An F4-Style Involutive Basis Algorithm,
2010
University of Southern Mississippi
An F4-Style Involutive Basis Algorithm, Miao Yu
Mathematics Student Presentations
This paper introduces a new algorithm for computing Gröbner bases. To avoid as much ambiguity as possible, this algorithm combines the F4 algorithm and basic algorithm of involutive bases and it replaces the symbolic precomputation of S-polynomials and ordinary division in F4 by a new symbolic precomputation of non-multiplicative prolongations and involutive division. This innovation makes the sparse matrix of F4 in a deterministic way. As an example the Cyclic-4 problem is presented.
Parallelization Of The Wolff Single-Cluster Algorithm,
2010
University of Latvia
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 …
On Independent Sets In Purely Atomic Probability Spaces With Geometric Distribution.,
2010
Columbus State University
On Independent Sets In Purely Atomic Probability Spaces With Geometric Distribution., Eugen J. Ionascu, Alin A. Stancu
Faculty Bibliography
We are interested in constructing concrete independent events in purely atomic probability spaces with geometric distribution. Among other facts we prove that there are uncountable many sequences of independent events.
A Predator-Prey Model In The Chemostat With Time Delay,
2010
Columbus State University
A Predator-Prey Model In The Chemostat With Time Delay, Guihong Fan
Faculty Bibliography
No abstract provided.
Solution To Problem 11366,
2010
Columbus State University
Solution To Problem 11366, Eugen J. Ionascu
Faculty Bibliography
No abstract provided.
The Probabilistic Zeta Function,
2010
College of Saint Benedict/Saint John's University
The Probabilistic Zeta Function, Bret Benesh
Mathematics Faculty Publications
This paper is a summary of results on the PG(s) function, which is the reciprocal of the probabilistic zeta function for finite groups. This function gives the probability that s randomly chosen elements generate a group G, and information about the structure of the group G is embedded in it.
Ozsváth-Szabó And Rasmussen Invariants Of Cable Knots,
2010
University of San Francisco
Ozsváth-Szabó And Rasmussen Invariants Of Cable Knots, Cornelia A. Van Cott
Mathematics
We study the behavior of the Ozsváth–Szabó and Rasmussen knot concordance invariants τ and s on Km,n, the (m,n)–cable of a knot K where m and n are relatively prime. We show that for every knot K and for any fixed positive integer m, both of the invariants evaluated on Km,n differ from their value on the torus knot Tm,n by fixed constants for all but finitely many n>0. Combining this result together with Hedden’s extensive work on the behavior of τ on (m,mr+1)–cables yields bounds on the value of τ on any (m,n)–cable of K. In addition, several …
Reply To "Comment On 'Cooperation In An Evolutionary Prisoner's Dilemma On Networks With Degree-Degree Correlations' ",
2010
University of San Francisco
Reply To "Comment On 'Cooperation In An Evolutionary Prisoner's Dilemma On Networks With Degree-Degree Correlations' ", Stephen Devlin, T Treloar
Mathematics
We respond to the comment of Zhu et al. [Phys. Rev. E 82, 038101 (2010)] and show that the results in question are not misleading.
Augmented Measurement System Assessment,
2010
University of San Francisco
Augmented Measurement System Assessment, Nathaniel Stevens, R Browne, S H. Steiner, R J. Mackay
Mathematics
The standard plan for the assessment of the variation due to a measurement system involves a number of operators repeatedly measuring a number of parts in a balanced design. In this article, we consider the performance of two types of (unbalanced) assessment plans. In each type, we use a standard plan augmented with a second component. In type A augmentation, each operator measures a different set of parts once each. In type B augmentation, each operator measures the same set of parts once each. The goal of the paper is to identify good augmented plans for estimating the gauge repeatability …
The Ro(G)-Graded Serre Spectral Sequence,
2010
Whittier College
The Ro(G)-Graded Serre Spectral Sequence, William C. Kronholm
Mathematics
In this paper the Serre spectral sequence of Moerdijk and Svensson is extended from Bredon cohomology to RO(G)RO(G)-graded cohomology for finite groups GG. Special attention is paid to the case G=Z/2G=Z/2 where the spectral sequence is used to compute the cohomology of certain projective bundles and loop spaces.
