uniform asymptotic stability of impulsive differential difference equations of neutral type by lyapunov s direct method abstract an initial value problem for an impulsive system of differential difference equations of neutral type is considered the impulses take place at fixed moments by means of lyapunov s direct method sufficient conditions for uniform asymptotic stability of the zero solution of such systems are found

minimization of a class of matrix trace functions by means of refined majorization a procedure is described for minimizing a class of matrix trace functions the procedure is a refinement of an earlier procedure for minimizing the class of matrix trace functions using majorization it contains a recently proposed algorithm by koschat and swayne for weighted procrustes rotation as a special case a number of trial analyses demonstrate that the refined majorization procedure is more efficient than the earlier majorization based procedure

lipschitz quasistability of impulsive differential difference equations with variable impulsive perturbations in the present paper by means of a suitable comparison lemma sufficient conditions for uniform lipschitz stability of an arbitrary solution of an impulsive system of differential difference equations with variable impulsive perturbations are obtained

stability with respect to part of the variables in systems with impulse effect abstract effective sufficient conditions are found for stability with respect to part of the variables in systems of ordinary differential equations with impulse effect the approach presented is based on the specially introduced piecewise continuous ljapunov functions

joint procrustes analysis for simultaneous nonsingular transformation of component score and loading matrices in component analysis solutions post multiplying a component score matrix by a nonsingular matrix can be compensated by applying its inverse to the corresponding loading matrix to eliminate this indeterminacy on nonsingular transformation we propose joint procrustes analysis jpa in which component score and loading matrices are simultaneously transformed so that the former matrix matches a target score matrix and the latter matches a target loading matrix the loss function of jpa is a function of the nonsingular transformation matrix and its inverse and is difficult to minimize straightforwardly to deal with this difficulty we reparameterize those matrices by their singular value decomposition which reduces the minimization to alternately solving quartic equations and performing the existing multivariate procedures this algorithm is assessed in a simulation study we further extend jpa for cases where targets are linear functions of unknown parameters we also discuss how the application of jpa can be extended in different fields

component analysis with different sets of constraints on different dimensions many of the classical multivariate data analysis and multidimensional scaling techniques call for approximations by lower dimensional configurations a model is proposed in which different sets of linear constraints are imposed on different dimensions in component analysis and classical multidimensional scaling frameworks a simple efficient and monotonically convergent algorithm is presented for fitting the model to the data by least squares the basic algorithm is extended to cover across dimension constraints imposed in addition to the dimensionwise constraints and to the case of a symmetric data matrix examples are given to demonstrate the use of the method

an existence result for first order impulsive functional differential equations in banach spaces abstract in this paper the leray schauder nonlinear alternative is used to investigate the existence of solutions to first order impulsive initial value problems for functional differential equations in banach spaces

constrained inverse regression for incorporating prior information inverse regression methods facilitate dimension reduction analyses of high dimensional data by extracting a small number of factors that are linear combinations of the original predictor variables but the estimated factors may not lend themselves readily to interpretation consistent with prior information our approach to solving this problem is to first incorporate prior information via theory or data driven constraints on model parameters and then apply the proposed method constrained inverse regression cir to extract factors that satisfy the constraints we provide chi squared and t tests to assess the significance of each factor and its estimated coefficients and we also generalize cir to other inverse regression methods in situations where both dimension reduction and factor interpretation are important finally we investigate cir s small sample performance test data driven constraints and present a marketing example to illustrate its use in discovering meaningful factors that influence th

monotone spline transformations for dimension reduction consider a set of data consisting of measurements ofn objects with respect top variables displayed in ann p matrix a monotone transformation of the values in each column represented as a linear combination of integrated basis splines is assumed determined by a linear combination of a new set of values characterizing each row object two different models are used one an eckart young decomposition model and the other a multivariate normal model examples for artificial and real data are presented the results indicate that both methods are helpful in choosing dimensionality and that the eckart young model is also helpful in displaying the relationships among the objects and the variables also results suggest that the resulting transformations are themselves illuminating

