the structured distance to the nearest system without property mathcal p for a system matrix m this paper explores the smallest frobenius norm additive structured perturbation delta m for which a system property mathcal p e g controllability observability stability etc fails to hold i e delta m is the structured perturbation with smallest frobenius norm such that there exists a property matrix r in mathcal p for which m delta m r drops rank the frobenius norm is used because of its direct dependence on the magnitude of each entry in the perturbation matrix necessary conditions on a locally minimum norm structured rank reducing perturbation delta m and associated property matrix r are set forth and proven an iterative algorithm is also set forth that computes a locally minimum norm structured perturbation and associated property matrix satisfying the necessary conditions algorithm convergence is proven using a discrete lyapunov function

a new approximate matrix factorization for implicit time integration in air pollution modeling implicit time stepping typically requires solution of one or several linear systems with a matrix i j per time step where j is the jacobian matrix if solution of these systems is expensive replacing i j with its approximate matrix factorization amf i r i v r v j often leads to a good compromise between 1stability and accuracy of the time integration on the one hand and its efficiency on the other hand for example in air pollution modeling amf has been successfully used in the framework of rosenbrock schemes the standard amf gives an approximation to i j with the error 2rv which can be significant in norm in this paper we propose a new amf in assumption that v is an m matrix the error of the new amf can be shown to have an upper bound r while still being asymptotically o 2 this new amf called amf is equal in costs to standard amf and as both analysis and numerical experiments reveal provides a better accuracy we also report on our experience with another cheaper amf and with amf preconditioned gmres

an efficient high order algorithm for solving systems of 3 d reaction diffusion equations we discuss an efficient higher order finite difference algorithm for solving systems of 3 d reaction diffusion equations with nonlinear reaction terms the algorithm is fourth order accurate in both the temporal and spatial dimensions it requires only a regular seven point difference stencil similar to that used in the standard second order algorithms such as the crank nicolson algorithm numerical examples are presented to demonstrate the efficiency and accuracy of the new algorithm

scaling and rotation invariant analysis approach to object recognition based on radon and fourier mellin transforms various types of orthogonal moments have been widely used for object recognition and classification however these moments do not natively possess scaling invariance essential image normalization and binarization prior to moments extraction will lead to error of resampling and requantifying this paper describes a new scaling and rotation invariant analysis method for object recognition in the proposed method the radon transform is utilized to project the image onto projection space to convert the rotation of the original image to a translation of the projection in the angle variable and the scaling of the original image to a scaling of the projection in the spatial variable together with an amplitude scaling of the projection and then the fourier mellin transform is applied to the result to convert the translation in the angle variable and the scaling in the spatial variable as well as the amplitude scaling of the projection to a phase shift and an amplitude scaling respectively in order to achieve a set of completely invariant descriptors a rotation and scaling invariant function is constructed a k nearest neighbors classifier is employed to implement classification theoretical and experimental results show the high classification accuracy of this approach as a result of using the rotation and scaling invariant function instead of image binarization and normalization it is also shown that this method is relatively robust in the presence of white noise

fast kernel based independent component analysis recent approaches to independent component analysis ica have used kernel independence measures to obtain highly accurate solutions particularly where classical methods experience difficulty for instance sources with near zero kurtosis fastkica fast hsic based kernel ica is a new optimization method for one such kernel independence measure the hilbert schmidt independence criterion hsic the high computational efficiency of this approach is achieved by combining geometric optimization techniques specifically an approximate newton like method on the orthogonal group with accurate estimates of the gradient and hessian based on an incomplete cholesky decomposition in contrast to other efficient kernel based ica algorithms fastkica is applicable to any twice differentiable kernel function experimental results for problems with large numbers of sources and observations indicate that fastkica provides more accurate solutions at a given cost than gradient descent on hsic comparing with other recently published ica methods fastkica is competitive in terms of accuracy relatively insensitive to local minima when initialized far from independence and more robust towards outliers an analysis of the local convergence properties of fastkica is provided

between controllable and uncontrollable the distance between a system a b and the set of uncontrollable systems is the minimum of the smallest singular value of i a b with respect to

