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Linear Systems (linear + system)
Kinds of Linear Systems Selected AbstractsAN ITERATIVE LMI APPROACH TO RFDF FOR LINEAR SYSTEM WITH TIME-VARYING DELAYSASIAN JOURNAL OF CONTROL, Issue 1 2006Maiying Zhong ABSTRACT This paper deals with robust fault detection filter (RFDF) problem for a class of linear uncertain systems with time-varying delays and model uncertainties. The RFDF design problem is formulated as an optimization problem by using L2 -induced norm to represent the robustness of residual to unknown inputs and modelling errors, and the sensitivity to faults. A sufficient condition to the solvability of formulated problem is established in terms of certain matrix inequalities, which can be solved with the aid of an iterative linear matrix inequality (ILMI) algorithm. Finally, a numerical example is given to illustrate the effectiveness of the proposed method. [source] Optimal Control of Iterative Solution Methods for Linear Systems of EquationsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005Uwe Helmke Iterative solution methods for linear systems of equations can be regarded as discrete-time control systems, for which a stabilizing feedback control has to be found. Well known algorithms such as GMRES(m) may exhibit unstable dynamics or sensitive dependence on initial conditions, thus preventing the algorithm to converge to the desired solution. Based on linear system feedback design techniques a new algorithm is proposed that does not suffer under such shortcomings. Global convergence to the desired solution is shown for any initial state. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Reliable State Feedback Control Synthesis For Uncertain Linear SystemsASIAN JOURNAL OF CONTROL, Issue 2 2003Guang-Hong Yang ABSTRACT This paper is concerned with the problem of designing reliable state- feedback control for a class of uncertain linear systems with norm bounded uncertainty. A procedure for designing reliable state-feedback control is presented for the case of actuator faults that can be modeled by a scaling factor. In the design, the performance of the normal system (without fault) is optimized, as the considered system operates under the normal condition most of the time. In addition, when actuator faults occur, the closed-loop system retains robust stability and satisfies a known quadratic performance bound. A numerical example is provided to illustrate the effectiveness of the proposed design method. [source] Fast simulation of skin slidingCOMPUTER ANIMATION AND VIRTUAL WORLDS (PREV: JNL OF VISUALISATION & COMPUTER ANIMATION), Issue 2-3 2009Xiaosong Yang Abstract Skin sliding is the phenomenon of the skin moving over underlying layers of fat, muscle and bone. Due to the complex interconnections between these separate layers and their differing elasticity properties, it is difficult to model and expensive to compute. We present a novel method to simulate this phenomenon at real-time by remeshing the surface based on a parameter space resampling. In order to evaluate the surface parametrization, we borrow a technique from structural engineering known as the force density method (FDM)which solves for an energy minimizing form with a sparse linear system. Our method creates a realistic approximation of skin sliding in real-time, reducing texture distortions in the region of the deformation. In addition it is flexible, simple to use, and can be incorporated into any animation pipeline. Copyright © 2009 John Wiley & Sons, Ltd. [source] A Local/Global Approach to Mesh ParameterizationCOMPUTER GRAPHICS FORUM, Issue 5 2008Ligang Liu Abstract We present a novel approach to parameterize a mesh with disk topology to the plane in a shape-preserving manner. Our key contribution is a local/global algorithm, which combines a local mapping of each 3D triangle to the plane, using transformations taken from a restricted set, with a global "stitch" operation of all triangles, involving a sparse linear system. The local transformations can be taken from a variety of families, e.g. similarities or rotations, generating different types of parameterizations. In the first case, the parameterization tries to force each 2D triangle to be an as-similar-as-possible version of its 3D counterpart. This is shown to yield results identical to those of the LSCM algorithm. In the second case, the parameterization tries to force each 2D triangle to be an as-rigid-as-possible version of its 3D counterpart. This approach preserves shape as much as possible. It is simple, effective, and fast, due to pre-factoring of the linear system involved in the global phase. Experimental results show that our approach provides almost isometric parameterizations and obtains more shape-preserving results than other state-of-the-art approaches. We present also a more general "hybrid" parameterization model which provides a continuous spectrum of possibilities, controlled by a single parameter. The two cases described above lie at the two ends of the spectrum. We generalize our local/global algorithm to compute these parameterizations. The local phase may also be accelerated by parallelizing the independent computations per triangle. [source] SIMD Optimization of Linear Expressions for Programmable Graphics HardwareCOMPUTER GRAPHICS FORUM, Issue 4 2004Chandrajit Bajaj Abstract The increased programmability of graphics hardware allows efficient graphical processing unit (GPU) implementations of a wide range of general computations on commodity PCs. An