regularized partial and or constrained redundancy analysis methods of incorporating a ridge type of regularization into partial redundancy analysis pra constrained redundancy analysis cra and partial and constrained redundancy analysis pcra were discussed the usefulness of ridge estimation in reducing mean square error mse has been recognized in multiple regression analysis for some time especially when predictor variables are nearly collinear and the ordinary least squares estimator is poorly determined the ridge estimation method was extended to pra cra and pcra where the reduced rank ridge estimates of regression coefficients were obtained by minimizing the ridge least squares criterion it was shown that in all cases they could be obtained in closed form for a fixed value of ridge parameter an optimal value of the ridge parameter is found by g fold cross validation illustrative examples were given to demonstrate the usefulness of the method in practical data analysis situations

mackey glass model of hematopoiesis with monotone feedback revisited for the blood cell production modeldxdt ax t f 0 q n q n x n t t we review known results permanence of solutions oscillation and stability of a positive equilibrium or a positive periodic solution are analyzed for non autonomous generalizations of this equation with both concentrated and distributed delays

groupwise dimension reduction via envelope method the family of sufficient dimension reduction sdr methods that produce informative combinations of predictors or indices are particularly useful for high dimensional regression analysis in many such analyses it becomes increasingly common that there is available a priori subject knowledge of the predictors for example they belong to different groups while many recent sdr proposals have greatly expanded the scope of the methods applicability how to effectively incorporate the prior predictor structure information remains a challenge in this article we aim at dimension reduction that recovers full regression information while preserving the predictor group structure built upon a new concept of the direct sum envelope we introduce a systematic way to incorporate the group information in most existing sdr estimators as a result the reduction outcomes are much easier to interpret moreover the envelope method provides a principled way to build a variety of prior structures into dimension reduc

a new existence theory for single and multiple positive periodic solutions to volterra integro differential equations with impulse effects this paper presents a new existence theory for single and multiple positive periodic solutions to a kind of nonautonomous volterra integro differential equations with impulse effects existence is established by using krasnoselskii fixed point theorem in cones this paper extends some previous results and reports some new results about impulsive differential equation

redundancy analysis for qualitative variables redundancy analysis also called principal components analysis of instrumental variables is a technique for two sets of variables one set being dependent of the other its aim is maximization of the explained variance of the dependent variables by a linear combination of the explanatory variables the technique is generalized to qualitative variables it then gives implicitly a simultaneous optimal scaling of the dependent qualitative variables examples are taken from the dutch life situation survey 1977 using satisfaction with life and happiness as dependent variables the analysis leads to one well being scale defined by the explanatory variables marital status schooling income and activity

generalized constrained multiple correspondence analysis a comprehensive approach for imposing both row and column constraints on multivariate discrete data is proposed that may be called generalized constrained multiple correspondence analysis gcmca in this method each set of discrete data is first decomposed into several submatrices according to its row and column constraints and then multiple correspondence analysis mca is applied to the decomposed submatrices to explore relationships among them this method subsumes existing constrained and unconstrained mca methods as special cases and also generalizes various kinds of linearly constrained correspondence analysis methods an example is given to illustrate the proposed method

periodic first order linear neutral delay differential equations some new asymptotic and stability results are given for a first order linear neutral delay differential equation with periodic coefficients and constant delays the asymptotic behavior of the solutions and the stability of the trivial solution are described by the use of an appropriate real root of an equation which is in a sense the corresponding characteristic equation

mackey glass model of hematopoiesis with non monotone feedback stability oscillation and control for the blood cell production model with a unimodal hump feedback email protected t email protected q ny email protected q n y n email protected we review the known results and investigate generalizations of this equation permanence oscillation and stability of the positive equilibrium are studied for non autonomous equations including equations with a distributed delay in addition a linear control is introduced and possibilities to stabilize an otherwise unstable positive equilibrium are explored

