new results on composite control of singularly perturbed uncertain linear systems abstract we consider the problem of stabilizing uncertain singularly perturbed linear time varying systems whose fast dynamics can be unstable we propose a class of nonlinear composite controllers which assure global uniform ultimate boundedness of the trajectories of the closed loop system provided the singular perturbation parameter is sufficiently small these controllers consist of a fast controller which stabilizes the fast dynamics and a slow controller which yields the desired stability properties for the slow dynamics we consider the structure of the fast controller to be simpler than structures previously proposed in the literature to obtain these controllers we first develop some new results for singularly perturbed systems under output feedback in particular it is shown that the matching assumption which deals with the manner in which the uncertainties enter the system and is made on the reduced order system is invariant under linear feedback of the fast variable

continuous time additive hopfield type neural networks with impulses we investigate the global stability characteristics of a system of equations modelling the dynamics of additive hopfield type neural networks with impulses in the continuous time case

detecting and describing heterogeneity in meta analysis the investigation of heterogeneity is a crucial part of any meta analysis while it has been stated that the test for heterogeneity has low power this has not been well quantified moreover the assumptions of normality implicit in the standard methods of meta analysis are often not scrutinized in practice here we simulate how the power of the test for heterogeneity depends on the number of studies included the total information that is total weight or inverse variance available and the distribution of weights among the different studies we show that the power increases with the total information available rather than simply the number of studies and that it is substantially lowered if as is quite common in practice one study comprises a large proportion of the total information we also describe normal plots that are useful in assessing whether the data conform to a fixed effect or random effects model together with appropriate tests and give an application to the analysis of a multi centre trial of blood pressure reduction we conclude that the test of heterogeneity should not be the sole determinant of model choice in meta analysis and inspection of relevant normal plots as well as clinical insight may be more relevant to both the investigation and modelling of heterogeneity

how to prove that a preconditioner cannot be superlinear in the general case of multilevel toeplitz matrices we recently proved that any multilevel circulant preconditioner is not superlinear a cluster it may provide cannot be proper the proof was based on the concept of quasi equimodular matrices although this concept does not apply for example to the sine transform matrices in this paper with a new concept of partially equimodular matrices we cover all trigonometric matrix algebras widely used in the literature we propose a technique for proving the nonsuperlinearity of certain frequently used preconditioners for some representative sample multilevel matrices at the same time we show that these preconditioners are in a certain sense the best among the sublinear preconditioners with only a general cluster for multilevel toeplitz matrices

impulsive stabilization of two kinds of second order linear delay differential equations in this paper we consider the impulsive stabilization problems for two kinds of 2nd order linear delay differential equations by the method of lyapunov functionals criteria on the exponential stabilization by impulses and exponential stabilization by periodical impulses are gained the control effects of impulses are especially stressed in the definitions and results some examples are also given to show the applications of our results

when should epidemiologic regressions use random coefficients summary regression models with random coefficients arise naturally in both frequentist and bayesian approaches to estimation problems they are becoming widely available in standard computer packages under the headings of generalized linear mixed models hierarchical models and multilevel models i here argue that such models offer a more scientifically defensible framework for epidemiologic analysis than the fixed effects models now prevalent in epidemiology the argument invokes an antiparsimony principle attributed to l j savage which is that models should be rich enough to reflect the complexity of the relations under study it also invokes the countervailing principle that you cannot estimate anything if you try to estimate everything often used to justify parsimony regression with random coefficients offers a rational compromise between these principles as well as an alternative to analyses based on standard variable selection algorithms and their attendant distortion of uncertainty assessments these points are illustrated with an analysis of data on diet nutrition and breast cancer

small sample inference for fixed effects from restricted maximum likelihood restricted maximum likelihood reml is now well established as a method for estimating the parameters of the general gaussian linear model with a structured covariance matrix in particular for mixed linear models conventionally estimates of precision and inference for fixed effects are based on their asymptotic distribution which is known to be inadequate for some small sample problems in this paper we present a scaled wald statistic together with an f approximation to its sampling distribution that is shown to perform well in a range of small sample settings the statistic uses an adjusted estimator of the covariance matrix that has reduced small sample bias this approach has the advantage that it reproduces both the statistics and f distributions in those settings where the latter is exact namely for hotelling t2 type statistics and for analysis of variance f ratios the performance of the modified statistics is assessed through simulation studies of four different reml analyses and the methods are illustrated using three examples

the eigenvalue distribution of products of toeplitz matrices clustering and attraction abstract we use a recent result concerning the eigenvalues of a generic non hermitian complex perturbation of a bounded hermitian sequence of matrices to prove that the asymptotic spectrum of the product of toeplitz sequences whose symbols have a real valued essentially bounded product h is described by the function h in the szego way then using mergelyan s theorem we extend the result to the more general case where h belongs to the tilli class the same technique gives us the analogous result for sequences belonging to the algebra generated by toeplitz sequences if the symbols associated with the sequences are bounded and the global symbol h belongs to the tilli class a generalization to the case of multilevel matrix valued symbols and a study of the case of laurent polynomials not necessarily belonging to the tilli class are also given