important factor in such implementations is how to fully exploit the SIMD computing capacities offered by modern graphics processors. Linear expressions in the form of, where A is a matrix, and and are vectors, constitute one of the most basic operations in many scientific computations. In this paper, we propose a SIMD code optimization technique that enables efficient shader codes to be generated for evaluating linear expressions. It is shown that performance can be improved considerably by efficiently packing arithmetic operations into four-wide SIMD instructions through reordering of the operations in linear expressions. We demonstrate that the presented technique can be used effectively for programming both vertex and pixel shaders for a variety of mathematical applications, including integrating differential equations and solving a sparse linear system of equations using iterative methods. [source] Stability and identification for rational approximation of frequency response function of unbounded soilEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 2 2010Xiuli Du Abstract Exact representation of unbounded soil contains the single output,single input relationship between force and displacement in the physical or transformed space. This relationship is a global convolution integral in the time domain. Rational approximation to its frequency response function (frequency-domain convolution kernel) in the frequency domain, which is then realized into the time domain as a lumped-parameter model or recursive formula, is an effective method to obtain the temporally local representation of unbounded soil. Stability and identification for the rational approximation are studied in this paper. A necessary and sufficient stability condition is presented based on the stability theory of linear system. A parameter identification method is further developed by directly solving a nonlinear least-squares fitting problem using the hybrid genetic-simplex optimization algorithm, in which the proposed stability condition as constraint is enforced by the penalty function method. The stability is thus guaranteed a priori. The infrequent and undesirable resonance phenomenon in stable system is also discussed. The proposed stability condition and identification method are verified by several dynamic soil,structure-interaction examples. Copyright © 2009 John Wiley & Sons, Ltd. [source] Efficiency of base isolation systems in structural seismic protection and energetic assessmentEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 10 2003Giuseppe Carlo Marano Abstract This paper concerns the seismic response of structures isolated at the base by means of High Damping Rubber Bearings (HDRB). The analysis is performed by using a stochastic approach, and a Gaussian zero mean filtered non-stationary stochastic process is used in order to model the seismic acceleration acting at the base of the structure. More precisely, the generalized Kanai,Tajimi model is adopted to describe the non-stationary amplitude and frequency characteristics of the seismic motion. The hysteretic differential Bouc,Wen model (BWM) is adopted in order to take into account the non-linear constitutive behaviour both of the base isolation device and of the structure. Moreover, the stochastic linearization method in the time domain is adopted to estimate the statistical moments of the non-linear system response in the state space. The non-linear differential equation of the response covariance matrix is then solved by using an iterative procedure which updates the coefficients of the equivalent linear system at each step and searches for the solution of the response covariance matrix equation. After the system response variance is estimated, a sensitivity analysis is carried out. The final aim of the research is to assess the real capacity of base isolation devices in order to protect the structures from seismic actions, by avoiding a non-linear response, with associated large plastic displacements and, therefore, by limiting related damage phenomena in structural and non-structural elements. In order to attain this objective the stochastic response of a non-linear n -dof shear-type base-isolated building is analysed; the constitutive law both of the structure and of the base devices is described, as previously reported, by adopting the BWM and by using appropriate parameters for this model, able to suitably characterize an ordinary building and the base isolators considered in the study. The protection level offered to the structure by the base isolators is then assessed by evaluating the reduction both of the displacement response and the hysteretic dissipated energy. Copyright © 2003 John Wiley & Sons, Ltd. [source] The spinorial method of classifying supersymmetric backgroundsFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 5-6 2006U. Gran Abstract We review how the classification of all supersymmetric backgrounds of IIB supergravity can be reduced to the evaluation of the Killing spinor equations and their integrability conditions, which contain the field equations, on five types of spinors. This is an extension of the work [hep-th/0503046] to IIB supergravity. By using the explicit expressions for the Killing spinor equations evaluated on the five types of spinors the Killing spinor equations become a linear system in terms of the fluxes, the geometry and the spacetime derivatives of the functions that determine the Killing spinors. This system can be solved to express the fluxes in terms of the geometry and to determine the conditions on the geometry of any supersymmetric background. Similarly, the integrability conditions of the Killing spinor equations are turned into a linear system. This can be used to determine the field equations that are implied by the Killing spinor equations for any supersymmetric background. These linear systems simplify for generic backgrounds with maximal and half-maximal number of H -invariant Killing spinors, H , Spin(9,1). In the maximal case, the Killing spinor equations factorise, whereas in the half-maximal case they do not. [source] A review of the adjoint-state method for computing the gradient of a functional with geophysical applicationsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2006R.