synchronization in general complex dynamical networks with coupling delays abstract complex networks have attracted increasing attention from various fields of science and engineering today due to the finite speeds of transmission and spreading as well as traffic congestions a signal or influence travelling through a complex network often is associated with time delays and this is very common in biological and physical networks in this paper we introduce complex dynamical network models with coupling delays for both continuous and discrete time cases and then investigate their synchronization phenomena and criteria based on these new complex network models we derive synchronization conditions for both delay independent and delay dependent asymptotical stabilities in terms of linear matrix inequalities lmi we finally use a network with a fixed delay and a specific coupling scheme as an example to illustrate the theoretical results

karhunen loeve expansion of a set of rotated templates we propose a novel method for efficiently calculating the eigenvectors of uniformly rotated images of a set of templates as we show the images can be optimally approximated by a linear series of eigenvectors which can be calculated without actually decomposing the sample covariance matrix

fast scattered data approximation with neumann and other boundary conditions abstract an important problem in applications such as signal and image procesing is the approximation of a function f from a finite set of randomly scattered data f x j a common and powerful approach is to construct a trigonometric least squares approximation based on the set of exponentials e 2 i kx this leads to fast numerical algorithms but suffers from disturbing boundary effects due to the underlying periodicity assumption on the data which is rarely satisfied in practice to overcome this drawback we impose neumann boundary conditions on the data this implies the use of cosine polynomials cos kx as basis functions we show that using cosine polynomials leads to a least squares problem involving certain toeplitz plus hankel matrices and derive estimates on the condition number of these matrices unlike other toeplitz plus hankel matrices these matrices cannot be diagonalized by the discrete cosine transform dct but they still allow a fast matrix vector multiplication via dct which gives rise to fast conjugate gradient type algorithms we show how the results can be generalized to higher dimensions we also consider anti symmetric boundary conditions leading to sine polynomials as proper trigonometric basis finally we demonstrate the performance of the proposed methods by an application to a two dimensional geophysical scattered data problem

the algebraic approach to the discrete cosine and sine transforms and their fast algorithms it is known that the discrete fourier transform dft used in digital signal processing can be characterized in the framework of the representation theory of algebras namely as the decomposition matrix for the regular module mathbb c z n mathbb c x x n 1 this characterization provides deep insight into the dft and can be used to derive and understand the structure of its fast algorithms in this paper we present an algebraic characterization of the important class of discrete cosine and sine transforms as decomposition matrices of certain regular modules associated with four series of chebyshev polynomials then we derive most of their known algorithms by pure algebraic means we identify the mathematical principle behind each algorithm and give insight into its structure our results show that the connection between algebra and digital signal processing is stronger than previously understood

signal flow graph approach to efficient and forward stable dst algorithms abstract in this paper signal flow graphs are mainly addressed for the efficient and forward stable discrete sine transform dst algorithms having sparse scaled orthogonal rotational rotational reflection and butterfly matrices in electrical engineering theoretical computer science control theory system engineering etc we often use signal flow graphs as a modeling tool which interconnects the system components or represents the realization of a system as electronic devices the objective in this paper is to establish the connection between algebraic operations used in sparse and scaled orthogonal factorizations of dst i iv matrices with the signal flow graph building blocks this paper elaborates signal flow graphs for the foundational frameworks with n 8 and n 16 and use these together with the digital structures to describe the dst algorithms having a n 1 point signal flow graph for dst i and n point signal flow graphs for dst ii iv the presented dst algorithms are completely recursive and solely based on corresponding matrices dst i iv these dst algorithms have low arithmetic complexity especially the low number of multiplications and significant speed improvement factor as opposed to most existing algorithms finally this paper establishes that the presented algorithms are forward stable dst algorithms