spectral behavior of matrix sequences and discretized boundary value problems abstract in this paper we provide theoretical tools for dealing with the spectral properties of general sequences of matrices of increasing dimension more specifically we give a unified treatment of notions such as distribution equal distribution localization equal localization clustering and sub clustering as a case study we consider the matrix sequences arising from the finite difference fd discretization of elliptic and semielliptic boundary value problems bvps the spectral analysis is then extended to toeplitz based preconditioned matrix sequences with special attention to the case where the coefficients of the differential operator are not regular belong to l 1 and to the case of multidimensional problems the related clustering properties allow the establishment of some ergodic formulas for the eigenvalues of the preconditioned matrices

stability of cohen grossberg neural networks with distributed delays global asymptotic stability and global exponential stability of the cohen grossberg neural networks and hopfield neural networks with infinite and finite distributed delays are investigated in this paper for hopfield neural networks with distributed delays local stability is also discussed the existence and global stability of periodic solutions of hopfield neural networks with distributed delays and periodic inputs are achieved by using the theory of dissipative systems

impulsive effects on stability of cohen grossberg neural networks with variable delays in this paper a model of impulsive cohen grossberg neural networks is first formulated by establishing some impulsive differential inequalities we investigate impulsive effects on the stability of cohen grossberg neural networks with variable delays and obtain some sufficient conditions ensuring global exponential stability of the impulsive delay system our criteria not only show that the stability still remains under certain impulsive perturbations for some continuous stable neural networks but also present an approach to stabilize the unstable neural networks by utilizing impulsive effects the results extend and improve some recent works for impulsive neural networks as well as non impulsive neural networks some examples and their simulations are given for illustration of the theoretical results

persistent impulsive effects on stability of functional differential equations with finite or infinite delay abstract in this paper the stability problem of impulsive functional differential equations ifdes is considered several criteria ensuring the uniform stability of ifdes with finite or infinite delay are derived by establishing some new razumikhin conditions different with the current existing ones our development results can be applied to delay systems with persistent impulsive effects finally an example and its computer simulation is given to show the effectiveness and advantages of the proposed method

improved stability criteria for a class of neural networks with variable delays and impulsive perturbations this paper further investigates the problem of stability analysis for a kind of neural networks with variable delays and nonlinear impulses with the help of m matrix the homeomorphism theory some effective inequalities and analysis techniques certain novel criteria on the existence uniqueness and exponential stability of the equilibrium point have been established moreover these criteria possess adjustable real parameters which extend and improve many existing results in the literature in the end two numerical examples are provided to illustrate the validation of the theoretical results

adaptive stabilization of non necessarily inversely stable first order systems by using estimates modification based on testing the sylvester determinant this paper presents an adaptive control scheme for first order continuous time systems the estimated plant model is controllable and then the adaptive scheme is free from singularities the singularities are avoided through a modification of the a priori estimated plant parameter vector so that its associated sylvester matrix is guaranteed to be non singular that property is achieved by ensuring that the absolute value of its determinant does not lie below a positive threshold in addition the use of a hysteresis switching function is not required for a modification of the estimates the global asymptotic stability of the closed loop scheme is ensured it is also proved that the problem is well posed even if chattering motion exists due to the modification process the results are also extended to the case of presence of uncertainties consisting of bounded noise and a class of unmodelled dynamics so that global stability of the scheme is ensured in this last case relative adaptation zones are used on the a priori estimates for robust stabilization purposes so that the estimation process is frozen when the size of the prediction error is small compared to the contribution of the unmodelled dynamics to the plant output

on the rate of convergence of the preconditioned conjugate gradient method we derive new estimates for the rate of convergence of the conjugate gradient method by utilizing isolated eigenvalues of parts of the spectrum we present a new generalized version of an incomplete factorization method and compare the derived estimates of the number of iterations with the number actually found for some elliptic difference equations and for a similar problem with a model empirical distribution function

bayes modal estimation in item response models this article describes a bayesian framework for estimation in item response models with two stage prior distributions on both item and examinee populations strategies for point and interval estimation are discussed and a general procedure based on the em algorithm is presented details are given for implementation under one two and three parameter binary logistic irt models novel features include minimally restrictive assumptions about examinee distributions and the exploitation of dependence among item parameters in a population of interest improved estimation in a moderately small sample is demonstrated with simulated data

bibo stabilization of piecewise switched linear systems with delays and nonlinear perturbations this paper deals with bibo stabilization of piecewise switched linear systems in presence of delays and nonlinear perturbations based on piecewise quadratic lyapunov functional the main contribution of the paper is the derivation of sufficient conditions of bibo stabilization in the form of algebraic riccati matrix equation the robust quadratic stability for such system is also discussed a numerical example is given to illustrate the effectiveness of the theoretical results