-E. Plessix SUMMARY Estimating the model parameters from measured data generally consists of minimizing an error functional. A classic technique to solve a minimization problem is to successively determine the minimum of a series of linearized problems. This formulation requires the Fréchet derivatives (the Jacobian matrix), which can be expensive to compute. If the minimization is viewed as a non-linear optimization problem, only the gradient of the error functional is needed. This gradient can be computed without the Fréchet derivatives. In the 1970s, the adjoint-state method was developed to efficiently compute the gradient. It is now a well-known method in the numerical community for computing the gradient of a functional with respect to the model parameters when this functional depends on those model parameters through state variables, which are solutions of the forward problem. However, this method is less well understood in the geophysical community. The goal of this paper is to review the adjoint-state method. The idea is to define some adjoint-state variables that are solutions of a linear system. The adjoint-state variables are independent of the model parameter perturbations and in a way gather the perturbations with respect to the state variables. The adjoint-state method is efficient because only one extra linear system needs to be solved. Several applications are presented. When applied to the computation of the derivatives of the ray trajectories, the link with the propagator of the perturbed ray equation is established. [source] Extension of weakly compressible approximations to incompressible thermal flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2008Mofdi El-Amrani Abstract Weakly compressible and advection approximations of incompressible isothermal flows were developed and tested in (Commun. Numer. Methods Eng. 2006; 22:831,847). In this paper, we extend the method to solve equations governing incompressible thermal flows. The emphasis is again on the reconstruction of unconditionally stable numerical scheme such that, restriction on time steps, projection procedures, solution of linear system of algebraic equations and staggered grids are completely avoided in its implementation. These features are achieved by combining a low-Mach asymptotic in compressible flow equations with a semi-Lagrangian method for the weakly compressible approach. The time integration is carried out using an explicit Runge,Kutta with variable stages. The method is applied to the natural convection flows in a squared cavity for both steady and transient computations. The numerical results demonstrate high resolution of the proposed method and confirm its capability to provide accurate and efficient simulations for thermal flow problems. Copyright © 2006 John Wiley & Sons, Ltd. [source] Adaptive preconditioning of linear stochastic algebraic systems of equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2007Y. T. Feng Abstract This paper proposes an adaptively preconditioned iterative method for the solution of large-scale linear stochastic algebraic systems of equations with one random variable that arise from the stochastic finite element modelling of linear elastic problems. Firstly, a Rank-one posteriori preconditioner is introduced for a general linear system of equations. This concept is then developed into an effective adaptive preconditioning scheme for the iterative solution of the stochastic equations in the context of a modified Monte Carlo simulation approach. To limit the maximum number of base vectors used in the scheme, a simple selection criterion is proposed to update the base vectors. Finally, numerical experiments are conducted to assess the performance of the proposed adaptive preconditioning strategy, which indicates that the scheme with very few base vectors can improve the convergence of the standard Incomplete Cholesky preconditioning up to 50%. Copyright © 2006 John Wiley & Sons, Ltd. [source] Least-square-based radial basis collocation method for solving inverse problems of Laplace equation from noisy dataINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2010Xian-Zhong Mao Abstract The inverse problem of 2D Laplace equation involves an estimation of unknown boundary values or the locations of boundary shape from noisy observations on over-specified boundary or internal data points. The application of radial basis collocation method (RBCM), one of meshless and non-iterative numerical schemes, directly induces this inverse boundary value problem (IBVP) to a single-step solution of a system of linear algebraic equations in which the coefficients matrix is inherently ill-conditioned. In order to solve the unstable problem observed in the conventional RBCM, an effective procedure that builds an over-determined linear