estimating a population of parameter values using bayes and empirical bayes methods abstract in standard bayes and empirical bayes component decision problems estimating inidividual parameters is the primary goal in multiple comparison problems and in comparisons of histograms of estimates however the primary goal is to produce parameter estimates that can be considered as an ensemble for example the histogram of estimates should be a good estimate of the histogram of parameters standard methods of estimating by the posterior expectation do minimize symmetric componentwise losses such as squared error but they produce ensembles of estimates with a sample variance smaller than the posterior expected sample variance for parameters in this article we propose new bayes and empirical bayes estimates that minimize a distance function between the empirical cdf of the estimates and the true parameters these estimators are weighted averages of the prior mean and the data with weight on the data being approximately the square root of that for the posterior expectation we give theoreti

bayesian computation via the gibbs sampler and related markov chain monte carlo methods the use of the gibbs sampler for bayesian computation is reviewed and illustrated in the context of some canonical examples other markov chain monte carlo simulation methods are also briefly described and comments are made on the advantages of sample based approaches for bayesian inference summaries

orthonormal and biorthonormal filter banks as convolvers and convolutional coding gain convolution theorems for filter bank transformers are introduced both uniform and nonuniform decimation ratios are considered and orthonormal as well as biorthonormal cases are addressed all the theorems are such that the original convolution reduces to a sum of shorter decoupled convolutions in the subbands that is there is no need to have cross convolution between subbands for the orthonormal case expressions for optimal bit allocation and the optimized coding gain are derived the contribution to coding gain comes partly from the nonuniformity of the signal spectrum and partly from nonuniformity of the filter spectrum with one of the convolved sequences taken to be the unit pulse function e coding gain expressions reduce to those for traditional subband and transform coding the filter bank convolver has about the same computational complexity as a traditional convolver if the analysis bank has small complexity compared to the convolution itself

identifiability in bilinear inverse problems with applications to subspace or sparsity constrained blind gain and phase calibration bilinear inverse problems bips the resolution of two vectors given their image under a bilinear mapping arise in many applications without further constraints bips are usually ill posed in practice the properties of natural signals are exploited to solve bips for example subspace constraints or sparsity constraints are imposed to reduce the search space these approaches have shown some success in practice however there are few results on uniqueness in bips for most bips the fundamental question of under what condition the problem admits a unique solution is yet to be answered for example blind gain and phase calibration bgpc is a structured bip which arises in many applications including inverse rendering in computational relighting albedo estimation with unknown lighting blind phase and gain calibration in sensor array processing and multichannel blind deconvolution mbd it is interesting to study the uniqueness of such problems in this paper we define identifiability of a bip up to a group of transformations we derive necessary and sufficient conditions for such identifiability i e the conditions under which the solutions can be uniquely determined up to the transformation group these conditions take the form of dividing the identifiability of the pair of unknown variables into the individual identifiability of each variable although verifying these individual conditions requires problem specific procedures this framework is universally applicable to all bips applying these results to bgpc we derive sufficient conditions for unique recovery under several scenarios including subspace joint sparsity and sparsity models for bgpc with joint sparsity or sparsity constraints we develop a procedure to compute the transformation groups corresponding to inherent ambiguities we also give necessary conditions in the form of tight lower bounds on sample complexities and demonstrate the tightness of these bounds by numerical experiments the results for bgpc not only demonstrate the application of the proposed general framework for identifiability analysis but are also of interest in their own right

posterior distribution of hierarchical models using car 1 distributions summary we examine properties of the conditional autoregressive model or car 1 model which is commonly used to represent regional effects in bayesian analyses of mortality rates we consider a bayesian hierarchical linear mixed model where the fixed effects have a vague prior such as a constant prior and the random effect follows a class of car 1 models including those whose joint prior distribution of the regional effects is improper we give sufficient conditions for the existence of the posterior distribution of the fixed and random effects and variance components we then prove the necessity of the conditions and give a one way analysis of variance example where the posterior may or may not exist finally we extend the result to the generalised linear mixed model which includes as a special case the poisson log linear model commonly used in disease mapping