a comparison of 20 heterogeneity variance estimators in statistical synthesis of results from studies a simulation study when we synthesize research findings via meta analysis it is common to assume that the true underlying effect differs across studies total variability consists of the within study and between study variances heterogeneity there have been established measures such as i2 to quantify the proportion of the total variation attributed to heterogeneity there is a plethora of estimation methods available for estimating heterogeneity the widely used dersimonian and laird estimation method has been challenged but knowledge of the overall performance of heterogeneity estimators is incomplete we identified 20 heterogeneity estimators in the literature and evaluated their performance in terms of mean absolute estimation error coverage probability and length of the confidence interval for the summary effect via a simulation study although previous simulation studies have suggested the paule mandel estimator it has not been compared with all the available estimators for dichotomous outcomes estimating heterogeneity through markov chain monte carlo is a good choice if an informative prior distribution for heterogeneity is employed eg by published cochrane reviews nonparametric bootstrap and positive dersimonian and laird perform well for all assessment criteria for both dichotomous and continuous outcomes hartung makambi estimator can be the best choice when the heterogeneity values are close to 0 07 for dichotomous outcomes and medium heterogeneity values 0 01 0 05 for continuous outcomes hence there are heterogeneity estimators nonparametric bootstrap dersimonian and laird and positive dersimonian and laird that perform better than the suggested paule mandel maximum likelihood provides the best performance for both types of outcome in the absence of heterogeneity

c g preconditioning for toeplitz matrices abstract we consider the problem of solving a toeplitz system of equations by conjugate gradient method when a sequence of nested toeplitz matrices is associated to a function the spectral behaviour of the matrices involved is closely related to the analytical properties of the generating function thus it is possible to devise efficient preconditioning techniques by using various functional approximation strategies this approach leads to attractive results in the case of ill conditioned matrices for which a wide class of preconditioners are proposed

harmless delays in cohen grossberg neural networks without assuming monotonicity and differentiability of the activation functions and any symmetry of interconnections we establish some sufficient conditions for the globally asymptotic stability of a unique equilibrium for the cohen grossberg neural network with multiple delays lyapunov functionals and functions combined with the razumikhin technique are employed the criteria are all independent of the magnitudes of the delays and thus the delays under these conditions are harmless 2002 elsevier science b v all rights reserved msc 34d23 34k20 92b20

toeplitz circulant preconditioners for toeplitz systems and their applications to queueing networks with batch arrivals the preconditioned conjugate gradient method is employed to solve toeplitz systems t n bf x bf b where the generating functions of the n by n toeplitz matrices t n are functions with zeros in this case circulant preconditioners are known to give poor convergence whereas band toeplitz preconditioners offer only linear convergence and can handle only real valued functions with zeros of even orders we propose here preconditioners which are products of band toeplitz matrices and circulant matrices the band toeplitz matrices are used to cope with the zeros of the given generating function and the circulant matrices are used to speed up the convergence rate of the algorithm our preconditioner can handle complex valued functions with zeros of arbitrary orders we prove that the preconditioned toeplitz matrices have singular values clustered around 1 for large n we apply our preconditioners to solve the stationary probability distribution vectors of markovian queueing models with batch arrivals we show that if the number of servers is fixed independent of the queue size n then the preconditioners are invertible and the preconditioned matrices have singular values clustered around 1 for large n numerical results are given to illustrate the fast convergence of our methods

bibo stabilization for system with multiple mixed delays and nonlinear perturbations the problem of bibo stabilization for multiple mixed time delayed control system with nonlinear perturbations is studied in this paper the new delay dependent bibo stabilization criteria are derived by the lyapunov functional and given in terms of existence of a positive definite solution to an auxiliary algebraic riccati matrix equation the robust quadratic stability for such system is also discussed the work of this paper will extend the results of some references

spectral behavior of preconditioned non hermitian multilevel block toeplitz matrices with matrix valued symbol this note is devoted to preconditioning strategies for non hermitian multilevel block toeplitz linear systems associated with a multivariate lebesgue integrable matrix valued symbol in particular we consider special preconditioned matrices where the preconditioner has a band multilevel block toeplitz structure and we complement known results on the localization of the spectrum with global distribution results for the eigenvalues of the preconditioned matrices in this respect our main result is as follows let i k k let m s be the linear space of complex s i s matrices and let f g i k m s be functions whose components f ij g ij i k c i j 1 s belong to l consider the matrices t n 1 g t n f where n n 1 n k varies in n k and t n f t n g are the multilevel block toeplitz matrices of size n 1 n k s generated by f g then t n 1 g t n f n n k g 1 f i e the family of matrices t n 1 g t n f n n k has a global asymptotic spectral distribution described by the function g 1 f provided g possesses certain properties which ensure in particular the invertibility of t n g for all n and the following topological conditions are met the essential range of g 1 f defined as the union of the essential ranges of the eigenvalue functions j g 1 f j 1 s does not disconnect the complex plane and has empty interior this result generalizes the one obtained by donatelli neytcheva serra capizzano in a previous work concerning the non preconditioned case g 1 the last part of this note is devoted to numerical experiments which confirm the theoretical analysis and suggest the choice of optimal gmres preconditioning techniques to be used for the considered linear systems

monte carlo comparison of anova mivque reml and ml estimators of variance components for the one way classification random model with unbalanced data we compare five estimators of 2 a and 2 e the among and within treatments variance components analysis of variance anova maximum likelihood ml restricted maximum likelihood reml and two minimum variance quadratic unbiased mivque estimators mivque 0 is mivque with a priori values 0 and 1 mivque a is mivque with the anova estimates used as a priori s we enforce nonnegativity for all estimators setting any negative estimate to zero in accord with usual practice the estimators are compared through their biases and mse s estimated by monte carlo simulation our results indicate that the anova estimators perform well except with seriously unbalanced data when 2 a 2 e 1 ml is excellent when 2 a 2 e 0 5 and mivque a is adequate further iteration to the reml estimates is unnecessary when 2 a 2 e 1 mivque 0 the default for sass procedure varcomp is poor for estimating 2 a and very poor for 2 e