system and combines with least-square technique is proposed to restore the stability of the solution in this paper. The present work investigates three examples of IBVPs using over-specified boundary conditions or internal data with simulated noise and obtains stable and accurate results. It underlies that least-square-based radial basis collocation method (LS-RBCM) poses a significant advantage of good stability against large noise levels compared with the conventional RBCM. Copyright © 2010 John Wiley & Sons, Ltd. [source] Local discretization error bounds using interval boundary element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009B. F. Zalewski Abstract In this paper, a method to account for the point-wise discretization error in the solution for boundary element method is developed. Interval methods are used to enclose the boundary integral equation and a sharp parametric solver for the interval linear system of equations is presented. The developed method does not assume any special properties besides the Laplace equation being a linear elliptic partial differential equation whose Green's function for an isotropic media is known. Numerical results are presented showing the guarantee of the bounds on the solution as well as the convergence of the discretization error. Copyright © 2008 John Wiley & Sons, Ltd. [source] FETI-DP, BDDC, and block Cholesky methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2006Jing Li Abstract The FETI-DP and BDDC algorithms are reformulated using Block Cholesky factorizations, an approach which can provide a useful framework for the design of domain decomposition algorithms for solving symmetric positive definite linear system of equations. Instead of introducing Lagrange multipliers to enforce the coarse level, primal continuity constraints in these algorithms, a change of variables is used such that each primal constraint corresponds to an explicit degree of freedom. With the new formulation of these algorithms, a simplified proof is provided that the spectra of a pair of FETI-DP and BDDC algorithms, with the same set of primal constraints, are essentially the same. Numerical experiments for a two-dimensional Laplace's equation also confirm this result. Copyright © 2005 John Wiley & Sons, Ltd. [source] A fast boundary cloud method for 3D exterior electrostatic analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004Vaishali Shrivastava Abstract An accelerated boundary cloud method (BCM) for boundary-only analysis of 3D electrostatic problems is presented here. BCM uses scattered points unlike the classical boundary element method (BEM) which uses boundary elements to discretize the surface of the conductors. BCM combines the weighted least-squares approach for the construction of approximation functions with a boundary integral formulation for the governing equations. A linear base interpolating polynomial that can vary from cloud to cloud is employed. The boundary integrals are computed by using a cell structure and different schemes have been used to evaluate the weakly singular and non-singular integrals. A singular value decomposition (SVD) based acceleration technique is employed to solve the dense linear system of equations arising in BCM. The performance of BCM is compared with BEM for several 3D examples. Copyright © 2004 John Wiley & Sons, Ltd. [source] A two-grid method for expanded mixed finite-element solution of semilinear reaction,diffusion equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003Yanping Chen Abstract We present a scheme for solving two-dimensional semilinear reaction,diffusion equations using an expanded mixed finite element method. To linearize the mixed-method equations, we use a two-grid algorithm based on the Newton iteration method. The solution of a non-linear system on the fine space is reduced to the solution of two small (one linear and one non-linear) systems on the coarse space and a linear system on the fine space. It is shown that the coarse grid can be much coarser than the fine grid and achieve asymptotically optimal approximation as long as the mesh sizes satisfy H=O(h1/3). As a result, solving such a large class of non-linear equation will not be much more difficult than solving one single linearized equation. Copyright © 2003 John Wiley & Sons, Ltd. [source] Physics-based preconditioner for iterative algorithms in multi-scatterer and multi-boundary method of moments formulationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2002Jürgen v. Hagen Abstract An efficient method to solve electromagnetic scattering problems involving several metallic scatterers or bodies composed of dielectric and metallic regions is proposed. So far, the method of moments has successfully been applied to large arrays of identical scatterers when it was combined with preconditioned iterative algorithms to solve for the linear system of equations. Here, the method is generalized to geometries that are composed of several metallic elements of different shapes and sizes, and also to scatterers that are composed of metallic and dielectric regions. The method uses in its core an iterative algorithm, preferably the transpose-free quasi-minimum residual (TFQMR) algorithm, and a block diagonal Jacobi preconditioner. For best performance, the blocks for the preconditioner are chosen according to individual scatterers or groups of scatterers for the array case, and according to the electric and magnetic current basis functions for dielectric/metallic scatterers. The iterative procedure