Analysis Of The Consistency Of A Mixed Integer Programming-Based Multi-Category Constrained Discriminant Model,
2010
Virginia Commonwealth University
Analysis Of The Consistency Of A Mixed Integer Programming-Based Multi-Category Constrained Discriminant Model, J. Paul Brooks, Eva K. Lee
Statistical Sciences and Operations Research Publications
Classification is concerned with the development of rules for the allocation of observations to groups, and is a fundamental problem in machine learning. Much of previous work on classification models investigates two-group discrimination. Multi-category classification is less-often considered due to the tendency of generalizations of two-group models to produce misclassification rates that are higher than desirable. Indeed, producing “good” two-group classification rules is a challenging task for some applications, and producing good multi-category rules is generally more difficult. Additionally, even when the “optimal” classification rule is known, inter-group misclassification rates may be higher than tolerable for a given classification model. …
Nonlinear Model Reduction Using Group Proper Orthogonal Decomposition,
2010
Missouri University of Science and Technology
Nonlinear Model Reduction Using Group Proper Orthogonal Decomposition, Benjamin T. Dickinson, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
We propose a new method to reduce the cost of computing nonlinear terms in projec- tion based reduced order models with global basis functions. We develop this method by extending ideas from the group nite element (GFE) method to proper orthogonal decomposition (POD) and call it the group POD method. Here, a scalar two-dimensional Burgers' equation is used as a model problem for the group POD method. Numerical results show that group POD models of Burgers' equation are as accurate and are computationally more e cient than standard POD models of Burgers' equation.
Optimality Of Balanced Proper Orthogonal Decomposition For Data Reconstruction,
2010
Missouri University of Science and Technology
Optimality Of Balanced Proper Orthogonal Decomposition For Data Reconstruction, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
Proper orthogonal decomposition (POD) finds an orthonormal basis yielding an optimal reconstruction of a given dataset. We consider an optimal data reconstruction problem for two general datasets related to balanced POD, which is an algorithm for balanced truncation model reduction for linear systems. We consider balanced POD outside of the linear systems framework, and prove that it solves the optimal data reconstruction problem. the theoretical result is illustrated with an example.
Balanced Pod Algorithm For Robust Control Design For Linear Distributed Parameter Systems,
2010
Missouri University of Science and Technology
Balanced Pod Algorithm For Robust Control Design For Linear Distributed Parameter Systems, John R. Singler, Belinda A. Batten
Mathematics and Statistics Faculty Research & Creative Works
A mathematical model of a physical system is never perfect; therefore, robust control laws are necessary for guaranteed stabilization of the nominal model and also "nearby" systems, including hopefully the actual physical system. We consider the computation of a robust control law for large-scale finite dimensional linear systems and a class of linear distributed parameter systems. The controller is robust with respect to left coprime factor perturbations of the nominal system. We present an algorithm based on balanced proper orthogonal decomposition to compute the nonstandard features of this robust control law. Numerical results are presented for a convection diffusion partial …
Computational Issues In Sensitivity Analysis For 1d Interface Problems,
2010
Missouri University of Science and Technology
Computational Issues In Sensitivity Analysis For 1d Interface Problems, L. G. Davis, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
This paper is concerned with the construction of accurate and e cient computational algorithms for the numerical approximation of sensitivities with respect to a parameter dependent interface location. Motivated by sensitivity analysis with respect to piezoelectric actuator placement on an
Boundary Data Maps For Schrödinger Operators On A Compact Interval,
2010
Missouri University of Science and Technology
Boundary Data Maps For Schrödinger Operators On A Compact Interval, Stephen L. Clark, Fritz Gesztesy, M. Mitrea
Mathematics and Statistics Faculty Research & Creative Works