global dynamics of hopfield neural networks involving variable delays abstract in this article a model describing dynamics of hopfield neural networks involving variable delays is considered existence and uniqueness of the equilibrium point under fairly general and easily verifiable conditions are also established further we derive sufficient criteria of global asymptotic stability gas of the equilibrium point

impulsive control for existence uniqueness and global stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays in this paper a class of recurrent neural networks with discrete and continuously distributed delays is considered sufficient conditions for the existence uniqueness and global exponential stability of a periodic solution are obtained by using contraction mapping theorem and stability theory on impulsive functional differential equations the proposed method which differs from the existing results in the literature shows that network models may admit a periodic solution which is globally exponentially stable via proper impulsive control strategies even if it is originally unstable or divergent two numerical examples and their computer simulations are offered to show the effectiveness of our new results

improved global robust stability of interval delayed neural networks via split interval generalizations abstract the problem of global robust stability of hopfield type delayed neural networks with the intervalized network parameters is revisited recently a computationally tractable i e linear matrix inequality lmi based global robust stability criterion derived from an earlier criterion based on dividing the given interval into more that two intervals has been presented in the present paper generalizations i e division of the given interval into m intervals where m is an integer greater than or equal to 2 is considered and some new lmi based global robust stability criteria are derived it is shown that in some cases m 2 may not suffice i e m 2 may be needed to realize the improvement an example showing the effectiveness of the proposed generalization is given the paper also provides a complete and systematic explanation of the split interval idea

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

impulsive stabilization of second order nonlinear delay differential systems modeling of many dynamic systems results in second order delay differential systems in this paper we prove that two kinds of delay systems without impulses can be stabilized by proper impulsive control respectively our results have improved and generated some of the known results found in the literature we also give an example to illustrate the obtained results

h sub 2 guaranteed cost control for singularly perturbed uncertain systems the h sub 2 guaranteed cost control problem for a singularly perturbed norm bounded uncertain system is addressed using the quadratic stabilizability framework after defining the corresponding slow and fast uncertain subsystems the set of quadratic stabilizing composite controls is characterized two riccati equations have to be solved one for the slow subsystem and the other for the fast subsystem choosing appropriately the weighting matrices it is shown how to pick up in the set of quadratic stabilizing composite controls a control minimizing an upper bound on the h sub 2 norm of a certain transfer matrix the case of the guaranteed cost control problem for the reduced system is also investigated

global attractivity in delayed hopfield neural network models two different approaches are employed to investigate the global attractivity of delayed hopfield neural network models without assuming the monotonicity and differentiability of the activation functions liapunov functionals and functions combined with the razumikhin technique are constructed and employed to establish sufficient conditions for global asymptotic stability independent of the delays in the case of monotone and smooth activation functions the theory of monotone dynamical systems is applied to obtain criteria for global attractivity of the delayed model such criteria depend on the magnitude of delays and show that self inhibitory connections can contribute to the global convergence

asymptotic h sub spl infin control of singularly perturbed systems with parametric uncertainties this paper deals with the problem of control of singularly perturbed linear continuous time systems the authors attention is focused on the design of a composite linear controller based on the slow and fast problems such that both stability and a prescribed h sub spl infin performance for the full order system are achieved the asymptotic behavior of the composite controller is studied which is independent of the singular perturbation spl epsiv when spl epsiv is sufficiently small furthermore the problem of robust control for the above system with parameter uncertainty is also investigated

global exponential stability in continuous time and discrete time delayed bidirectional neural networks convergence dynamics of continuous time bidirectional neural networks with constant transmission delays are studied without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions lyapunov functionals and halanay type inequalities are constructed and employed to derive delay independent sufficient conditions under which the continuous time networks converge exponentially to the equilibria associated with temporally uniform external inputs to the networks discrete time analogues of the continuous time networks are formulated and we study their dynamical characteristics it is shown that the convergence dynamics of the continuous time networks are preserved by the discrete time analogues without any restriction on the discretization step size several examples are given to illustrate the advantages of the discrete time analogues in numerically simulating the continuous time networks

spectral analysis of coupled pdes and of their schur complements via generalized locally toeplitz sequences in 2d spectral analysis of coupled pdes and of their schur complements via generalized locally toeplitz sequences in 2d

penalized normal likelihood and ridge regularization of correlation and covariance matrices high dimensionality causes problems in various areas of statistics a particular situation that rarely has been considered is the testing of hypotheses about multivariate regression models in which