the nonoscillatory solutions of delay differential equations with impulses abstract we obtain a sufficient condition for the impulsive delay differential equation t i 1 n p i t r i t t t k t k t k i k t k k n to have a nonoscillatory solution

existence results for impulsive second order periodic problems abstract this paper provides existence results for the nonlinear impulsive periodic boundary value problem u f t u u u t i j i u t i u t i m i u t i i 1 2 m u 0 u t u 0 u t where f car 0 t r 2 and j i m i c r the basic assumption is the existence of lower upper functions 1 2 associated with the problem here we generalize and extend the existence results of our previous papers

a new existence theory for positive periodic solutions to functional differential equations with impulse effects the principle of this paper is to deal with a new existence theory for positive periodic solutions to a kind of nonautonomous functional differential equations with impulse actions at fixed moments easily verifiable sufficient criteria are established the approach is based on the fixed point theorem in cones the paper extends some previous results and obtains some new results

principal component analysis with external information on both subjects and variables a method for structural analysis of multivariate data is proposed that combines features of regression analysis and principal component analysis in this method the original data are first decomposed into several components according to external information the components are then subjected to principal component analysis to explore structures within the components it is shown that this requires the generalized singular value decomposition of a matrix with certain metric matrices the numerical method based on the qr decomposition is described which simplifies the computation considerably the proposed method includes a number of interesting special cases whose relations to existing methods are discussed examples are given to demonstrate practical uses of the method

asymptotic stability of impulsive control neutral type systems in this paper we consider a delay control system of neutral type applying lyapunov functions and razumikhin technique combining with an impulsive feedback control we established some criteria for asymptotic stability of the system an example is also discussed to illustrate the main results we show that by means of appropriate impulsive perturbations we can control the stability behaviour of the system

stability under persistent disturbances of impulsive differential difference equations of neutral type abstract effective sufficient conditions for stability under persistent disturbances of the zero solution of impulsive systems of differential difference equations of neutral type are found the main results are stated in a theorem in its proof an analogue of gronwall bellman s inequality for piecewise continuous functions is used as a corollary the existence of a global solution of a system with quadratic nonlinearities is proved for sufficiently small initial data

gleaning in the field of dual scaling some historical background and preliminary technical information are first presented and then a number of hidden but important methodological aspects of dual scaling are illustrated and discussed normed versus projected weights the amount of information accounted for by each solution a perfect solution to the problem of multidimensional unfolding multidimensional quantification space graphical display number of option problems option standardization versus item standardization and asymmetry of symmetric dual scaling contrary to the common perception that dual scaling and similar quantification methods are now mathematically transparent the present study demonstrates how much more needs to be clarified for routine use of the method to arrive at valid conclusions data analysis must be carried out in such a way that common sense intuition and sound logic will prevail

generalised bilinear regression summary this paper discusses the application of generalised linear methods to bilinear models by criss cross regression it proposes an extension to segmented bilinear models in which the expectation matrix is linked to a sum in which each segment has specified row and column covariance matrices as well as a coefficient parameter matrix that is specified only by its rank this extension includes a variety of biadditive models including the generalised tukey degree of freedom for non additivity model that consists of two bilinear segments one of which is constant the extension also covers a variety of other models for which least squares fits had not hitherto been available such as higher way layouts combined into the rows and columns of a matrix and a harmonic model which can be reparameterised so a lower rank fit is equivalent to a constant phase parameter a number of practical applications are provided including displaying fits by biplots and using them to diagnose models

a multivariate reduced rank growth curve model with unbalanced data a multivariate reduced rank growth curve model is proposed that extends the univariate reducedrank growth curve model to the multivariate case in which several response variables are measured over multiple time points the proposed model allows us to investigate the relationships among a number of response variables in a more parsimonious way than the traditional growth curve model in addition the method is more flexible than the traditional growth curve model for example response variables do not have to be measured at the same time points nor the same number of time points it is also possible to apply various kinds of basis function matrices with different ranks across response variables it is not necessary to specify an entire set of basis functions in advance examples are given for illustration

