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Articles 271 - 300 of 537

Full-Text Articles in Statistics and Probability

Statistical Analysis Of Microarray Data In Sleep Deprivation, Stephanie Marie Berhorst Jan 2013

Statistical Analysis Of Microarray Data In Sleep Deprivation, Stephanie Marie Berhorst

Masters Theses

"Microarray technology is a useful tool for studying the expression levels of thousands of genes or exons within a single experiment. Data from microarray experiments present many challenges for researchers since costly resources often limit the experimenter to small sample sizes and large amounts of data are generated. The researcher must carefully consider the appropriate statistical analysis to use that aligns with the experimental design employed. In this work, statistical issues are investigated and addressed for a microarray experiment that examines how expression levels change over time as individuals are sleep deprived. Over the course of 48 hours of sleep …

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Oscillation Results For Fourth-Order Nonlinear Dynamic Equations, Chenghui Zhang, Tongxing Li, Ravi P. Agarwal, Martin Bohner Dec 2012

Oscillation Results For Fourth-Order Nonlinear Dynamic Equations, Chenghui Zhang, Tongxing Li, Ravi P. Agarwal, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

This work is concerned with the oscillation of a certain class of fourth-order nonlinear dynamic equations on time scales. a new oscillation result and an example are included. © 2012 Elsevier Ltd. All rights reserved.

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Jensen's Functionals On Time Scales, Matloob Anwar, Rabia Bibi, Martin Bohner, Josip Pečarić Dec 2012

Jensen's Functionals On Time Scales, Matloob Anwar, Rabia Bibi, Martin Bohner, Josip Pečarić

Mathematics and Statistics Faculty Research & Creative Works

We consider Jensen's functionals on time scales and discuss its properties and applications. Further, we define weighted generalized and power means on time scales. by applying the properties of Jensen's functionals on these means, we obtain several refinements and converses of Hölder's inequality on time scales. Copyright © 2012 Matloob Anwar et al.

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An Impulsive Delay Differential Inequality And Applications, Xiaodi Li, Martin Bohner Sep 2012

An Impulsive Delay Differential Inequality And Applications, Xiaodi Li, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

An impulsive delay differential inequality is formulated in this paper. an estimate of the rate of decay of solutions to this inequality is obtained. It can be applied to the study of dynamical behavior of delay differential equations from the impulsive control point of view. as an application, we consider a class of impulsive control systems with time-varying delays and establish a sufficient condition to guarantee the global exponential stability. It is shown that, via proper impulsive control law, a linear delay differential system can be exponentially stabilized even if it is initially unstable. a numerical example is given to …

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An Efficient Second Order In Time Scheme For Approximating Long Time Statistical Properties Of The Two Dimensional Navier-Stokes Equations, Xiaoming Wang Aug 2012

An Efficient Second Order In Time Scheme For Approximating Long Time Statistical Properties Of The Two Dimensional Navier-Stokes Equations, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We investigate the long-time behavior of the following efficient second order in time scheme for the 2D Navier-Stokes equations in a periodic box: The scheme is a combination of a 2nd-order in time backward-differentiation and a particular explicit Adams-Bashforth treatment of the advection term. Therefore, only a linear constant coefficient Poisson solver is needed at each time step. We prove uniform in time bounds on this scheme in L 2, H per1 and H per2 provided that the time-step is sufficiently small. These time uniform estimates further lead to the convergence of long-time statistics (stationary statistical properties) of the scheme …

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Oscillation And Spectral Theory For Linear Hamiltonian Systems With Nonlinear Dependence On The Spectral Parameter, Martin Bohner, Werner Kratz, Roman Šimon Hilscher Aug 2012

Oscillation And Spectral Theory For Linear Hamiltonian Systems With Nonlinear Dependence On The Spectral Parameter, Martin Bohner, Werner Kratz, Roman Šimon Hilscher

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we consider linear Hamiltonian differential systems which depend in general nonlinearly on the spectral parameter and with Dirichlet boundary conditions. Our results generalize the known theory of linear Hamiltonian systems in two respects. Namely, we allow nonlinear dependence of the coefficients on the spectral parameter and at the same time we do not impose any controllability and strict normality assumptions. We introduce the notion of a finite eigenvalue and prove the oscillation theorem relating the number of finite eigenvalues which are less than or equal to a given value of the spectral parameter with the number of …

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Experimental And Computational Validation And Verification Of The Stokes-Darcy And Continuum Pipe Flow Models For Karst Aquifers With Dual Porosity Structure, Xiaolong Hu, Xiaoming Wang, Max Gunzburger, Fei Hua, Yanzhao Cao Jun 2012