the glt class as a generalized fourier analysis and applications recently the class of generalized locally toeplitz glt sequences has been introduced as a generalization both of classical toeplitz sequences and of variable coefficient differential operators and for every sequence of the class it has been demonstrated that it is possible to give a rigorous description of the asymptotic spectrum in terms of a function the symbol that can be easily identified this generalizes the notion of a symbol for differential operators discrete and continuous or for toeplitz sequences for which it is identified through the fourier coefficients and is related to the classical fourier analysis the glt class has nice algebraic properties and indeed it has been proven that it is stable under linear combinations and products in this paper we prove that the considered class is closed under inversion as well when the sequence which is inverted shows a sparsely vanishing symbol sparsely vanishing symbol a symbol which vanishes at most in a set of zero lebesgue measure furthermore we show that the glt class virtually includes any finite difference or finite element discretization of pdes and based on this we demonstrate that our results on glt sequences can be used in a pde setting in various directions 1 as a generalized fourier analysis for the study of iterative and semi iterative methods when dealing with variable coefficients non rectangular domains non uniform gridding or triangulations 2 in order to provide a tool for the stability analysis of pde numerical schemes e g a necessary von neumann criterium for variable coefficient systems of pdes is obtained uniformly with respect to the boundary conditions 3 for a multigrid analysis of convergence and for providing spectral information on large preconditioned systems in the variable coefficient case etc the final part of the paper deals indeed with problems 1 3 and other possible directions in which the glt analysis can be conveniently employed

boundedness and stability for cohen grossberg neural network with time varying delays abstract in this paper a model is considered to describe the dynamics of cohen grossberg neural network with variable coefficients and time varying delays uniformly ultimate boundedness and uniform boundedness are studied for the model by utilizing the hardy inequality combining with the halanay inequality and the lyapunov functional method some new sufficient conditions are derived for the model to be globally exponentially stable the activation functions are not assumed to be differentiable or strictly increasing moreover no assumption on the symmetry of the connection matrices is necessary these criteria are important in signal processing and the design of networks

bibo stabilization of feedback control systems with time dependent delays abstract this paper investigates the bounded input bounded output bibo stability in a class of control system of nonlinear differential equations with time delay the proofs are based on our studies on the boundedness of the solutions of a general class of nonlinear volterra integral equations

bibo stabilization of time delayed system with nonlinear perturbation time delayed control system with the nonlinear perturbation is considered novel bibo stabilization criteria are established by the lyapunov functional and formulated in terms of existence of a positive definite solution to an auxiliary algebraic riccati matrix equation the robust quadratic stability for such systems is also discussed a numerical example is given to illustrate the effectiveness of our result

h and bibo stabilization of delay systems of neutral type frequency domain tests for the h and bibo stability of large classes of delay systems of neutral type are derived the results are applied to discuss the stabilizability of such systems by finite dimensional controllers

variation of the parameters formula and the problem of bibo for singular measure differential systems with impulse effect recently we first presented and studied singular measure differential systems with impulsive solutions some fundamental theory was established in the present paper with the help of the drazin inverse the variation of the parameters formula of singular measure differential systems is obtained as an application the problem of boundary input and boundary output bibo is investigated

stability bounds of singularity perturbed systems a necessary and sufficient condition is developed for computing the upper bound in sub 0 of the parasitic parameter in in a singularly perturbed system which ensures stability of such a system if 0

boundedness and global exponential stability for delayed differential equations with applications the boundedness of solutions for a class of n dimensional differential equations with distributed delays is established by assuming the existence of instantaneous negative feedbacks which dominate the delay effect as an important by product some criteria for global exponential stability of equilibria are obtained the results are illustrated with applications to delayed neural networks and population dynamics models

stability of artificial neural networks with impulses sufficient conditions are obtained for the existence and asymptotic stability of a unique equilibrium of a hopfield type neural network with lipschitzian activation functions without assuming their boundedness monotonicity or differentiability and subjected to impulsive state displacements at fixed instants of time both the continuous time and their corresponding discrete time networks are considered the sufficient conditions of the discrete time network do not restrict the step size appearing in the discretization process and these conditions approach as the step size tends to zero those of the conditions of the continuous time networks the sufficient conditions are in terms of the parameters of the network only and are easy to verify also when the impulsive jumps are absent the results reduce to those of the non impulsive systems

optimal quasi optimal and superlinear band toeplitz preconditioners for asymptotically ill conditioned positive definite toeplitz systems in this paper we are concerned with the solution of n x n hermitian toeplitz systems with nonnegative generating functions f the preconditioned conjugate gradient pcg method with the well known circulant preconditioners fails in the case where f has zeros in this paper we consider as preconditioners band toeplitz matrices generated by trigonometric polynomials g of fixed degree l we use different strategies of approximation of f to devise a polynomial g which has some analytical properties of f is easily computable and is such that the corresponding preconditioned system has a condition number bounded by a constant independent of n for each strategy we analyze the cost per iteration and the number of iterations required for the convergence within a preassigned accuracy we obtain different estimates of l for which the total cost of the proposed pcg methods is optimal and the related rates of convergence are superlinear finally for the most economical strategy we perform various numerical experiments which fully confirm the effectiveness of approximation theory tools in the solution of this kind of linear algebra problems

extreme singular values and eigenvalues of non hermitian block toeplitz matrices abstract in this paper we are concerned with the analysis of the distribution and localization of the singular values of toeplitz matrices tn f generated by a p variate lebesgue integrable matrix valued function f q p c h k q we prove that the union of the essential ranges of the singular values of f is a proper weak cluster for the whole set of the singular values of tn f by showing that the number of outliers is strongly depending on the regularity features of the underlying function f in particular if f is continuous or from the krein algebra and p 1 then the cluster is proper other results concerning the extreme spectral behavior of tn f second order ergodic formulas and localization of eigenvalues of preconditioned matrices tn 1 g tn f are presented some examples of applications to the preconditioning of these results are also discussed