a nonparametric based rib suppression method for chest radiographs this paper presents an automated and comprehensive system for eliminating rib shadows in chest radiographs which integrates lung field identification rib segmentation rib intensity estimation and suppression we designed a region of interest roi based method to estimate a suitable initial lung boundary for active shape model asm deformation by determining the translation and scaling parameters from the lung roi by considering the anatomical structure of the rib cage we developed a locale sampling scheme to achieve nonparametric rib modeling this scheme integrates knowledge based generalized hough transform ght for accurate rib segmentation we subsequently estimated rib intensity using the real coded genetic algorithm rcga experimental results indicate that the relative conspicuity of the nodules increased after rib suppression compared to the original image additionally the proposed system uses only one standard chest radiograph and the dual energy subtraction technique is not required thus this system is suitable for radiologists and computer aided diagnosis cad schemes for detecting lung nodules in chest radiographs

linearized factorization techniques for multidimensional reaction diffusion equations an iterative predictor corrector technique for the elimination of the approximate factorization errors which result from the factorization of linearized q methods in multidimensional reaction diffusion equations is proposed and its convergence and linear stability are analyzed four approximate factorization techniques which do not account for the approximate factorization errors are developed the first technique uses the full jacobian matrix of the reaction terms requires the inversion of in general dense matrices and its approximate factorization errors are second order accurate in time the second and third methods approximate the jacobian matrix by diagonal or triangular ones which are easily inverted but their approximate factorization errors are however first order accurate in time the fourth approximately factorized method has approximate factorization errors which are second order accurate in time and requires the inversion of lower and upper triangular matrices the techniques are applied to a nonlinear two species two dimensional system of reaction diffusion equations in order to determine the approximate factorization errors and those resulting from the approximations to the jacobian matrix as functions of the allocation of the reaction terms space and time

functions of a matrix and krylov matrices for a given nonderogatory matrix a formulas are given for functions of a in terms of krylov matrices of a relations between the coefficients of a polynomial of a and the generating vector of a krylov matrix of a are provided with the formulas linear transformations between krylov matrices and functions of a are introduced and associated algebraic properties are derived hessenberg reduction forms are revisited equipped with appropriate inner products and related properties and matrix factorizations are given

methods for reducing approximate factorization errors in two and three factored schemes three methods are presented for reducing approximate factorization af errors that exist in two and three factored schemes such as the popular adi lu and lu ssor methods for problems in which af errors are larger than both time discretization and time linearization errors these methods can be used to lower the af errors so that larger time step sizes can be used when transient solutions are of interest when only steady state solutions are of interest these methods can be used to accelerate the convergence rate the methods presented also can be used to stabilize schemes that are unstable because of af errors e g the three factored adi scheme applied to the linear advection equation with central difference approximation of the spatial derivatives the three methods presented can be added easily to existing codes using any two or three factored schemes

robust controllability assessment via semi definite programming abstract this paper presents a new framework for systematic assessment of the controllability of uncertain linear time invariant lti systems the objective is to evaluate controllability of an uncertain system with norm bounded perturbation over the entire uncertain region the method is based on a singular value minimization problem over the entire complex plane to solve the problem first a necessary and sufficient condition is proposed to avert the difficulties of griding over the complex plane and to verify the controllability of directed and undirected networks in a single step secondly the results are utilized to formulate the problem as two lyapunov based linear matrix inequalities lmis for undirected networks and four lmis for directed ones the proposed approach is subsequently extended to evaluate the maximum guaranteed distance to uncontrollability of a system through a quasi convex optimization problem whose solution is guaranteed to be globally optimal by duality analogous results are established for robust observability of directed and undirected networks the proposed framework is implemented efficiently using lmi tools and provides a fast and reliable tool for the assessment of robust controllability and by duality robust observability it is also extendable to robust control system design problems such as control node selection for uncertain systems

computing the radius of controllability for state space systems abstract in this paper we discuss the problem of computing the nearest uncontrollable system to a given control system represented by a matrix pair a b in order to do so we construct a sequence of structured matrices from given system matrices a and b controllability of the pair a b is equivalent to a condition on the null space dimension of an appropriate matrix in this sequence we show that the dimension of the reachability space is also related to the above condition further it is shown that the nearest structured low rank approximation slra of this structured matrix corresponds to a nearest uncontrollable system to the pair a b

