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 …
Rayleigh Wave Dispersion Curve Inversion: Occam Versus The L1-Norm,
2010
Boise State University
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. …
Foliations And Global Inversion,
2010
Trinity University
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 …
Modeling Super-Spreading Events For Sars,
2010
Marshall University
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.
Positive Solutions For A System Of Singular Second Order Nonlocal Boundary Value Problems,
2010
National University of Sciences and Technology, Rawalpindi, Pakistan
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.
Periodic Solutions Of Neutral Delay Integral Equations Of Advanced Type,
2010
University of Dayton
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.
The Topology Of Incidence Pseudographs,
2010
Otterbein University
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 …
Support Varieties And Representation Type Of Small Quantum Groups,
2010
University of South Alabama
Support Varieties And Representation Type Of Small Quantum Groups, Jorg Feldvoss, Sarah Witherspoon
University Faculty and Staff Publications
In this paper, we provide a wildness criterion for any finite dimensional Hopf algebra with finitely generated cohomology. This generalizes a result of Farnsteiner to not necessarily cocommutative Hopf algebras over ground fields of arbitrary characteristic. Our proof uses the theory of support varieties for modules, one of the crucial ingredients being a tensor product property for some special modules. As an application, we prove a conjecture of Cibils stating that small quantum groups of rank at least two are wild.
Curve Interpolation And Coding Theory,
2010
Gettysburg College
Curve Interpolation And Coding Theory, Darren B. Glass
Math Faculty Publications
Whether it is downloading files from the Internet, having conversations between cell phones, or sending information from a laptop to a printer, we often want to transmit data in situations where we need to worry about interference from other signals that may cause errors in the transmission. The branch of mathematics known as coding theory is dedicated to finding ways to tell when these are errors in transmission and, when possible, how to correct those errors. The goal of coding theory is to build as much redundancy as possible into a message without greatly increasing its length. [excerpt]
Review: Nontangential Limits In Pt(Μ)-Spaces And The Index Of Invariant Subgroups,
2010
Pomona College
Review: Nontangential Limits In Pt(Μ)-Spaces And The Index Of Invariant Subgroups, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
Review: Common Cyclic Vectors For Unitary Operators,
2010
Pomona College
Review: Common Cyclic Vectors For Unitary Operators, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
Recognizing Graph Theoretic Properties With Polynomial Ideals,
2010
University of California - Davis
Recognizing Graph Theoretic Properties With Polynomial Ideals, Jesus A. De Loera, Christopher J. Hillar, Peter N. Malkin, Mohamed Omar
All HMC Faculty Publications and Research
Many hard combinatorial problems can be modeled by a system of polynomial equations. N. Alon coined the term polynomial method to describe the use of nonlinear polynomials when solving combinatorial problems. We continue the exploration of the polynomial method and show how the algorithmic theory of polynomial ideals can be used to detect k-colorability, unique Hamiltonicity, and automorphism rigidity of graphs. Our techniques are diverse and involve Nullstellensatz certificates, linear algebra over finite fields, Gröbner bases, toric algebra, convex programming, and real algebraic geometry.