Experimental And Computational Validation And Verification Of The Stokes-Darcy And Continuum Pipe Flow Models For Karst Aquifers With Dual Porosity Structure, Xiaolong Hu, Xiaoming Wang, Max Gunzburger, Fei Hua, Yanzhao Cao

Mathematics and Statistics Faculty Research & Creative Works

In our previous study, we developed the Stokes-Darcy (SD) model was developed for flow in a karst aquifer with a conduit bedded in matrix, and the Beavers-Joseph (BJ) condition was used to describe the matrix-conduit interface. We also studied the mathematical well-posedness of a coupled continuum pipe flow (CCPF) model as well as convergence rates of its finite element approximation. in this study, to compare the SD model with the CCPF model, we used numerical analyses to validate finite element discretisation methods for the two models. using computational experiments, simulation codes implementing the finite element discretisations are then verified. Further …

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Second-Order Convex Splitting Schemes For Gradient Flows With Ehrlich-Schwoebel Type Energy: Application To Thin Film Epitaxy, Jie Shen, Cheng Wang, Xiaoming Wang, Steven M. Wise May 2012

Second-Order Convex Splitting Schemes For Gradient Flows With Ehrlich-Schwoebel Type Energy: Application To Thin Film Epitaxy, Jie Shen, Cheng Wang, Xiaoming Wang, Steven M. Wise

Mathematics and Statistics Faculty Research & Creative Works

We construct unconditionally stable, unconditionally uniquely solvable, and second order accurate (in time) schemes for gradient flows with energy of the form {equation presented} dx. the construction of the schemes involves the appropriate combination and extension of two classical ideas: (i) appropriate convex-concave decomposition of the energy functional and (ii) the secant method. as an application, we derive schemes for epitaxial growth models with slope selection (F(y) = 1/4 (|y| 2 - 1) 2) or without slope selection (F(y) = -1/2 ln(1 + |y| 2)). Two types of unconditionally stable uniquely solvable second-order schemes are presented. the first type inherits …

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Long Time Stability Of A Classical Efficient Scheme For Two-Dimensional Navier-Stokes Equations, S. Gottlieb, F. Tone, C. Wang, X. Wang, D. Wirosoetisno May 2012

Long Time Stability Of A Classical Efficient Scheme For Two-Dimensional Navier-Stokes Equations, S. Gottlieb, F. Tone, C. Wang, X. Wang, D. Wirosoetisno

Mathematics and Statistics Faculty Research & Creative Works

This paper considers the long-time stability property of a popular semi-implicit scheme for the two-dimensional incompressible Navier-Stokes equations in a periodic box that treats the viscous term implicitly and the nonlinear advection term explicitly. We consider both the semi discrete (discrete in time but continuous in space) and fully discrete schemes with either Fourier Galerkin spectral or Fourier pseudo spectral (collocation) methods. We prove that in all cases, the scheme is long time stable provided that the timestep is sufficiently small. the long-time stability in the L 2 and H 1 norms further leads to the convergence of the global …

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Model Reduction Of Linear Pde Systems: A Continuous Time Eigensystem Realization Algorithm, John R. Singler Jan 2012

Model Reduction Of Linear Pde Systems: A Continuous Time Eigensystem Realization Algorithm, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

The Eigensystem Realization Algorithm (ERA) is a well known system identification and model reduction algorithm for discrete time systems. Recently, Ma, Ahuja, and Rowley (Theoret. Comput. Fluid Dyn. 25(1) : 233-247, 2011) showed that ERA is theoretically equivalent to the balanced POD algorithm for model reduction of discrete time systems. We propose an ERA for model reduction of continuous time linear partial differential equation systems. The algorithm differs from other existing approaches as it is based on a direct approximation of the Hankel integral operator of the system. We show that the algorithm produces accurate balanced reduced order models for …

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Mathematical Modeling And Simulation Of Biologically Inspired Hair Receptor Arrays In Laminar Unsteady Flow Separation, John R. Singler, Belinda A. Batten, Benjamin T. Dickinson Jan 2012

Mathematical Modeling And Simulation Of Biologically Inspired Hair Receptor Arrays In Laminar Unsteady Flow Separation, John R. Singler, Belinda A. Batten, Benjamin T. Dickinson