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

matrix algebra preconditioners for multilevel toeplitz matrices are not superlinear let f be a d variate 2 periodic continuous function and let tn f n n n1 n d be the multiindexed sequence of multilevel n n toeplitz matrices n n n i ni generated by f let a an n be a sequence of matrix algebras simultaneously diagonalized by unitary transforms we show that there exist infinitely many linearly independent trigonometric polynomials and continuous nonpolynomial functions f such that rank tn f pn o n n d 1 n 1 i for any matrix sequence p pn a this implies that no superlinear matrix algebra preconditioner exists in the multilevel toeplitz case the above mentioned result improves the analysis of the author and e tyrtyshnikov siam j matrix anal appl 21 2 1999 431 where the same was proved under the assumption that the involved algebras are of circulant type 2002 elsevier science inc all rights reserved

a nondegenerate penalized likelihood estimator for variance parameters in multilevel models group level variance estimates of zero often arise when fitting multilevel or hierarchical linear models especially when the number of groups is small for situations where zero variances are implausible a priori we propose a maximum penalized likelihood approach to avoid such boundary estimates this approach is equivalent to estimating variance parameters by their posterior mode given a weakly informative prior distribution by choosing the penalty from the log gamma family with shape parameter greater than 1 we ensure that the estimated variance will be positive we suggest a default log gamma 2 penalty with 0 which ensures that the maximum penalized likelihood estimate is approximately one standard error from zero when the maximum likelihood estimate is zero thus remaining consistent with the data while being nondegenerate we also show that the maximum penalized likelihood estimator with this default penalty is a good approximation to the posterior median obtained under a noninformative prior

assessment and propagation of model uncertainty in most examples of inference and prediction the expression of uncertainty about unknown quantities y on the basis of known quantities x is based on a model m that formalizes assumptions about how x and y are related m will typically have two parts structural assumptions s such as the form of the link function and the choice of error distribution in a generalized linear model and parameters whose meaning is specific to a given choice of s it is common in statistical theory and practice to acknowledge parametric uncertainty about given a particular assumed structure s it is less common to acknowledge structural uncertainty about s itself a widely used approach involves enlisting the aid of x to specify a plausible single best choice s for s and then proceeding as if s were known to be correct in general this approach fails to assess and propagate structural uncertainty fully and may lead to miscalibrated uncertainty assessments about y given x when miscalibration occurs it will often result in understatement of inferential or predictive uncertainty about y leading to inaccurate scientific summaries and overconfident decisions that do not incorporate sufficient hedging against uncertainty in this paper i discuss a bayesian approach to solving this problem that has long been available in principle but is only now becoming routinely feasible by virtue of recent computational advances and examine its implementation in examples that involve forecasting the price of oil and estimating the chance of catastrophic failure of the us space shuttle

bayesian estimation of item response curves item response curves for a set of binary responses are studied from a bayesian viewpoint of estimating the item parameters for the two parameter logistic model with normally distributed ability restricted bivariate beta priors are used to illustrate the computation of the posterior mode via the em algorithm the procedure is illustrated by data from a mathematics test

bayesian estimation in the three parameter logistic model a bayesian procedure is developed for the estimation of parameters in the two parameter logistic item response model joint modal estimates of the parameters are obtained and procedures for the specification of prior information are described through simulation studies it is shown that bayesian estimates of the parameters are superior to maximum likelihood estimates in the sense that they are a more meaningful since they do not drift out of range and b more accurate in that they result in smaller mean squared differences between estimates and true values

delay dependent stability analysis for impulsive bam neural networks with time varying delays in this paper we investigate a class of impulsive bam neural networks with time varying delays by establishing the delay differential inequality with impulsive initial conditions and employing m matrix theory we find some new sufficient conditions ensuring the existence uniqueness and global exponential stability of the equilibrium point for impulsive bam neural networks with time varying delays in particular the estimate of the exponential convergence rate is also provided which depends on the system parameters an example is given to show the effectiveness of the results obtained here

global stabilization for linear continuous time varying systems in this paper stabilization problem via static output feedback controls for linear time varying systems is investigated based on the lyapunov function techniques we show that for linear time varying systems the global null controllability guarantees the output feedback stabilization the verifiable stabilizability conditions and output feedback control design are stated the result can be applicable to the output feedback stabilizability of a class of nonlinear time varying systems numerical examples illustrated the conditions are given

estimating multiple classification latent class models this paper presents a new class of models for persons by items data the essential new feature of this class is the representation of the persons every person is represented by its membership tomultiple latent classes each of which belongs to onelatent classification the models can be considered as a formalization of the hypothesis that the responses come about in a process that involves the application of a number ofmental operations two algorithms for maximum likelihood ml and maximum a posteriori map estimation are described they both make use of the tractability of the complete data likelihood to maximize the observed data likelihood properties of the map estimators i e uniqueness and goodness of recovery and the existence of asymptotic standard errors were examined in a simulation study then one of these models is applied to the responses to a set of fraction addition problems finally the models are compared to some related models in the literature