We provide a systematic study of boundary data maps, that is, 2 x 2 matrix-valued Dirichlet-to-Neumann and more generally, Robin-to-Robin maps, associated with one-dimensional Schrödinger operators on a compact interval [0, R] with separated boundary conditions at 0 and R. Most of our results are formulated in the non-self-adjoint context. Our principal results include explicit representations of these boundary data maps in terms of the resolvent of the underlying Schrödinger operator and the associated boundary trace maps, Krein-type resolvent formulas relating Schrödinger operators corresponding to different (separated) boundary conditions, and a derivation of the Herglotz property of boundary data maps …
High Accuracy Combination Method For Solving The Systems Of Nonlinear Volterra Integral And Integro-Differential Equations With Weakly Singular Kernels Of The Second Kind,
2010
Missouri University of Science and Technology
High Accuracy Combination Method For Solving The Systems Of Nonlinear Volterra Integral And Integro-Differential Equations With Weakly Singular Kernels Of The Second Kind, Xiaoming He, Lu Pan, Tao Lü
Mathematics and Statistics Faculty Research & Creative Works
This paper presents a high accuracy combination algorithm for solving the systems of nonlinear Volterra integral and integro-differential equations with weakly singular kernels of the second kind. Two quadrature algorithms for solving the systems are discussed, which possess high accuracy order and the asymptotic expansion of the errors. By means of combination algorithm, we may obtain a numerical solution with higher accuracy order than the original two quadrature algorithms. Moreover an a posteriori error estimation for the algorithm is derived. Both of the theory and the numerical examples show that the algorithm is effective and saves storage capacity and computational …
The Hodrick-Prescott Filter: A Special Case Of Penalized Spline Smoothing,
2010
Missouri University of Science and Technology
The Hodrick-Prescott Filter: A Special Case Of Penalized Spline Smoothing, Robert Paige L., A. A. Trindade
Mathematics and Statistics Faculty Research & Creative Works
We prove that the Hodrick-Prescott Filter (HPF), a commonly used method for smoothing econometric time series, is a special case of a linear penalized spline model with knots placed at all observed time points (except the first and last) and uncorrelated residuals. This equivalence then furnishes a rich variety of existing data-driven parameter estimation methods, particularly restricted maximum likelihood (REML) and generalized cross-validation (GCV). This has profound implications for users of HPF who have hitherto typically relied on subjective choice, rather than estimation, for the smoothing parameter. By viewing estimates as roots of an appropriate quadratic estimating equation, we also …
Incorporating Genome Annotation In The Statistical Analysis Of Genomic And Epigenomic Tiling Array Data,
2010
Missouri University of Science and Technology
Incorporating Genome Annotation In The Statistical Analysis Of Genomic And Epigenomic Tiling Array Data, Gayla R. Olbricht
Mathematics and Statistics Faculty Research & Creative Works
"A wealth of information and technologies are currently available for the genomewide investigation of many types of biological phenomena. Genomic annotation databases provide information about the DNA sequence of a particular organism and give locations of different types of genomic elements, such as the exons and introns of genes. Microarrays are a powerful type of technology that make use of DNA sequence information to investigate different types of biological phenomena on a genome-wide level. Tiling arrays are a unique type of microarray that provide unbiased, highdensity coverage of a genomic region, making them well suited for many applications, such as …
Optimal Control And Feedback Design Of State-Constrained Parabolic Systems In Uncertainty Conditions,
2010
Wayne State University
Optimal Control And Feedback Design Of State-Constrained Parabolic Systems In Uncertainty Conditions, Boris S. Mordukhovich
Mathematics Research Reports
The paper concerns minimax control problems for linear multidimensional parabolic systems with distributed uncertain perturbations and control functions acting in the Dirichlet boundary conditions. The underlying parabolic control system is functioning under hard/pointwise constraints on control and state variables. The main goal is to design a feedback control regulator that ensures the required state performance and robust stability under any feasible perturbations and minimize an energy-type functional under the worst perturbations from the given area. We develop a constructive approach to the minimax control design of constrained parabolic systems that is based on certain characteristic features of the parabolic dynamics …