canonical analysis of contingency tables with linear constraints a generalized least squares approach is presented for incorporating linear constraints on the standardized row and column scores obtained from a canonical analysis of a contingency table the method is easy to implement and may simplify considerably the interpretation of a data matrix the approach is compared to a restricted maximum likelihood procedure

stochastic simulation model for nonstationary time series using an autoregressive wavelet decomposition applications to rainfall and temperature 1 a time series simulation scheme based on wavelet decomposition coupled to an autoregressive model is presented for hydroclimatic series that exhibit band limited low frequency variability many nonlinear dynamical systems generate time series that appear to have amplitude and frequency modulated oscillations that may correspond to the recurrence of different solution regimes the use of wavelet decomposition followed by an autoregressive model of each leading component is explored as a model for such time series the first example considered is the lorenz 84 low order model of extratropical circulation which has been used to illustrate how chaos and intransitivity multiple stable solutions can lead to low frequency variability the central england temperature cet time series the nino3 4 series that is a surrogate for el nino southern oscillation and seasonal rainfall from everglades national park florida are then modeled with this approach the proposed simulation model yields better results than a traditional linear autoregressive ar time series model in terms of reproducing the time frequency properties of the observed rainfall while preserving the statistics usually reproduced by the ar models

canonical correlation analysis with linear constraints abstract we develop canonical correlation analysis by imposing linear constraints upon parameters corresponding to two sets of variables the results of our method which we call canolc are shown in terms of projection operators both orthogonal and oblique further calc correspondence analysis with linear constraints turns out to be a special case of canolc

matrices with special reference to applications in psychometrics multidimensional scaling item response theory and factor analysis may be considered three major contributions of psychometricians to statistics matrix theory played an important role in early developments of these techniques unfortunately nonlinear models are currently very prevalent in these areas still one can identify several areas of psychometrics where matrix algebra plays a prominent role they include analysis of asymmetric square tables multiway data analysis reduced rank regression analysis and multiple set t set canonical correlation analysis among others in this article we review some of the important matrix results in these areas and suggest future studies

principal components analysis of sampled functions this paper describes a technique for principal components analysis of data consisting ofn functions each observed atp argument values this problem arises particularly in the analysis of longitudinal data in which some behavior of a number of subjects is measured at a number of points in time in such cases information about the behavior of one or more derivatives of the function being sampled can often be very useful as for example in the analysis of growth or learning curves it is shown that the use of derivative information is equivalent to a change of metric for the row space in classical principal components analysis the reproducing kernel for the hilbert space of functions plays a central role and defines the best interpolating functions which are generalized spline functions an example is offered of how sensitivity to derivative information can reveal interesting aspects of the data

exponential stability of linear delay impulsive differential equations for an impulsive delay differential equation with bounded delay and bounded coefficients the following result is established if each solution is bounded on 0 together with its derivative for each bounded right hand side then the equation is exponentially stable an explicit stability theorem is presented

generalized bilinear models generalized bilinear models are presented for the statistical analysis of two way arrays these models combine bilinear models and generalized linear modeling and yield a family of models that includes many existing models as well as suggest other potentially useful ones this approach both unifies and extends models for two way arrays including the ability to treat response and explanatory variables differently in the models and the incorporation of external information about the variables directly into the analysis a unifying framework for the generalized bilinear models is provided by considering four particular cases which have been proposed and used in the existing statistical literature a three step procedure is proposed to analyze data sets by generalized bilinear models two data sets of different nature are analyzed

functional multiple set canonical correlation analysis we propose functional multiple set canonical correlation analysis for exploring associations among multiple sets of functions the proposed method includes functional canonical correlation analysis as a special case when only two sets of functions are considered as in classical multiple set canonical correlation analysis computationally the method solves a matrix eigen analysis problem through the adoption of a basis expansion approach to approximating data and weight functions we apply the proposed method to functional magnetic resonance imaging fmri data to identify networks of neural activity that are commonly activated across subjects while carrying out a working memory task