converges quickly for an optimally chosen preconditioner, and is robust even for a non-optimal preconditioner. Reported run times are compared to run times of an efficiently programmed LU factorization, and are shown to be significantly lower. Copyright © 2002 John Wiley & Sons, Ltd. [source] An accurate gradient and Hessian reconstruction method for cell-centered finite volume discretizations on general unstructured gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2010Lee J. Betchen Abstract In this paper, a novel reconstruction of the gradient and Hessian tensors on an arbitrary unstructured grid, developed for implementation in a cell-centered finite volume framework, is presented. The reconstruction, based on the application of Gauss' theorem, provides a fully second-order accurate estimate of the gradient, along with a first-order estimate of the Hessian tensor. The reconstruction is implemented through the construction of coefficient matrices for the gradient components and independent components of the Hessian tensor, resulting in a linear system for the gradient and Hessian fields, which may be solved to an arbitrary precision by employing one of the many methods available for the efficient inversion of large sparse matrices. Numerical experiments are conducted to demonstrate the accuracy, robustness, and computational efficiency of the reconstruction by comparison with other common methods. Copyright © 2009 John Wiley & Sons, Ltd. [source] Method of fundamental solutions for partial-slip fibrous filtration flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2009Shunliu Zhao Abstract In this study a Stokeslet-based method of fundamental solutions (MFS) for two-dimensional low Reynolds number partial-slip flows has been developed. First, the flow past an infinitely long cylinder is selected as a benchmark. The numerical accuracy is investigated in terms of the location and the number of the Stokeslets. The benchmark study shows that the numerical accuracy increases when the Stokeslets are submerged deeper beneath the cylinder surface, as long as the formed linear system remains numerically solvable. The maximum submergence depth increases with the decrease in the number of Stokeslets. As a result, the numerical accuracy does not deteriorate with the dramatic decrease in the number of Stokeslets. A relatively small number of Stokeslets with a substantial submergence depth is thus chosen for modeling fibrous filtration flows. The developed methodology is further examined by application to Taylor,Couette flows. A good agreement between the numerical and analytical results is observed for no-slip and partial-slip boundary conditions. Next, the flow about a representative set of infinitely long cylindrical fibers confined between two planar walls is considered to represent the fibrous filter flow. The obtained flowfield and pressure drop agree very well with the experimental data for this setup of fibers. The developed MFS with submerged Stokeslets is then applied to partial-slip flows about fibers to investigate the slip effect at fiber,fluid interface on the pressure drop. The numerical results compare qualitatively with the analytical solution available for the limit case of infinite number of fibers. Copyright © 2008 John Wiley & Sons, Ltd. [source] A collocated, iterative fractional-step method for incompressible large eddy simulationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2008Giridhar Jothiprasad Abstract Fractional-step methods are commonly used for the time-accurate solution of incompressible Navier,Stokes (NS) equations. In this paper, a popular fractional-step method that uses pressure corrections in the projection step and its iterative variants are investigated using block-matrix analysis and an improved algorithm with reduced computational cost is developed. Since the governing equations for large eddy simulation (LES) using linear eddy-viscosity-based sub-grid models are similar in form to the incompressible NS equations, the improved algorithm is implemented in a parallel LES solver. A collocated grid layout is preferred for ease of extension to curvilinear grids. The analyzed fractional-step methods are viewed as an iterative approximation to a temporally second-order discretization. At each iteration, a linear system that has an easier block-LU decomposition compared with the original system is inverted. In order to improve the numerical efficiency and parallel performance, modified ADI sub-iterations are used in the velocity step of each iteration. Block-matrix analysis is first used to determine the number of iterations required to reduce the iterative error to the discretization error of. Next, the computational cost is reduced through the use of a reduced stencil for the pressure Poisson equation (PPE). Energy-conserving, spatially fourth-order discretizations result in a 7-point stencil in each direction for the PPE. A smaller 5-point stencil is achieved by using a second-order spatial discretization for the pressure gradient operator correcting the volume fluxes. This is shown not to reduce the spatial accuracy of the scheme, and a fourth-order continuity equation is still satisfied to machine precision. The above results are verified in three flow problems including LES of a temporal mixing layer. Copyright © 2008 John Wiley & Sons, Ltd. [source] A domain decomposition approach to finite volume solutions of the Euler equations on unstructured triangular meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2001Victoria Dolean