algebraic signal processing theory 1 d space in our paper titled ldquoalgebraic signal processing theory foundation and 1 d timerdquo appearing in this issue of the ieee transactions on signal processing we presented the algebraic signal processing theory an axiomatic and general framework for linear signal processing the basic concept in this theory is the signal model defined as the triple a m phi where a is a chosen algebra of filters m an associated a module of signals and phi is a generalization of the z transform each signal model has its own associated set of basic sp concepts including filtering spectrum and fourier transform examples include infinite and finite discrete time where these notions take their well known forms in this paper we use the algebraic theory to develop infinite and finite space signal models these models are based on a symmetric space shift operator which is distinct from the standard time shift we present the space signal processing concepts of filtering or convolution ldquoz transform rdquo spectrum and fourier transform for finite length space signals we obtain 16 variants of space models which have the 16 discrete cosine and sine transforms dcts dsts as fourier transforms using this novel derivation we provide missing signal processing concepts associated with the dcts dsts establish them as precise analogs to the dft get deep insight into their origin and enable the easy derivation of many of their properties including their fast algorithms

multiplication free approximate algorithms for compressed domain linear operations on images we propose a method for devising approximate multiplication free algorithms for compressed domain linear operations on images e g downsampling translation filtering etc we demonstrate that the approximate algorithms give output images that are perceptually nearly equivalent to those of the exact processing while the computational complexity is significantly reduced

an iterative shrinkage approach to total variation image restoration the problem of restoration of digital images from their degraded measurements plays a central role in a multitude of practically important applications a particularly challenging instance of this problem occurs in the case when the degradation phenomenon is modeled by an ill conditioned operator in such a situation the presence of noise makes it impossible to recover a valuable approximation of the image of interest without using some a priori information about its properties such a priori information commonly referred to as simply priors is essential for image restoration rendering it stable and robust to noise moreover using the priors makes the recovered images exhibit some plausible features of their original counterpart particularly if the original image is known to be a piecewise smooth function one of the standard priors used in this case is defined by the rudin osher fatemi model which results in total variation tv based image restoration the current arsenal of algorithms for tv based image restoration is vast in this present paper a different approach to the solution of the problem is proposed based upon the method of iterative shrinkage aka iterated thresholding in the proposed method the tv based image restoration is performed through a recursive application of two simple procedures viz linear filtering and soft thresholding therefore the method can be identified as belonging to the group of first order algorithms which are efficient in dealing with images of relatively large sizes another valuable feature of the proposed method consists in its working directly with the tv functional rather then with its smoothed versions moreover the method provides a single solution for both isotropic and anisotropic definitions of the tv functional thereby establishing a useful connection between the two formulae finally a number of standard examples of image deblurring are demonstrated in which the proposed method can provide restoration results of superior quality as compared to the case of sparse wavelet deconvolution

bayesian analysis of space time variation in disease risk the analysis of variation of risk for a given disease in space and time is a key issue in descriptive epidemiology when the data are scarce maximum likelihood estimates of the area specific risk and of its linear time trend can be seriously affected by random variation in this paper we propose a bayesian model in which both area specific intercept and trend are modelled as random effects and correlation between them is allowed for this model is an extension of that originally proposed for disease mapping it is illustrated by the analysis of the cumulative prevalence of insulin dependent diabetes mellitus as observed at the military examination of 18 year old conscripts born in sardinia during the period 1936 1971 data concerning the genetic differentiation of the sardinian population are used to interpret the results