Mathematics and Statistics Faculty Research & Creative Works

Bats possess arrays of distributed flow-sensitive hair-like mechanoreceptors on their dorsal and ventral wing surfaces. Bat wing hair receptors are known to play a significant role in flight maneuverability and are directionally most sensitive to reversed flow over the wing. in this work, we consider the mechanics of flexible hair-like structures for the time accurate detection and visualization of hydrodynamic images associated with unsteady near surface flow phenomena. a nonlinear viscoelastic model of a hair-like structure coupled to an unsteady nonuniform flow is proposed. Writing the hair model in nondimensional form, we identify five dimensionless groups that govern hair behavior. …

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A Linear Energy Stable Scheme For A Thin Film Model Without Slope Selection, Wenbin Chen, Sidafa Conde, Cheng Wang, Xiaoming Wang, Steven M. Wise Jan 2012

A Linear Energy Stable Scheme For A Thin Film Model Without Slope Selection, Wenbin Chen, Sidafa Conde, Cheng Wang, Xiaoming Wang, Steven M. Wise

Mathematics and Statistics Faculty Research & Creative Works

We present a linear numerical scheme for a model of epitaxial thin film growth without slope selection. the PDE, which is a nonlinear, fourth-order parabolic equation, is the L2 gradient flow of the energy ∫Ω(-1/2 ln(1 + |ø|2) + ε2 2 |Ø(x)|2) dx. the idea of convex-concave decomposition of the energy functional is applied, which results in a numerical scheme that is unconditionally energy stable, i.e., energy dissipative. the particular decomposition used here places the nonlinear term in the concave part of the energy, in contrast to a previous convexity splitting scheme. as a result, the numerical scheme is fully …

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Productivity Formulae Of An Infinite-Conductivity Hydraulically Fractured Well Producing At Constant Wellbore Pressure Based On Numerical Solutions Of A Weakly Singular Integral Equation Of The First Kind, Chaolang Hu, Jing Lu, Xiaoming He Jan 2012

Productivity Formulae Of An Infinite-Conductivity Hydraulically Fractured Well Producing At Constant Wellbore Pressure Based On Numerical Solutions Of A Weakly Singular Integral Equation Of The First Kind, Chaolang Hu, Jing Lu, Xiaoming He

Mathematics and Statistics Faculty Research & Creative Works

In order to increase productivity, it is important to study the performance of a hydraulically fractured well producing at constant wellbore pressure. This paper constructs a new productivity formula, which is obtained by solving a weakly singular integral equation of the first kind, for an infinite-conductivity hydraulically fractured well producing at constant pressure. And the two key components of this paper are a weakly singular integral equation of the first kind and a steady-state productivity formula. A new midrectangle algorithm and a Galerkin method are presented in order to solve the weakly singular integral equation. The numerical results of these …

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Almost Oscillatory Three Dimensional Dynamic Systems, Elvan Akin, Zuzana Dosla, Bonita Lawrence Jan 2012

Almost Oscillatory Three Dimensional Dynamic Systems, Elvan Akin, Zuzana Dosla, Bonita Lawrence

Mathematics and Statistics Faculty Research & Creative Works

In this article, we investigate oscillation and asymptotic properties for 3D systems of dynamic equations. We show the role of nonlinearities and we apply our results to the adjoint dynamic systems.

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Absolute Differentiation In Metric Spaces, W. J. Charatonik, Matt Insall Jan 2012

Absolute Differentiation In Metric Spaces, W. J. Charatonik, Matt Insall

Mathematics and Statistics Faculty Research & Creative Works

In this article, we introduce a new notion of (strong) absolute derivative, for functions derived between metric spaces, and we investigate various properties and uses of this concept, especially regarding the geometry of abstract metric spaces carrying no other structure.

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Equivalent Circuit Model Of Coaxial Probes For Patch Antennas, Y. S. Hu, Yanzhi Zhang, Jun Fan Jan 2012

Equivalent Circuit Model Of Coaxial Probes For Patch Antennas, Y. S. Hu, Yanzhi Zhang, Jun Fan

Mathematics and Statistics Faculty Research & Creative Works

An equivalent circuit model of coaxial probes is derived directly from the intrinsic via circuit model. as all the higher-order evanescent modes have been included analytically in the parasitic circuit elements, only the propagating mode needs to be considered by the simplest uniform-current model of a coaxial probe in numerical solvers such as -nite element method (FEM) or -nite divergence time domain (FDTD). This avoids dense meshes or sub-gridding techniques and greatly reduces the computational efforts for accurate calculation of the probe input impedance. the derived equivalent circuit model and the new feeding technique have been validated by both analytical …

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Abel Dynamic Equations Of The First And Second Kind, Sabrina Heike Streipert Jan 2012

