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2010

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Articles 361 - 390 of 690

Full-Text Articles in Mathematics

On The Interlace Polynomials Of Forests, C. Anderson, Jonathan Cutler, A. J. Radcliffe, L. Traldi Jan 2010

On The Interlace Polynomials Of Forests, C. Anderson, Jonathan Cutler, A. J. Radcliffe, L. Traldi

Department of Mathematics Faculty Scholarship and Creative Works

The interlace polynomials were introduced by Arratia, Bollobás and Sorkin (2004) [3-5]. These invariants generalize to arbitrary graphs some special properties of the Euler circuits of 2-in, 2-out digraphs. Among many other results, Arratia, Bollobás and Sorkin (2004) [3-5] give explicit formulas for the interlace polynomials of certain types of graphs, including paths; it is natural to wonder whether or not it is possible to extend these formulas to larger classes of graphs. We give a combinatorial description of the interlace polynomials of trees and forests.

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Singular Points Of Real Sextic Curves I, David A. Weinberg, Nicholas J. Willis Jan 2010

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.

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Covariant Quantum Fields On Noncommutative Spacetimes, A. P. Balachandran, A. Ibort, G. Marmo, M. Martone Jan 2010

Covariant Quantum Fields On Noncommutative Spacetimes, A. P. Balachandran, A. Ibort, G. Marmo, M. Martone

Physics - All Scholarship

A spinless covariant field $\phi$ on Minkowski spacetime $\M^{d+1}$ obeys the relation $U(a,\Lambda)\phi(x)U(a,\Lambda)^{-1}=\phi(\Lambda x+a)$ where $(a,\Lambda)$ is an element of the Poincar\'e group $\Pg$ and $U:(a,\Lambda)\to U(a,\Lambda)$ is its unitary representation on quantum vector states. It expresses the fact that Poincar\'e transformations are being unitary implemented. It has a classical analogy where field covariance shows that Poincar\'e transformations are canonically implemented. Covariance is self-reproducing: products of covariant fields are covariant. We recall these properties and use them to formulate the notion of covariant quantum fields on noncommutative spacetimes. In this way all our earlier results on dressing, statistics, etc. for …

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Numerical Investigation Of Aeroelastic Mode Distribution For Aircraft Wing Model In Subsonic Air Flow, Marianna A. Shubov, Stephen B. Wineberg, Robert Holt Jan 2010

Numerical Investigation Of Aeroelastic Mode Distribution For Aircraft Wing Model In Subsonic Air Flow, Marianna A. Shubov, Stephen B. Wineberg, Robert Holt

Mathematics & Statistics

In this paper, the numerical results on two problems originated in aircraft wing modeling have been presented. The first problem is concerned with the approximation to the set of the aeroelastic modes, which are the eigenvalues of a certain boundary-value problem. The affirmative answer is given to the following question: can the leading asymptotical terms in the analytical formulas be used as reasonably accurate description of the aeroelastic modes? The positive answer means that these leading terms can be used by engineers for practical calculations. The second problem is concerned with the flutter phenomena in aircraft wings in a subsonic, …

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An F4-Style Involutive Basis Algorithm, Miao Yu Jan 2010

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.

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Parallelization Of The Wolff Single-Cluster Algorithm, Jevgenijs Kaupužs, Jānis Rimšāns, Roderick V.N. Melnik Jan 2010

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 …

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On Independent Sets In Purely Atomic Probability Spaces With Geometric Distribution., Eugen J. Ionascu, Alin A. Stancu Jan 2010

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.

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A Predator-Prey Model In The Chemostat With Time Delay, Guihong Fan Jan 2010

A Predator-Prey Model In The Chemostat With Time Delay, Guihong Fan

Faculty Bibliography

No abstract provided.

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Solution To Problem 11366, Eugen J. Ionascu Jan 2010

Solution To Problem 11366, Eugen J. Ionascu

Faculty Bibliography

No abstract provided.

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The Probabilistic Zeta Function, Bret Benesh Jan 2010

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.

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Ozsváth-Szabó And Rasmussen Invariants Of Cable Knots, Cornelia A. Van Cott Jan 2010

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 …

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Reply To "Comment On 'Cooperation In An Evolutionary Prisoner's Dilemma On Networks With Degree-Degree Correlations' ", Stephen Devlin, T Treloar Jan 2010

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.

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Augmented Measurement System Assessment, Nathaniel Stevens, R Browne, S H. Steiner, R J. Mackay Jan 2010

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 …

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The Ro(G)-Graded Serre Spectral Sequence, William C. Kronholm Jan 2010

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.

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Analysis Of The Consistency Of A Mixed Integer Programming-Based Multi-Category Constrained Discriminant Model, J. Paul Brooks, Eva K. Lee Jan 2010

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. …

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Nonlinear Model Reduction Using Group Proper Orthogonal Decomposition, Benjamin T. Dickinson, John R. Singler Jan 2010

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.

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Optimality Of Balanced Proper Orthogonal Decomposition For Data Reconstruction, John R. Singler Jan 2010

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.