discriminant component pruning regularization and interpretation of multilayered backpropagation networks neural networks are often employed as tools in classification tasks the use of large networks increases the likelihood of the task s being learned although it may also lead to increased complexity pruning is an effective way of reducing the complexity of large networks we present discriminant components pruning dcp a method of pruning matrices of summed contributions between layers of a neural network attempting to interpret the underlying functions learned by the network can be aided by pruning the network generalization performance should be maintained at its optimal level following pruning we demonstrate dcp s effectiveness at maintaining generalization performance applicability to a wider range of problems and the usefulness of such pruning for network interpretation possible enhancements are discussed for the identification of the optimal reduced rank and inclusion of nonlinear neural activation functions in the pruning algorithm

impulsive stabilization of functional differential equations via liapunov functionals abstract in this paper we consider the impulsive stabilization problems for a class of impulsive functional differential equation of the form x t f t x t t t 0 x i k t x t t t k k z our method is based on the application of the liapunov second method together with liapunov functionals

confidence regions for indscal using the jackknife and bootstrap techniques bootstrap and jackknife techniques are used to estimate ellipsoidal confidence regions of group stimulus points derived from indscal the validity of these estimates is assessed through monte carlo analysis asymptotic estimates of confidence regions based on a multiscale solution are also evaluated our findings suggest that the bootstrap and jackknife techniques may be used to provide statements regarding the accuracy of the relative locations of points in space our findings also suggest that multiscale asymptotic estimates of confidence regions based on small samples provide an optimistic view of the actual statistical reliability of the solution

relationships among several methods of linearly constrained correspondence analysis this paper shows essential equivalences among several methods of linearly constrained correspondence analysis they include fisher s method of additive scoring hayashi s second type of quantification method ter braak s canonical correspondence analysis nishisato s type of quantification method ter braak s canonical correspondence analysis nishisato s anova of categorical data correspondence analysis of manipulated contingency tables bockenholt and bockenholt s least squares canonical analysis with linear constraints and van der heijden and meijerink s zero average restrictions these methods fall into one of two classes of methods corresponding to two alternative ways of imposing linear constraints the reparametrization method and the null space method a connection between the two is established through khatri s lemma

multivariate nonstationary oscillation simulation of climate indices with empirical mode decomposition the objective of the current study is to build a stochastic model to simulate climate indices that are teleconnected with the hydrologic regimes of large scale water resources systems such as the great lakes system climate indices generally contain nonstationary oscillations nsos we adopted a stochastic simulation model based on empirical mode decomposition emd the procedure for the model is to decompose the observed series and then to simulate the decomposed components with the nso resampling nsor technique because the model has only been previously applied to single variables a multivariate version of nsor m nsor is developed to consider the links between the climate indices and to reproduce the nso process the proposed m nsor model is tested in a simulation study on the rossler system the simulation results indicate that the m nsor model reproduces the significant oscillatory behaviors of the system and the marginal statistical characteristics subsequently the m nsor model is applied to three climate indices i e arctic oscillation el nino southern oscillation and pacific decadal oscillation for the annual and winter data sets the results of the proposed model are compared to those of the contemporaneous shifting mean and contemporaneous autoregressive moving average model the results indicate that the proposed m nsor model is superior to the contemporaneous shifting mean and contemporaneous autoregressive moving average model for reproducing the nso process while the other basic statistics are comparatively well preserved in both cases the current study concludes that the proposed m nsor model can be a good alternative to simulate nso processes and their teleconnections with climate indices

stability of linear impulsive neutral delay differential equations with constant coefficients abstract in this article we have developed a new method regarding asymptotic behavior and stability for the solutions of first order linear impulsive neutral delay differential equations with constant coefficients and constant delays the asymptotic behavior of the solutions and the stability of the zero solution were investigated using a real root suitable for the characteristic equation furthermore we obtained similar results for impulsive delay differential equations finally three examples are given for the stability of the zero solution of the impulsive neutral delay differential equation