stability in impulsive cohen grossberg type bam neural networks with distributed delays in this paper a class of impulsive cohen grossberg type bi directional associative memory bam neural networks with distributed delays is investigated by establishing an integro differential inequality with impulsive initial conditions and employing the homeomorphism theory the m matrix theory and inequality technique some new general sufficient conditions ensuring the existence uniqueness and global exponential stability of equilibrium point for impulsive cohen grossberg type bam neural networks with distributed delays are obtained in particular the estimate of the exponential convergence rate is also provided which depends on the system parameters and impulsive disturbed intension an example is given to show the effectiveness of the results obtained here

variance components testing in the longitudinal mixed effects model this article discusses the asymptotic behavior of likelihood ratio tests for nonzero variance components in the longitudinal mixed effects linear model described by laird and ware 1982 biometrics 38 963 974 our discussion of the large sample behavior of likelihood ratio tests for nonzero variance components is based on the results for nonstandard testing situations by self and liang 1987 journal of the american statistical association 82 605 610

a korovkin based approximation of multilevel toeplitz matrices with rectangular unstructured blocks via multilevel trigonometric matrix spaces in this paper we are concerned with the approximation of multilevel toeplitz matrices generated by multivariate rectangular matrix valued continuous also l2 functions f i p rightarrow cal c s times t with i pi pi we first define a class cal a t of multilevel trigonometric matrix spaces with unstructured s times t blocks second we introduce a multi sequence of linear approximation operators cal p n x n n 1 n 2 ldots n p acting on complex matrices of dimensions n 1 cdots n p s times n 1 cdots n p t n j in cal n and giving the minimizer of the distance of x from a fixed representative of cal a t with regard to the frobenius norm then by stating and proving new versions of the korovkin theorem for f ranging in the banach space bf c i p cal c s times t cdot infty and by linking these theorems to the operators cal p n we prove the goodness of the proposed approximation in terms of the strong and weak equidistribution of the eigenvalues singular values of a n f and cal p n a n f the discussed results provide a very uniform tool for treating the preconditioning problem with applications to a wide variety of structures as analyzed in the twin paper s serra capizzano calcolo in press

exponential stability of impulsive cellular neural networks with time delay via lyapunov functionals this paper investigates the problem of exponential stability for a class of impulsive cellular neural networks with time delay by dividing the network state variables into subgroups according to the characters of the neural networks some sufficient conditions for exponential stability are derived by lyapunov functionals and the method of variation of parameters these conditions are given in terms of some blocks of the interconnection matrix which extend and improve some of the known results in the literature our results show that impulses may be used to stabilize the cellular neural networks with time delay if they are not stable or exponentially stable on the other hand if impulses are input disturbances criteria on the magnitude and frequency of the impulses are also established to maintain the stability property of the original system our results generalize and improve some known results two examples with numerical simulations are given to illustrate our results

existence and impulsive stability for second order retarded differential equations we consider certain impulsive second order delay differential equations and give conditions for the existence of solutions moreover we prove that the non impulsive equations can be stabilized by the imposition of proper impulse controls generalizing recent results by li and weng we also comment on some possible applications and give examples

globally exponential stabilization of neural networks with mixed time delays via impulsive control the impulsive stabilization problem of neural networks with discrete time varying delays and unbounded continuously distributed delays is considered by using impulse time dependent lyapunov function based techniques to capture the hybrid structure characteristics of the considered impulsive neural networks two novel global exponential stability criteria are obtained in terms of linear matrix inequalities which are capable of dealing with the case where both the continuous and discrete dynamics are unstable when the original continuous time delayed neural networks are not stable sufficient conditions are developed for the design of exponentially stable linear impulsive state feedback controllers four numerical examples are given to illustrate the less conservatism and effectiveness of the proposed results

permanence of a discrete n species cooperation system with time delays and feedback controls in this paper a discrete n species cooperation system with time delays and feedback controls is proposed by applying the comparison theorem of difference equation sufficient conditions are obtained for the permanence of the system

fast band toeplitz preconditioners for hermitian toeplitz systems this paper considers the solutions of hermitian toeplitz systems where the toeplitz matrices are generated by nonnegative functions f the preconditioned conjugate gradient method with well known circulant preconditioners fails in the case when f has zeros this paper employs toeplitz matrices of fixed bandwidth as preconditioners their generating functions g are trigonometric polynomials of fixed degree and are determined by minimizing the maximum relative error f g f infty it is shown that the condition number of systems preconditioned by the band toeplitz matrices are o 1 for f with or without zeros when f is positive the preconditioned systems converge at the same rate as other well known circulant preconditioned systems an a priori bound of the number of iterations required for convergence is also given