identifiability and convergence issues for markov chain monte carlo fitting of spatial models the marked increase in popularity of bayesian methods in statistical practice over the last decade owes much to the simultaneous development of markov chain monte carlo mcmc methods for the evaluation of requisite posterior distributions however along with this increase in computing power has come the temptation to fit models larger than the data can readily support meaning that often the propriety of the posterior distributions for certain parameters depends on the propriety of the associated prior distributions an important example arises in spatial modelling wherein separate random effects for capturing unstructured heterogeneity and spatial clustering are of substantive interest even though only their sum is well identified by the data increasing the informative content of the associated prior distributions offers an obvious remedy but one that hampers parameter interpretability and may also significantly slow the convergence of the mcmc algorithm in this paper we investigate the relationship among identifiability bayesian learning and mcmc convergence rates for a common class of spatial models in order to provide guidance for prior selection and algorithm tuning we are able to elucidate the key issues with relatively simple examples and also illustrate the varying impacts of covariates outliers and algorithm starting values on the resulting algorithms and posterior distributions

the discretew transform four different versions of the discretew transform dwt are introduced the dwt may be decomposed into the discrete cosine transform dct and the discrete sine transform dst eight versions of both dct and dst are introduced for the decomposition of the dwt the relationship among different versions of dwt and their relation with the discrete fourier transform dft are given convolution theorems represented by different versions of the dwt are derived

a fast recursive algorithm for computing the discrete cosine transform the discrete cosine transform dct is widely applied in various fields including image data compression because it operates like the karhunen loeve transform for stationary random data this paper presents a recursive algorithm for dct with a structure that allows the generation of the next higher order dct from two identical lower order dct s as a result the method for implementing this recursive dct requires fewer multipliers and adders than other dct algorithms

the eigenstructure of finite field trigonometric transforms in this paper we discuss the eigenstructure of finite field trigonometric transforms fftt this transform family includes different types of cosine and sine transforms that correspond in the finite field case to the well known discrete cosine and sine transforms defined over the real numbers more specifically we determine the eigenvalues of the fftt matrices and study their multiplicities we propose procedures for constructing the associated eigenvectors applications of the developed theory to multiuser communication systems and error correcting codes are also suggested

orthogonal modes of frequency modulation and the sturm liouville frequency modulation model sinusoidal signals and complex exponentials play a critical role in lti system theory in that they are eigenfunctions of the lti convolution operator while processing frequency modulated fm waveforms using lti systems restrictive assumptions must be placed on the system so that a quasi eigenfunction approximation holds upon deviation from these assumptions fm waveforms incur significant distortion in this paper a sturm liouville s l model for frequency modulation introduced by the author is extended to a study orthogonal modes of continuous and discrete frequency modulation and b to develop system theoretical underpinnings for fm waveforms these fm modes have the same special connection with respect to the fm s l system operator that complex exponentials have with lti systems and the convolution operator the finite s l fm spectrum or transform that measures the strength of the orthogonal fm modes present in a fm signal analogous to the discrete fourier spectrum for sinusoids is introduced finally similarities between the orthogonal s l fm modes and angular mathieu functions are exposed and a conjecture connecting the two is put forth

empirical bayes estimates of age standardized relative risks for use in disease mapping there have been many attempts in recent years to map incidence and mortality from diseases such as cancer such maps usually display either relative rates in each district as measured by a standardized mortality ratio smr or some similar index or the statistical significance level for a test of the difference between the rates in that district and elsewhere neither of these approaches is fully satisfactory and we propose a new approach using empirical bayes estimation the resulting estimators represent a weighted compromise between the smr the overall mean relative rate and a local mean of the relative rate in nearby areas the compromise solution depends on the reliability of each individual smr and on estimates of the overall amount of dispersion of relative rates over different districts

delay dependent robust stability criteria for uncertain systems with interval time varying delay this paper proposes an approach for the robust stability of uncertain systems with interval time varying delay the key features of the approach include the introduction of uncorrelated augmented matrix items into the lyapunov functional and the use of a tighter bounding technology unlike existing methodologies the proposed approach involves neither free weighting matrices nor any model transformation it can however lead to much less conservative stability criteria than the existing ones for the systems under consideration numerical examples show that the proposed criteria improve the existing results significantly with much less computational effort