existence and multiplicity of positive periodic solutions to functional differential equations with impulse effects abstract this paper deals with a new existence theory for single and multiple positive periodic solutions to a kind of nonautonomous functional differential equations with impulse actions at fixed moments by employing a fixed point theorem in cones easily verifiable sufficient criteria are established the paper extends some previous results and reports some new results about impulsive functional differential equations

a study of the characteristics of white noise using the empirical mode decomposition method based on numerical experiments on white noise using the empirical mode decomposition emd method we find empirically that the emd is effectively a dyadic filter the intrinsic mode function imf components are all normally distributed and the fourier spectra of the imf components are all identical and cover the same area on a semi logarithmic period scale expanding from these empirical findings we further deduce that the product of the energy density of imf and its corresponding averaged period is a constant and that the energy density function is chi squared distributed furthermore we derive the energy density spread function of the imf components through these results we establish a method of assigning statistical significance of information content for imf components from any noisy data southern oscillation index data are used to illustrate the methodology developed here

a note on dual scaling of successive categories data three methods for dual scaling of successive categories data are formulated they are mathematically equivalent and provide an appropriate technique to determine stimulus values and category boundaries on a joint scale a problem that nishisato s method 1980a failed to handle

cross validatory choice of the number of components from a principal component analysis a method is described for choosing the number of components to retain in a principal component analysis when the aim is dimensionality reduction the correspondence between principal component analysis and the singular value decomposition of the data matrix is used the method is based on successively predicting each element in the data matrix after deleting the corresponding row and column of the matrix and makes use of recently published algorithms for updating a singular value decomposition these are very fast which renders the proposed technique a practicable one for routine data analysis

analyzing rectangular tables by joint and constrained multidimensional scaling abstract this paper selectively discusses multidimensional scaling methods addressing both theory and applications most of the discussion is focussed upon the analysis of rectangular tables the term joint mds is introduced for an analysis which gives a meaningful joint representation of the set of row and the set of column objects of such a table so that the dissimilarities either within sets or between sets are optimally approximated from this perspective it is possible to give an unified account of the relationships between classical multidimensional scaling principal components analysis and correspondence analysis by imposing constraints the general model can be structurally changed in a number of ways for example it can be made discrete that is in principle it subsumes subset models and quadratic assignment as special cases it can also be made more flexible in the sense that external information may be used in order to tune the analysis to specific hypotheses finally an elegant joint mds model called multidimensional unfolding is discussed as a technique unfolding unfortunately suffers from being extremely sensitive to ill conditioned data a new way of coping with this problem is indicated and an application is given in which the bootstrap technique succesfully establishes the stability of the results

a maximum likelihood method for fitting the wandering vector model after introducing some extensions of a recently proposed probabilistic vector model for representing paired comparisons choice data an iterative procedure for obtaining maximum likelihood estimates of the model parameters is developed the possibility of testing various hypotheses by means of likelihood ratio tests is discussed finally the algorithm is applied to some existing data sets for illustrative purposes

influence in principal components analysis summary in linear regression the theoretical influence function and the various sample versions of it have an established place as diagnostic tools these same functions are developed here to provide methods for the detection of influential observations in principal components analysis the perturbation theory of real symmetric matrices unifies this development some interesting points of contrast with the regression case are noted and explained theoretically

a new family of constrained principal component analysis cpca abstract several decompositions of the orthogonal projector p x x x x x are proposed with a prospect of their use in constrained principal component analysis cpca in cpca the main data matrix x is first decomposed into several additive components by the row side and or column side predictor variables g and h the decomposed components are then subjected to singular value decomposition svd to explore structures within the components unlike the previous proposal the current proposal ensures that the decomposed parts are columnwise orthogonal and stay inside the column space of x mathematical properties of the decompositions and their data analytic implications are investigated extensions to regularized pca are also envisaged considering analogous decompositions of ridge operators