Abel Dynamic Equations Of The First And Second Kind, Sabrina Heike Streipert

Masters Theses

"In this work, we study Abel dynamic equations of the first and the second kind. After a brief introduction to time scales, we introduce the Abel differential equations of the first and the second kind, as well as the canonical Abel form in the continuous case. Using the existing information, we derive novel results for time scales. We provide formulas for the Abel dynamic equations of the second kind and present a solution method. We furthermore achieve a special class of Abel equations of the first kind and discuss the canonical Abel equation. We get relations between common dynamic equations …

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Sieve Bootstrap Based Prediction Intervals And Unit Root Tests For Time Series, Maduka Rupasinghe Jan 2012

Sieve Bootstrap Based Prediction Intervals And Unit Root Tests For Time Series, Maduka Rupasinghe

Doctoral Dissertations

"The application of the sieve bootstrap procedure, which resamples residuals obtained by fitting a finite autoregressvie (AR) approximation to empirical time series, to obtaining prediction intervals for integrated, long-memory, and seasonal time series as well as constructing a test for seasonal unit roots, is considered. The advantage of this resampling method is that it does not require knowledge about the underlying process generating a given time series and has been shown to work well for ARMA processes. We extend the application of the sieve bootstrap to ARIMA and FARIMA processes. The asymptotic properties of the sieve bootstrap prediction intervals for …

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Integral Inequalities On Time Scales Via The Theory Of Isotonic Linear Functionals, Matloob Anwar, Rabia Bibi, Martin Bohner, Josip Pečarić Sep 2011

Integral Inequalities On Time Scales Via The Theory Of Isotonic Linear Functionals, Matloob Anwar, Rabia Bibi, Martin Bohner, Josip Pečarić

Mathematics and Statistics Faculty Research & Creative Works

We apply the theory of isotonic linear functionals to derive a series of known inequalities, extensions of known inequalities, and new inequalities in the theory of dynamic equations on time scales. © 2011 Matloob Anwar et al.

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Analysis And Finite Element Approximation Of A Coupled, Continuum Pipe-Flow/Darcy Model For Flow In Porous Media With Embedded Conduits, Yanzhao Cao, Max Gunzburger, Fei Hua, Xiaoming Wang Sep 2011

Analysis And Finite Element Approximation Of A Coupled, Continuum Pipe-Flow/Darcy Model For Flow In Porous Media With Embedded Conduits, Yanzhao Cao, Max Gunzburger, Fei Hua, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We consider the continuum Darcy/pipe flow model for flows in a porous matrix containing embedded conduits; such coupled flows are present in, e.g., karst aquifers. the mathematical well-posedness of the coupled problem as well as convergence rates of finite element approximation are established in the two-dimensional case. Computational results are also provided. © 2010 Wiley Periodicals, Inc.

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A Parallel Robin-Robin Domain Decomposition Method For The Stokes-Darcy System, Wenbin Chen, Max Gunzburger, Fei Hua, Xiaoming Wang Jul 2011

A Parallel Robin-Robin Domain Decomposition Method For The Stokes-Darcy System, Wenbin Chen, Max Gunzburger, Fei Hua, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We propose a new parallel Robin-Robin domain decomposition method for the coupled Stokes-Darcy system with Beavers-Joseph-Saffman-Jones interface boundary condition. in particular, we prove that, with an appropriate choice of parameters, the scheme converges geometrically independent of the mesh size. © 2011 Society for Industrial and Applied Mathematics.

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A Range And Existence Theorem For Pseudomonotone Perturbations Of Maximal Monotone Operators, Vy Khoi Le May 2011

A Range And Existence Theorem For Pseudomonotone Perturbations Of Maximal Monotone Operators, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we prove a range and existence theorem for multivalued pseudomonotone perturbations of maximal monotone operators. We assume a general coercivity condition on the sum of a maximal monotone and a pseudomonotone operator instead of a condition on the pseudomonotone operator only. An illustrative example of a variational inequality in a Sobolev space with variable exponent is given.