optimal rank matrix algebras preconditioners abstract when a linear system ax y is solved by means of iterative methods mainly cg and gmres and the convergence rate is slow one may consider a preconditioner p and move to the preconditioned system p 1 ax p 1 y the use of such preconditioner changes the spectrum of the matrix defining the system and could result into a great acceleration of the convergence rate the construction of optimal rank preconditioners is strongly related to the possibility of splitting a as a p r e where e is a small perturbation and r is of low rank tyrtyshnikov 1996 1 in the present work we extend the black dot algorithm for the computation of such splitting for p circulant see oseledets and tyrtyshnikov 2006 2 to the case where p is in a for several known low complexity matrix algebras a the algorithm so obtained is particularly efficient when a is toeplitz plus hankel like we finally discuss in detail the existence and the properties of the decomposition a p r e when a is toeplitz also extending to the circulant and hartley type cases some results previously known for p circulant

letter to the editor stability analysis on delayed neural networks based on an improved delay partitioning approach in this paper the asymptotical stability is investigated for a class of delayed neural networks dnns in which one improved delay partitioning idea is employed by choosing an augmented lyapunov krasovskii functional and utilizing general convex combination method two novel conditions are obtained in terms of linear matrix inequalities lmis and the conservatism can be greatly reduced by thinning the partitioning of delay intervals moreover the lmi based criteria heavily depend on both the upper and lower bounds on time delay and its derivative which is different from the existent ones though the results are not presented via standard lmis they still can be easily checked by resorting to matlab lmi toolbox finally three numerical examples are given to demonstrate that our results can be less conservative than the present ones

fast dct domain filtering using the dct and the dst a method for efficient spatial domain filtering directly in the discrete cosine transform dct domain is developed and proposed it consists of using the discrete sine transform dst and the dct for transform domain processing on the in jpeg basis of the previously derived convolution multiplication properties of discrete trigonometric transforms the proposed scheme requires neither zero padding of the input data nor kernel symmetry it is demonstrated that in typical applications the proposed algorithm is significantly more efficient than the conventional filtered spatial domain and earlier proposed dct domain methods the proposed method is applicable to any dct based image compression standard such as jpeg mpeg and h 261

tridiagonal commuting matrices and fractionalizations of dct and dst matrices of types i iv v and viii in this paper we first establish new relationships in matrix forms among discrete fourier transform dft generalized dft gdft and various types of discrete cosine transform dct and discrete sine transform dst matrices two new independent tridiagonal commuting matrices for each of dct and dst matrices of types i iv v and viii are then derived from the existing commuting matrices of dft and gdft with these new commuting matrices the orthonormal sets of hermite like eigenvectors for dct and dst matrices can be determined and the discrete fractional cosine transform dfrct and the discrete fractional sine transform dfrst are defined the relationships among the discrete fractional fourier transform dfrft fractional gdft and various types of dfrct and dfrst are developed to reduce computations for dfrft and fractional gdft

kronecker product approximations for image restoration with whole sample symmetric boundary conditions reflexive boundary conditions bcs assume that the array values outside the viewable region are given by a symmetry of the array values inside the reflection guarantees the continuity of the image in fact there are usually two choices for the symmetry symmetry around the meshpoint and symmetry around the midpoint the first is called whole sample symmetry in signal and image processing the second is half sample many researchers have developed some fast algorithms for the problems of image restoration with the half sample symmetric bcs over the years however little attention has been given to the whole sample symmetric bcs in this paper we consider the use of the whole sample symmetric boundary conditions in image restoration the blurring matrices constructed from the point spread functions psfs for the bcs have block toeplitz plus pseudohankel with toeplitz plus pseudohankel blocks structures recently regardless of symmetric properties of the psfs a technique of kronecker product approximations was successfully applied to restore images with the zero bcs half sample symmetric bcs and anti reflexive bcs respectively all these results extend quite naturally to the whole sample symmetric bcs since the resulting matrices have similar structures it is interesting to note that when the size of the true psf is small the computational complexity of the algorithm obtained for the kronecker product approximation of the resulting matrix in this paper is very small it is clear that in this case all calculations in the algorithm are implemented only at the upper left corner submatrices of the big matrices finally detailed experimental results reporting the performance of the proposed algorithm are presented