Abstract We report on our recent efforts on the formulation and the evaluation of a domain decomposition algorithm for the parallel solution of two-dimensional compressible inviscid flows. The starting point is a flow solver for the Euler equations, which is based on a mixed finite element/finite volume formulation on unstructured triangular meshes. Time integration of the resulting semi-discrete equations is obtained using a linearized backward Euler implicit scheme. As a result, each pseudo-time step requires the solution of a sparse linear system for the flow variables. In this study, a non-overlapping domain decomposition algorithm is used for advancing the solution at each implicit time step. First, we formulate an additive Schwarz algorithm using appropriate matching conditions at the subdomain interfaces. In accordance with the hyperbolic nature of the Euler equations, these transmission conditions are Dirichlet conditions for the characteristic variables corresponding to incoming waves. Then, we introduce interface operators that allow us to express the domain decomposition algorithm as a Richardson-type iteration on the interface unknowns. Algebraically speaking, the Schwarz algorithm is equivalent to a Jacobi iteration applied to a linear system whose matrix has a block structure. A substructuring technique can be applied to this matrix in order to obtain a fully implicit scheme in terms of interface unknowns. In our approach, the interface unknowns are numerical (normal) fluxes. Copyright © 2001 John Wiley & Sons, Ltd. [source] Direct adaptive command following and disturbance rejection for minimum phase systems with unknown relative degreeINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 1 2007Jesse B. Hoagg Abstract This paper considers parameter-monotonic direct adaptive command following and disturbance rejection for single-input single-output minimum-phase linear time-invariant systems with knowledge of the sign of the high-frequency gain (first non-zero Markov parameter) and an upper bound on the magnitude of the high-frequency gain. We assume that the command and disturbance signals are generated by a linear system with known characteristic polynomial. Furthermore, we assume that the command signal is measured, but the disturbance signal is unmeasured. The first part of the paper is devoted to a fixed-gain analysis of a high-gain-stabilizing dynamic compensator for command following and disturbance rejection. The compensator utilizes a Fibonacci series construction to control systems with unknown-but-bounded relative degree. We then introduce a parameter-monotonic adaptive law and guarantee asymptotic command following and disturbance rejection. Copyright © 2006 John Wiley & Sons, Ltd. [source] Differential transient MEG and fMRI responses to visual stimulation onset rateINTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 1 2008August S. Tuan Abstract While recent analysis of functional magnetic resonance imaging (fMRI) data utilize a generalized nonlinear convolution model (e.g., dynamic causal modeling), most conventional analyses of local responses utilize a linear convolution model (e.g., the general linear model). These models assume a linear relationship between the blood oxygenated level dependent (BOLD) signal and the underlying neuronal response. While previous studies have shown that this "neurovascular coupling" process is approximately linear, short stimulus durations are known to produce a larger fMRI response than expected from a linear system. This divergence from linearity between the stimulus time-course and BOLD signal could be caused by neuronal onset and offset transients, rather than a nonlinearity in the hemodynamics related to BOLD contrast. We tested this hypothesis by measuring MEG and fMRI responses to stimuli with ramped contrast onsets and offsets in place of abrupt transitions. MEG results show that the ramp successfully reduced the transient onset of neural activity. However, the nonlinearity in the fMRI response, while also reduced, remained. Predictions of fMRI responses from MEG signals show a weaker nonlinearity than observed in the actual fMRI data. These results suggest that the fMRI BOLD nonlinearity seen with short duration stimuli is not solely due to transient neuronal activity. © 2008 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 18, 17,28, 2008 [source] Equivalence principle for optimization of sparse versus low-spread representations for signal estimation in noiseINTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 1 2005Radu V. Balan Abstract Estimation of a sparse signal representation, one with the minimum number of nonzero components, is hard. In this paper, we show that for a nontrivial set of the input data the corresponding optimization problem is equivalent to and can be solved by an algorithm devised for a simpler optimization problem. The simpler optimization problem corresponds to estimation of signals under a low-spread constraint. The goal of the two optimization problems is to minimize the Euclidian norm of the linear approximation error with an lp penalty on the coefficients, for p = 0 (sparse) and p = 1 (low-spread), respectively. The l0 problem is hard, whereas the l1 problem can be solved efficiently by an iterative algorithm. Here we precisely define the l0 optimization problem, construct an associated l1 optimization problem, and show that for a set with open interior of the input data the optimizers of the two optimization problems have the same support. The associated