matrix algebra preconditioners for multilevel toeplitz systems do not insure optimal convergence rate in the last decades several matrix algebra optimal and superlinear preconditioners those assuring a strong clustering at the unity have been proposed for the solution of polynomially ill conditioned toeplitz linear systems the corresponding generalizations for multilevel structures are neither optimal nor superlinear see e g contemp math 281 2001 193 concerning the notion of superlinearity it has been recently shown that the proper clustering cannot be obtained in general see linear algebra appl 343 344 2002 303 siam j matrix anal appl 22 1 1999 431 math comput 72 2003 1305 in this paper by exploiting a proof technique previously proposed by the authors see contemp math 323 2003 313 we prove that the spectral equivalence and the essential spectral equivalence up to a constant number of diverging eigenvalues are impossible too in conclusion optimal matrix algebra preconditioners in the multilevel setting simply do not exist in general and therefore the search for optimal iterative solvers should be oriented to different directions with special attention to multilevel multigrid techniques

some results on complex toeplitz eigenvalues we consider the asymptotics of the eigenvalues of toeplitz matrices generated by a complex valued symbol f which is essentially bounded we prove that if the essential range of f has empty interior and does not separate the complex plane then the corresponding toeplitz eigenvalues have the canonical distribution in the sense of widom the assumptions on the symbol only concern the topological structure of its essential range and are completely independent of its smoothness properties we also prove some clustering properties of eigenvalues and some new distribution results

clinical heterogeneity in random effect meta analysis between study boundary estimate problem random effect meta analysis is commonly applied to estimate overall effects with unexplained heterogeneity across studies however standard methods including restricted maximum likelihood ml or reml frequently produce near zero estimates for between study variance parameters consequently these methods are reduced to simple and unrealistic fixed effect models resulting in an ignorance of the substantial clinical heterogeneity and sometimes leading to incorrect conclusions to solve the boundary estimate problem we propose 1 an adjusted maximum likelihood method for the between study variance that maximizes a likelihood defined as a product of a standard likelihood and a gaussian class of adjustment factor and 2 a framework using sensitivity analysis by developing a new criterion to check for the occurrence of the boundary estimate although the adjustment introduces bias to the overall effects to ensure strictly positive estimates of the between study variance when the number of studies k is small the bias asymptotically approaches zero resulting in the same estimates derived from the reml method moreover the adjusted maximum likelihood estimator of the between study variance is consistent for large k and interestingly the reml method and our method are equivalent in terms of mean squared error criterion up to o k 1 we illustrate our approach with a motivating example to examine the controversial result of a meta analysis for 24 randomized controlled trials of human albumin numerical evaluations show that our approach produces no boundary estimates but similar synthesized results with the standard maximum likelihood methods as those produced by conventional methods especially with a small number of studies

avoiding zero between study variance estimates in random effects meta analysis fixed effects meta analysis has been criticized because the assumption of homogeneity is often unrealistic and can result in underestimation of parameter uncertainty random effects meta analysis and meta regression are therefore typically used to accommodate explained and unexplained between study variability however it is not unusual to obtain a boundary estimate of zero for the residual between study standard deviation resulting in fixed effects estimates of the other parameters and their standard errors to avoid such boundary estimates we suggest using bayes modal bm estimation with a gamma prior on the between study standard deviation when no prior information is available regarding the magnitude of the between study standard deviation a weakly informative default prior can be used with shape parameter 2 and rate parameter close to 0 that produces positive estimates but does not overrule the data leading to only a small decrease in the log likelihood from its maximum we review the most commonly used estimation methods for meta analysis and meta regression including classical and bayesian methods and apply these methods as well as our bm estimator to real datasets we then perform simulations to compare bm estimation with the other methods and find that bm estimation performs well by i avoiding boundary estimates ii having smaller root mean squared error for the between study standard deviation and iii better coverage for the overall effects than the other methods when the true model has at least a small or moderate amount of unexplained heterogeneity

symbol approach in a signal restoration problem involving block toeplitz matrices we consider a special type of signal restoration problem where some of the sampling data are not available the formulation related to samples of the function and its derivative leads to a possibly large linear system associated to a nonsymmetric block toeplitz matrix which can be equipped with a 2x2 matrix valued symbol the aim of the paper is to study the eigenvalues of the matrix we first identify in detail the symbol and its analytical features then by using recent results on the eigenvalue distribution of block toeplitz matrix sequences we formally describe the cluster sets and the asymptotic spectral distribution of the matrix sequences related to our problem the localization areas the extremal behavior and the conditioning are only observed numerically but their behavior is strongly related to the analytical properties of the symbol even though a rigorous proof is still missing in the block case

dynamic of a non autonomous predator prey system with infinite delay and diffusion in the present paper a nonlinear non autonomous predator prey dispersion model with continuous delay is studied sufficient conditions which guarantee the existence of a periodic positive solution are obtained by using gaines and mawhin s continuation theorem of coincidence degree theory moreover globally asymptotically stability of the system is also obtained by means of a suitable lyapunov functional the applications show that these criteria are easily verified

maximum likelihood estimation of limited and discrete dependent variable models with nested random effects abstract gauss hermite quadrature is often used to evaluate and maximize the likelihood for random component probit models unfortunately the estimates are biased for large cluster sizes and or intraclass correlations we show that adaptive quadrature largely overcomes these problems we then extend the adaptive quadrature approach to general random coefficient models with limited and discrete dependent variables the models can include several nested random effects intercepts and coefficients representing unobserved heterogeneity at different levels of a hierarchical dataset the required multivariate integrals are evaluated efficiently using spherical quadrature rules simulations show that adaptive quadrature performs well in a wide range of situations