generalized commuting matrices and their eigenvectors for dfts offset dfts and other periodic operations it is well known that some matrices such as dickinson steiglitz s matrix can commute with the discrete fourier transform dft and that one can use them to derive the complete and orthogonal dft eigenvector set recently candan found the general form of the dft commuting matrix in this paper we further extend the previous work and find the general form of the commuting matrix for any periodic quasi periodic and offset quasi periodic operations using the general commuting matrix we can derive the complete and orthogonal eigenvector sets for offset dfts dcts of types 1 4 5 and 8 dsts of types 1 4 5 and 8 discrete hartley transforms of types 1 and 4 the walsh transform and the projection operation the operation that maps a whole vector space into a subspace successfully moreover several novel ways of finding dft eigenfunctions are also proposed furthermore we also extend our theories to the continuous case i e if a continuous transform is periodic quasi periodic or offset quasi periodic such as the ft and some cyclic operations in optics we can find the general form of the commuting operation and then find the complete and orthogonal eigenfunctions set for the continuous transform

hierarchical bayesian spatiotemporal analysis of revascularization odds using smoothing splines hierarchical bayesian models are proposed for over dispersed longitudinal spatially correlated binomial data this class of models accounts for correlation among regions by using random effects and allows a flexible modelling of spatiotemporal odds by using smoothing splines the aim is i to develop models which will identify temporal trends of odds and produce smoothed maps including regional effects ii to specify markov chain monte carlo mcmc inference for fitting such models iii to study the sensitivity of such bayesian binomial spline spatiotemporal analyses to prior assumptions and iv to compare mechanisms for assessing goodness of fit an analysis of regional variation for revascularization odds of patients hospitalized for acute coronary syndrome in quebec motivates and illustrates the methods developed

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

data compression properties of the hartley transform the data compression performance of the hartley transform on a markov 1 signal is theoretically compared to that of the fourier transform covariance distribution and residue correlation measurements have been computed for the hartley fourier and cosine transforms the hartley transform achieves better coding performance than the fourier transform but is inferior to the cosine transform

modelling complexity applications of gibbs sampling in medicine summary we review applications of gibbs sampling in medicine involving longitudinal spatial covariate measurement and survival models applications in immunology pharmacology transplantation cancer screening industrial epidemiology and genetic epidemiology are discussed

synchronization criteria for a generalized complex delayed dynamical network model abstract it has been demonstrated that most complex networks display synchronization phenomena and this problem has attracted great attention of various fields including science and engineering in this paper a generalized complex dynamical network model with time varying delays was presented kronecker product was adopted to investigate this model moreover several synchronization criteria were derived for both delay independent and delay dependent asymptotical stability especially it has been shown that synchronization of such dynamical network is determined by the linear matrix inequality consisting of coupling configuration matrices inner coupling matrices and isolated cells at last illustrative examples were given to validate the above acquired

diagonalizing properties of the discrete cosine transforms since its introduction in 1974 by ahmed et al the discrete cosine transform dct has become a significant tool in many areas of digital signal processing especially in signal compression there exist eight types of discrete cosine transforms dcts we obtain the eight types of dcts as the complete orthonormal set of eigenvectors generated by a general form of matrices in the same way as the discrete fourier transform dft can be obtained as the eigenvectors of an arbitrary circulant matrix these matrices can be decomposed as the sum of a symmetric toeplitz matrix plus a hankel or close to hankel matrix scaled by some constant factors we also show that all the previously proposed generating matrices for the dcts are simply particular cases of these general matrix forms using these matrices we obtain for each dct a class of stationary processes verifying certain conditions with respect to which the corresponding dct has a good asymptotic behavior in the sense that it approaches karhunen loeve transform performance as the block size n tends to infinity as a particular result we prove that the eight types of dcts are asymptotically optimal for all finite order markov processes we finally study the decorrelating power of the dcts obtaining expressions that show the decorrelating behavior of each dct with respect to any stationary processes

