to an integrable equation: starting from a purely soliton solution one can ’modify’ …

Interaction Of Excited States In Two-Species Bose-Einstein Condensates: A Case Study, Todd Kapitula, Kody J. H. Law, Panayotis G. Kevrekidis

University Faculty Publications and Creative Works

In this paper we consider the existence and spectral stability of excited states in two-species Bose-Einstein condensates in the case of a pancake magnetic trap. Each new excited state found in this paper is to leading order a linear combination of two one-species dipoles, each of which is a spectrally stable excited state for one-species condensates. The analysis is done via a Lyapunov-Schmidt reduction and is valid in the limit of weak nonlinear interactions. Some conclusions, however, can be made at this limit which remain true even when the interactions are large.

High Accuracy Multiscale Multigrid Computation For Partial Differential Equations, Yin Wang

University of Kentucky Doctoral Dissertations

Scientific computing and computer simulation play an increasingly important role in scientific investigation and engineering designs, supplementing traditional experiments, such as in automotive crash studies, global climate change, ocean modeling, medical imaging, and nuclear weapons. The numerical simulation is much cheaper than experimentation for these application areas and it can be used as the third way of science discovery beyond the experimental and theoretical analysis. However, the increasing demand of high resolution solutions of the Partial Differential Equations (PDEs) with less computational time has increased the importance for researchers and engineers to come up with efficient and scalable computational techniques …

Singular Points Of Real Sextic Curves I, David A. Weinberg, Nicholas J. Willis

Faculty Publications - Department of Mathematics

A complete classification of the individual types of singular points is given for irreducible real sextic curves. This classification is derived by using the computer algebra system Maple. There are 191 types of singular points for real irreducible sextic curves. We clarify that the classification is based on computing just enough of the Puiseux expansion to separate the branches. A significant portion of the proof consists of a sequence of large symbolic computations that can be done nicely using Maple.

Bass’ Nk Groups And Cd H-Fibrant Hochschild Homology, G. Cortiñas, C. Haesemeyer, Mark E. Walker, C. Weibel

Department of Mathematics: Faculty Publications

The K-theory of a polynomial ring R[t ] contains the K-theory of R as a summand. For R commutative and containing Q, we describe K∗(R[t ])/K∗(R) in terms of Hochschild homology and the cohomology of Kähler differentials for the cdh topology.

We use this to address Bass’ question, whether K_n(R) = K_n(R[t ]) implies K_n(R) = K_n(R[t₁, t₂]). The answer to this question is affirmative when R is essentially of …

Parallelization Of The Wolff Single-Cluster Algorithm, Jevgenijs Kaupužs, Jānis Rimšāns, Roderick V.N. Melnik

Mathematics Faculty Publications

A parallel [open multiprocessing (OpenMP)] implementation of the Wolff single-cluster algorithm has been developed and tested for the three-dimensional (3D) Ising model. The developed procedure is generalizable to other lattice spin models and its effectiveness depends on the specific application at hand. The applicability of the developed methodology is discussed in the context of the applications, where a sophisticated shuffling scheme is used to generate pseudorandom numbers of high quality, and an iterative method is applied to find the critical temperature of the 3D Ising model with a great accuracy. For the lattice with linear size L=1024, we have …

Methods Of Variational Analysis In Pessimistic Bilevel Programming, Samarathunga M. Dassanayaka

Wayne State University Dissertations

Bilevel programming problems are of growing interest both from theoretical and practical points of view. These models are used in various applications, such as economic planning, network design, and so on. The purpose of this dissertation is to study the pessimistic (or strong) version of bilevel programming problems in finite-dimensional spaces. Problems of this type are intrinsically nonsmooth (even for smooth initial data) and can be treated by using appropriate tools of modern variational analysis and generalized differentiation developed by B. Mordukhovich.

This dissertation begins with analyzing pessimistic bilevel programs, formulation of the problems, literature review, practical application, existence of …