exponential methods for one dimensional reaction diffusion equations abstract non iterative exponential time linearization and iterative exponential quasilinearization techniques for one dimensional reaction diffusion equations based on the discretization of the time derivative the freezing of the coefficients of the resulting linear ordinary differential equations and the piecewise analytical solution of these ordinary differential equations are presented and applied to the nagumo and fisher equations these techniques yield three point finite difference expressions that depend in an exponential manner on either the diffusion reaction and transient terms or the diffusion and reaction terms it is shown that first order accurate in time exponential time linearization and exponential quasilinearization methods which account for reaction and diffusion processes in the ordinary differential operator are more robust than standard second order accurate techniques even for very large time steps and grid sizes and yield results in excellent accord with those obtained by means of non standard finite difference schemes and nodal integral formulations for the nagumo and fisher equations unlike non standard finite difference methods the exponential schemes presented in this paper do not require any knowledge of the exact solution of the differential equation and can be easily derived in a rather systematic manner compared with nodal integral formulations the exponential techniques presented here only require the solution of second order ordinary differential equations

linearization methods for reaction diffusion equations multidimensional problems four types of linearization methods for the numerical solution of multidimensional reaction diffusion equations are presented the first two types are based on the discretization of the time variable time linearization and approximate factorization the first type also discretizes the spatial coordinates results in block tridiagonal matrices and provides discrete solutions in space and time the second type employs space linearization yields linear ordinary differential equations in space and produces either piecewise continuous or piecewise differentiable solutions the third type is based on the discretization of the spatial coordinates and time linearization and yields continuous solutions in time the fourth type uses time and space linearization and results in a multidimensional linear elliptic equation whose solution by means of separation of variables provides continuous approximations in space and discrete in time the fourth type also yields nine point finite difference expressions compared with the five point ones of the first three types

on the structured distance to uncontrollability this article is concerned with the structured distance to uncontrollability of a linear time invariant system and relates this concept to a variation of the value the developed framework is applied to derive computational expressions for the class of real perturbations as well as for hermitian symmetric and skew symmetric perturbations in a relatively simple manner examples demonstrate that the structured distance can differ from the standard unstructured distance to uncontrollability by an arbitrary amount it is also shown how systems of higher order can be addressed

ultrasonic image classification based on support vector machine with two independent component features imbalance of gender ratio at birth has been a serious phenomenon in china to solve this problem a scheme for ultrasonic image classification is proposed for preventing fetus gender examination with non medical purposes tens of thousands of ultrasonic images with and without sexual organs are collected to establish a professional database these images are preprocessed firstly by cropping de noising and compression and then independent component analysis ica is applied for feature extraction under two architectures which give local and global information respectively the first architecture treats the images as random variables and the pixels as outcomes while the second treats the pixels as random variables and the images as outcomes after training of selected samples a support vector machine svm classifier which combined the two ica representations is established for recognition and a good performance is given for testing data finally some new technique is suggested for algorithm improvement in the future

fast pedestrian detection system with a two layer cascade of classifiers this work presents a novel pedestrian detection system that uses haar like feature extraction and a covariance matrix descriptor to identify the distinctions of pedestrians an approach that adopts an integral image is also applied to reduce the computational loads required in both the haar like feature extraction and evaluation of the covariance matrix descriptor based on the fisher linear discriminant analysis flda classification algorithm the proposed system can classify pedestrians efficiently additionally the detection procedure of the proposed system is accelerated using a two layer cascade of classifiers the front end constructed based on haar like features can select candidate regions quickly wherever pedestrians may be present moreover the back end constructed based on the covariance matrix descriptor can determine accurately whether pedestrians are positioned in candidate regions if a region tests positive through the two layer cascade classifiers pedestrian images are likely captured test video sequences during the experiments are taken from a test set of the inria person database using 30 input frames per second each with a resolution of 320x240 pixels experimental results demonstrate that the proposed system can detect pedestrians efficiently and accurately significantly contributing to efforts to develop a real time system

support vector machine for breast mr image classification mr images have been used extensively in clinical trials in recent years because they are harmless to the human body and can obtain detailed information by scanning the same slice with various frequencies and parameters in this paper we want to detect the breast tissues within multi spectral mr images in the image classification we apply a support vector machine svm to breast multi spectral magnetic resonance images to classify the tissues of the breast in order to verify the feasibility and efficiency of this method evaluations using classification rate and likelihood ratios are adopted based on manifold assessment and a series of experiments are conducted and compared with the commonly used c means cm for performance evaluation the results show that the svm method is a promising and effective spectral technique for mr image classification