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Balanced Pod For Model Reduction Of Linear Pde Systems: Convergence Theory, John R. Singler Jan 2011

Balanced Pod For Model Reduction Of Linear Pde Systems: Convergence Theory, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

We consider convergence analysis for a model reduction algorithm for a class of linear infinite dimensional systems. The algorithm computes an approximate balanced truncation of the system using solution snapshots of specific linear infinite dimensional differential equations. The algorithm is related to the proper orthogonal decomposition, and it was first proposed for systems of ordinary differential equations by Rowley (Int. J. Bifurc. Chaos Appl. Sci. Eng. 15(3), 997-1013, 2005). For the convergence analysis, we consider the algorithm in terms of the Hankel operator of the system, rather than the product of the system Gramians as originally proposed by Rowley. For …

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Balanced Pod For Linear Pde Robust Control Computations, John R. Singler, Belinda A. Batten Jan 2011

Balanced Pod For Linear Pde Robust Control Computations, 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 nite 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. Convergence theory is given, and numerical results are presented …

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A Model Based Feedback Controller For Wing-Twist Via Piezoceramic Actuation, John R. Singler, Belinda A. Batten Jan 2011

A Model Based Feedback Controller For Wing-Twist Via Piezoceramic Actuation, John R. Singler, Belinda A. Batten

Mathematics and Statistics Faculty Research & Creative Works

In this paper we present a model for a rubber plate with piezoceramic actuators to represent a bioinspired flexible wing. Using a Galerkin based finite element approximation to the system, we compute a linear quadratic based tracking control for piezoelectric actuators placed along both leading and trailing edges. Using these piezoceramic devices, we demonstrate the effectiveness of model based feedback control in achieving a desired wing tip position; this modified shape is analogous to aircraft roll moment generation via wing twist.

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Convergent Snapshot Algorithms For Infinite-Dimensional Lyapunov Equations, John R. Singler Jan 2011

Convergent Snapshot Algorithms For Infinite-Dimensional Lyapunov Equations, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

We consider two algorithms to approximate the solution Z of a class of stable operator Lyapunov equations of the form AZ + ZA* + BB* = 0. The algorithms utilize time snapshots of solutions of certain linear infinite-dimensional differential equations to construct the approximations. Matrix approximations of the operators a and B are not required and the algorithms are applicable as long as the rank of B is relatively small. The first algorithm produces an optimal low-rank approximate solution using proper orthogonal decomposition. The second algorithm approximates the product of the solution with a few vectors and can be implemented …

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Sub-Supersolution Method In Variational Inequalities With Multivalued Operators Given By Integrals, Vy Khoi Le Jan 2011

Sub-Supersolution Method In Variational Inequalities With Multivalued Operators Given By Integrals, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

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Global Stability Of Complex-Valued Neural Networks On Time Scales, Martin Bohner, V. Sree Hari Rao, Suman Sanyal Jan 2011

Global Stability Of Complex-Valued Neural Networks On Time Scales, Martin Bohner, V. Sree Hari Rao, Suman Sanyal

Mathematics and Statistics Faculty Research & Creative Works

In this paper, activation dynamics of complex-valued neural networks are studied on general time scales. Besides presenting conditions guaranteeing the existence of a unique equilibrium pattern, its global exponential stability is discussed. Some numerical examples for different time scales are given in order to highlight the results. © 2011 Foundation for Scientific Research and Technological Innovation.

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Robustness Analysis Of Slow Learning In Iterative Learning Control Systems, John R. Singler, Douglas A. Bristow Jan 2011

Robustness Analysis Of Slow Learning In Iterative Learning Control Systems, John R. Singler, Douglas A. Bristow

Mechanical and Aerospace Engineering Faculty Research & Creative Works

This paper examines robust stability and robust transient growth in Iterative Learning Control (ILC). It is well known that small perturbations in system dynamics can result in very large transient growth of some ILC systems. Even larger perturbations can result in instability. One ad hoc technique commonly employed to improve robustness is to slow the learning rate by reducing the learning filter gain or lowpass filtering the error signal. Here, pseudospectra analysis is used to analyze the robustness of ILC algorithms with slow learning. It is found that robustness bounds can be increased and transient growth decreased with decreasing learning …

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Towards Transient Growth Analysis And Design In Iterative Learning Control, Douglas A. Bristow, John R. Singler Jan 2011

Towards Transient Growth Analysis And Design In Iterative Learning Control, Douglas A. Bristow, John R. Singler

Mechanical and Aerospace Engineering Faculty Research & Creative Works

In this article the problem of bounding transient growth in iterative learning control (ILC) is examined. While transient growth is not a desirable property, the alternative, robust monotonic convergence, leads to fundamental performance limitations. to circumvent these limitations, this article considers the possibility that some transient growth, if properly limited, is a viable and practical option. Towards this end, this article proposes tools for analysing worst-case transient growth in ILC. the proposed tools are based on pseudospectra analysis, which is extended to apply to ILC of uncertain systems. Two practical problems in norm-optimal ILC weighting parameter design are considered. Using …

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