l1 optimization problem is used to find the support of the l0 optimizer. Once the support of the l0 problem is known, the actual solution is easily found by solving a linear system of equations. However, we point out our approach does not solve the harder optimization problem for all input data and thus may fail to produce the optimal solution in some cases. © 2005 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 15, 10,17, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.20034 [source] A new insight on the quantum quantitative structure-properties relationshipsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 10 2008Ramon Carbó-Dorca Abstract The theoretical basis of quantum Quantitative Structure-Properties Relationship (QSPR) is analyzed. After setting up a QQSPR operator structure, the first order fundamental QQSPR equation, which turns to be a linear system, is deduced. Some QQSPR algorithms are described afterwards: they are based on the approximate resolution fundamental QQSPR equation. To show the practical computational use of the theory, the definition of a simple QQSPR predictive model is also developed. Finally an application example is given, based on the Cramer steroid set. The new procedures can be easily extended to classical QSPR problems. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source] H, control for discrete-time Markovian jump linear systems with partly unknown transition probabilitiesINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 8 2009Lixian Zhang Abstract In this paper, the problem of H, control for a class of discrete-time Markovian jump linear system with partly unknown transition probabilities is investigated. The class of systems under consideration is more general, which covers the systems with completely known and completely unknown transition probabilities as two special cases. Moreover, in contrast to the uncertain transition probabilities studied recently, the concept of partly unknown transition probabilities proposed in this paper does not require any knowledge of the unknown elements. The H, controllers to be designed include state feedback and dynamic output feedback, since the latter covers the static one. The sufficient conditions for the existence of the desired controllers are derived within the matrix inequalities framework, and a cone complementary linearization algorithm is exploited to solve the latent equation constraints in the output-feedback control case. Two numerical examples are provided to show the validness and potential of the developed theoretical results. Copyright © 2008 John Wiley & Sons, Ltd. [source] Exponential H, filtering for switched linear systems with interval time-varying delayINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 5 2009Dong Wang Abstract This paper deals with the problem of exponential H, filtering for a class of continuous-time switched linear system with interval time-varying delay. The time delay under consideration includes two cases: one is that the time delay is differentiable and bounded with a constant delay-derivative bound, whereas the other is that the time delay is continuous and bounded. Switched linear filters are designed to ensure that the filtering error systems under switching signal with average dwell time are exponentially stable with a prescribed H, noise attenuation level. Based on the free-weighting matrix approach and the average dwell technology, delay-dependent sufficient conditions for the existence of such a filter are derived and formulated in terms of linear matrix inequalities (LMIs). By solving that corresponding LMIs, the desired filter parameterized matrices and the minimal average dwell time are obtained. Finally, two numerical examples are presented to demonstrate the effectiveness of the developed results. Copyright © 2008 John Wiley & Sons, Ltd. [source] Constructive algorithm for dynamic observer error linearization via integrators: single output caseINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 1 2007Kyung T. Yu Abstract Dynamic observer error linearization which has been introduced recently is a new framework for observer design. Although this approach unifies several existing results on the problem and extends the class of systems that can be transformed into an observable linear system with an injection term of known signals, constructive algorithms to check the applicability are not available yet. In this paper, a constructive algorithm is proposed to solve the problem under some restrictions on the system structure and on the auxiliary dynamics introduced in the problem. The algorithm is constructive in the sense that the components of the transformation can be obtained step-by-step. Copyright © 2006 John Wiley & Sons, Ltd. [source] Robust H2 filtering of linear systems with time delaysINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 10 2003E. Fridman Abstract The problem of robust H2 estimation of a combination of states of a stationary linear system with time delays is considered. Since the problem is infinite dimensional in nature, an attempt is being made to develop finite dimensional methods that will guarantee a preassigned estimation accuracy. The approach of minimizing the trace of a matrix that overbounds the exact covariance of the estimation error is considered. Sufficient conditions are given in the form of linear matrix inequalities (LMIs). The results are illustrated by a numerical example. Copyright © 2003 John Wiley & Sons, Ltd. [source] | ||||||||||||||||||||||||||||||||||