on diffusive methods and exponentially fitted techniques liouville s transformations are employed to reduce a one dimensional time dependent convection diffusion reaction operator to a diffusion reaction one which upon a control volume second order accurate discretization results in the same finite difference methods as those of exponentially fitted techniques two variants of these techniques are considered depending on the continuity and or smoothness of the analytical albeit approximate solution to the ordinary differential equations that result upon discretization of the time variable time linearization and piecewise spatial linearization of linear equations it is shown that these exponential techniques include those of allen and southwell il in and el mistikawy and werle for steady linear convection diffusion operators and are linearly stable and monotonic it is also shown that exponentially fitted techniques account for the characteristic times of reaction diffusion and residence and the time step employed in the discretization of the time variable can use adaptive refinement techniques and can account for the convection diffusion and reaction the convection and diffusion the reaction and diffusion and the diffusion processes however the latter three require iterative techniques to find the numerical solution

invariant feature extraction for 3d model retrieval an adaptive approach using euclidean and topological metrics with the fast development of 3d model construction and widespread popularity of 3d graphic engines more applications employ 3d geometric models to provide an interactive environment as the number of 3d models increases some 3d model retrieval systems have been proposed for indexing and matching these models an important issue in a retrieval system is feature extraction an efficient and invariant feature is a global shape distribution that collects some geometric properties of a model the d2 shape descriptor by osada et al is a one dimensional histogram of euclidean distances between two random points although the d2 is effective for some cases it changes when the model deforms we propose two shape descriptors in this paper gd which is the topological metric and asf which combines both euclidean and topological metrics the topological metric is an invariant deformation factor the two features are also robust against common geometric processing including scaling rotation resampling compression and remeshing in experiments we implement these methods and confirm their feasibility

solving overdetermined eigenvalue problems we propose a new interpretation of the generalized overdetermined eigenvalue problem left bf a lambda bf b right bf v approx 0 for two m times n m n matrices bf a and bf b its stability analysis and an efficient algorithm for solving it usually the matrix pencil bf a lambda bf b does not have any rank deficient member therefore we aim to compute lambda for which bf a lambda bf b is as close as possible to rank deficient i e we search for lambda that locally minimize the smallest singular value over the matrix pencil bf a lambda bf b practically the proposed algorithm requires cal o mn 2 operations for computing all the eigenpairs we also describe a method to compute practical starting eigenpairs the effectiveness of the new approach is demonstrated with numerical experiments a matlab based implementation of the proposed algorithm can be found at http www mat univie ac at neum software oeig

properties of numerical algorithms related to computing controllability the numerical properties of some methods for computing controllability are used in an expository way to motivate a wider understanding of numerical computations in particular the numerical rank of a matrix the numerical stability of algorithms the sensitivity of problems and the scaling of problems are discussed a numerically stable algorithm is given for computing controllability but it is pointed out that a measure of the distance of the given system from the nearest uncontrollable system would be more useful and this appears to be an open computational problem

iterative solution of elliptic problems by approximate factorization an iterative method for the numerical solution of singularly perturbed second order linear elliptic problems is presented it is a defect correction iteration in which the approximate operator is the product of two first order operators which is readily inverted numerically the approximate operator is generated by formal asymptotic factorization of the original operator hence this is a quasi analytic defect correction iteration quad both its continuous and discrete versions are analyzed in one dimension the scheme is extended to a variety of two dimensional operators and it is analyzed for a model advection diffusion equation numerical calculations show the effectiveness of the scheme over a wide range of values of the small parameter

implicit compact linearized θ methods with factorization for multidimensional reaction diffusion equations an iterative predictor corrector technique for the elimination of the approximate factorization errors which result from the factorization of implicit three point compact linearized q methods in multidimensional reaction diffusion equations is proposed and its convergence and linear stability are analyzed four compact approximate factorization techniques which do not account for the approximate factorization errors and which involve three point stencils for each one dimensional operator are developed the first technique uses the full jacobian matrix of the reaction terms requires the inversion of in general dense matrices and its approximate factorization errors are second order accurate in time the second and third methods approximate the jacobian matrix by diagonal or triangular ones which are easily inverted but their approximate factorization errors are however first order accurate in time the fourth approximately factorized compact implicit method has approximate factorization errors which are second order accurate in time and requires the inversion of lower and upper triangular matrices the techniques are applied to a nonlinear two species two dimensional system of reaction diffusion equations in order to determine the approximate factorization errors and those resulting from the approximations to the jacobian matrix as functions of the allocation of the reaction terms space and time