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Balanced Pod Algorithm For Robust Control Design For Linear Distributed Parameter Systems, John R. Singler, Belinda A. Batten Jan 2010

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 …

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Computational Issues In Sensitivity Analysis For 1d Interface Problems, L. G. Davis, John R. Singler Jan 2010

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

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Boundary Data Maps For Schrödinger Operators On A Compact Interval, Stephen L. Clark, Fritz Gesztesy, M. Mitrea Jan 2010

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 …

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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 Jan 2010

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 …

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The Hodrick-Prescott Filter: A Special Case Of Penalized Spline Smoothing, Robert Paige L., A. A. Trindade Jan 2010

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 …

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Incorporating Genome Annotation In The Statistical Analysis Of Genomic And Epigenomic Tiling Array Data, Gayla R. Olbricht Jan 2010

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 …

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Optimal Control And Feedback Design Of State-Constrained Parabolic Systems In Uncertainty Conditions, Boris S. Mordukhovich Jan 2010

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 …

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Rayleigh Wave Dispersion Curve Inversion: Occam Versus The L1-Norm, Matthew M. Haney, Leming Qu Jan 2010

Rayleigh Wave Dispersion Curve Inversion: Occam Versus The L1-Norm, Matthew M. Haney, Leming Qu

Mathematics Faculty Publications and Presentations

We compare inversions of Rayleigh wave dispersion curves for shear wave velocity depth profiles based on the L2-norm (Occam's Inversion) and L1-norm (TV Regularization). We forward model Rayleigh waves using a finite-element method instead of the conventional technique based on a recursion formula and root-finding. The forward modeling naturally leads to an inverse problem that is overparameterized in depth. Solving the inverse problem with Occam's Inversion gives the smoothest subsurface model that satisfies the data. However, the subsurface need not be smooth and we therefore also solve the inverse problem with TV Regularization, a procedure that does not penalize discontinuities. …

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Foliations And Global Inversion, Eduardo C. Balreira Jan 2010

Foliations And Global Inversion, Eduardo C. Balreira

Mathematics Faculty Research

We consider topological conditions under which a locally invertible map admits a global inverse. Our main theorem states that a local diffeomorphism f : M → Rn is bijective if and only if Hn−1(M) = 0 and the pre-image of every affine hyperplane is non-empty and acyclic. The proof is based on some geometric constructions involving foliations and tools from intersection theory. This topological result generalizes in finite dimensions the classical analytic theorem of Hadamard-Plastock, including its recent improvement by Nollet-Xavier. The main theorem also relates to a conjecture of the aforementioned authors, involving the well known …

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Modeling Super-Spreading Events For Sars, Thembinkosi P. Mkhatshwa Jan 2010

Modeling Super-Spreading Events For Sars, Thembinkosi P. Mkhatshwa

Theses, Dissertations and Capstones

One of the intriguing characteristics of the 2003 severe acute respiratory syndrome (SARS) epidemics was the occurrence of super spreading events (SSEs). Super-spreading events for a specific infectious disease occur when infected individuals infect more than the average number of secondary cases. The understanding of these SSEs is critical to under- standing the spread of SARS. In this thesis, we present a modification of the basic SIR (Susceptible - Infected - Removed) disease model, an SIPR (Susceptible - Regular Infected - Super-spreader - Removed) model, which captures the effect of the SSEs.

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Positive Solutions For A System Of Singular Second Order Nonlocal Boundary Value Problems, Naseer Ahmad Asif, Paul W. Eloe, Rahmat Ali Khan Jan 2010

Positive Solutions For A System Of Singular Second Order Nonlocal Boundary Value Problems, Naseer Ahmad Asif, Paul W. Eloe, Rahmat Ali Khan

Mathematics Faculty Publications

Sufficient conditions for the existence of positive solutions for a coupled system of nonlinear nonlocal boundary value problems of the type (see PDF for details) are obtained. The nonlinearities (see PDF) are continuous and may be singular at t = 0, t = 1, x = 0, or y = 0. … An example is provided to illustrate the results.

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Periodic Solutions Of Neutral Delay Integral Equations Of Advanced Type, Muhammad Islam, Nasrin Sultana, James Booth Jan 2010

Periodic Solutions Of Neutral Delay Integral Equations Of Advanced Type, Muhammad Islam, Nasrin Sultana, James Booth

Mathematics Faculty Publications

We study the existence of continuous periodic solutions of a neutral delay integral equation of advanced type. In the analysis we employ three fixed point theorems: Banach, Krasnosel'skii, and Krasnosel'skii-Schaefer. Krasnosel'skii-Schaefer fixed point theorem requires an a priori bound on all solutions. We employ a Liapunov type method to obtain such bound.

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The Topology Of Incidence Pseudographs, Thomas R. James, Reinhard Klette Jan 2010

The Topology Of Incidence Pseudographs, Thomas R. James, Reinhard Klette

Mathematics Faculty Scholarship

Incidence pseudographs model a (re°exive and symmetric) inci- dence relation between sets of various dimensions, contained in a count- able family. Work by Klaus Voss in 1993 suggested that this general discrete model allows to introduce a topology, and some authors have done some studies into this direction in the past (also using alternative discrete models such as, for example, abstract complexes or orders on sets of cells). This paper provides a comprehensive overview about the topology of incidence pseudographs. This topology has various appli- cations, such as in modeling basic data in 2D or 3D digital picture analysis, or …

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