iterative and non iterative full and approximate factorization methods for multidimensional reaction diffusion equations a variety of second order accurate in both space and time full and approximate factorization methods for the numerical solution of two dimensional reaction diffusion equations is presented these methods may use time linearization and yield linearly implicit techniques and one dimensional operators in each direction it is shown that if the factorization errors are neglected linearly implicit approximate factorization methods provide uncoupled equations whereas if these errors are considered the equations are coupled and must be solved iteratively it is also shown that the allocation of the reaction and diffusion terms to the one dimensional operators plays a paramount role in determining the accuracy of approximate factorization methods and preserving the symmetry of the original differential problem iterative full and approximate factorization methods that do require iterations are also presented and for the problem considered here these methods are shown to converge in about two iterations and provide solutions in agreement with those obtained with linearly implicit full and approximate factorization techniques

exactness of sums of squares relaxations involving 3x3 matrices and lorentz cones we consider a family pm n of cones of positive maps and a semidefinite relaxation of these cones the cone pm n can be described as the set of those linear mappings from the space rm into the space of real symmetric n n matrices which map the m dimensional lorentz cone into the cone of real symmetric positive semidefinite matrices we describe the cone pm n as a cone of nonnegative polynomials in several variables we show that the considered semidefinite relaxation is in fact a sums of squares relaxation corresponding to this description of pm n our main result is that for n 3 the relaxation is exact hence it yields the exact result for optimisation problems over the cones pm 3 in particular the matrix ellipsoid problem for real symmetric 3 3 matrices can be rewritten as feasibility problem of a linear matrix inequality for m 4 n 4 there exist points in pm n which do not lie in the semidefinite set corresponding to the relaxation hence the relaxation is exact if and only if min n m 3

efficient numerical schemes for gradient vector flow since its publication more than 10 years ago the gradient vector flow gvf technique has been used and adapted to various models and problems its effectiveness has greatly contributed to its popularity the main drawback of gvf and its generalisation however is their expensive computation load and its consequence on the capture range in this work we propose and compare different efficient numerical schemes to solve the gvf and its generalisations

estimating distances from quadruples satisfying stability properties to quadruples not satisfying them abstract we consider quadruples of matrices e a b c defining generalized linear multivariable time invariant dynamical systems e x t ax t bu t y t cx t with a e square matrices and b c rectangular matrices using geometrical techniques we present upper bounds and lower bounds for the distances between a quadruple and the nearest non structurally stable uncontrollable and or unobservable one in terms of the singular values of matrices associated to the quadruple

approximate factorization for time dependent partial differential equations abstract the first application of approximate factorization in the numerical solution of time dependent partial differential equations pdes can be traced back to the celebrated papers of peaceman and rachford and of douglas of 1955 for linear problems the peaceman rachford douglas method can be derived from the crank nicolson method by the approximate factorization of the system matrix in the linear system to be solved this factorization is based on a splitting of the system matrix in the numerical solution of time dependent pdes we often encounter linear systems whose system matrix has a complicated structure but can be split into a sum of matrices with a simple structure in such cases it is attractive to replace the system matrix by an approximate factorization based on this splitting this contribution surveys various possibilities for applying approximate factorization to pdes and presents a number of new stability results for the resulting integration methods

an information maximization approach to blind separation and blind deconvolution we derive a new self organizing learning algorithm that maximizes the information transferred in a network of nonlinear units the algorithm does not assume any knowledge of the input distributions and is defined here for the zero noise limit under these conditions information maximization has extra properties not found in the linear case linsker 1989 the nonlinearities in the transfer function are able to pick up higher order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation this enables the network to separate statistically independent components in the inputs a higher order generalization of principal components analysis we apply the network to the source separation or cocktail party problem successfully separating unknown mixtures of up to 10 speakers we also show that a variant on the network architecture is able to perform blind deconvolution cancellation of unknown echoes and reverberation in a speech signal finally we derive dependencies of information transfer on time delays we suggest that information maximization provides a unifying framework for problems in blind signal processing

linearization methods for reaction diffusion equations 1 d problems three types of linearized finite difference methods are presented the first type is based on a formulation which provides discrete solutions in both space and time it is shown that this type is a linearly implicit rosenbrock s or a w method depending on whether the full or an appropriate jacobian is employed the second one requires the solution of two point linear ordinary differential equations and provides either piecewise continuous or piecewise differentiable solutions in space and discrete in time the third type is based on the discretization of the spatial coordinate and provides a system of linear ordinary differential equations in time which can be integrated analytically therefore the third type of linearized finite difference methods provides continuous solutions in time and discrete in space and may be transformed into one of the first type by discretizing the time variable