tensor tensor products with invertible linear transforms abstract research in tensor representation and analysis has been rising in popularity in direct response to a the increased ability of data collection systems to store huge volumes of multidimensional data and b the recognition of potential modeling accuracy that can be provided by leaving the data and or the operator in its natural multidimensional form in recent work 1 the authors introduced the notion of the t product a generalization of matrix multiplication for tensors of order three which can be extended to multiply tensors of arbitrary order 2 the multiplication is based on a convolution like operation which can be implemented efficiently using the fast fourier transform fft the corresponding linear algebraic framework from the original work was further developed in 3 and it allows one to elegantly generalize all classical algorithms from numerical linear algebra in this paper we extend this development so that tensor tensor products can be defined in a so called transform domain for any invertible linear transform in order to properly motivate this transform based approach we begin by defining a new tensor tensor product alternative to the t product we then show that it can be implemented efficiently using dcts and that subsequent definitions and factorizations can be formulated by appealing to the transform domain using this new product as our guide we then generalize the transform based approach to any invertible linear transform we introduce the algebraic structures induced by each new multiplication in the family which is that of c algebras and modules finally in the spirit of 4 we give a matrix algebra based interpretation of the new family of tensor tensor products and from an applied perspective we briefly discuss how to choose a transform we demonstrate the convenience of our new framework within the context of an image deblurring problem and we show the potential for using one of these new tensor tensor products and resulting tensor svd for hyperspectral image compression

synchronization analysis of delayed complex networks with time varying couplings abstract in this paper a new method is presented to analyze the linear stability of the synchronized state in arbitrarily coupled complex dynamical systems with time delays the coupling configurations are not restricted to the symmetric and irreducible connections or the non negative off diagonal links the stability criteria are obtained by using lyapunov krasovskii functional method and subspace projection method these criteria reveal the relationship between coupling matrices and stability of the dynamical networks

dct dst and gauss markov fields conditions for equivalence the correspondence addresses the intriguing question of which random models are equivalent to the discrete cosine transform dct and discrete sine transform dst common knowledge states that these transforms are asymptotically equivalent to first order gauss causal markov random processes we establish that the dct and the dst are exactly equivalent to homogeneous one dimensional 1 d and two dimensional 2 d gauss noncausal markov random fields defined on finite lattices with appropriate boundary conditions

symmetric convolution using unitary transform matrices we demonstrate relationships between the convolutional and unitary forms of certain trigonometric transform matrices we then use the new relationships to derive forms of the symmetric convolution multiplication property based on unitary rather than convolutional forms of the transform matrices

enhancement of color images by scaling the dct coefficients this paper presents a new technique for color enhancement in the compressed domain the proposed technique is simple but more effective than some of the existing techniques reported earlier the novelty lies in this case in its treatment of the chromatic components while previous techniques treated only the luminance component the results of all previous techniques along with that of the proposed one are compared with respect to those obtained by applying a spatial domain color enhancement technique that appears to provide very good enhancement the proposed technique computationally more efficient than the spatial domain based method is found to provide better enhancement compared to other compressed domain based approaches

l m fold image resizing in block dct domain using symmetric convolution image resizing is to change an image size by upsampling or downsampling of a digital image most still images and video frames on digital media are given in a compressed domain image resizing of a compressed image can be performed in the spatial domain via decompression and recompression in general resizing of a compressed image in a compressed domain is much faster than that in the spatial domain we propose a novel approach to resize images with l m resizing ratio in the discrete cosine transform dct domain which exploits the multiplication convolution property of dct multiplication in the spatial domain corresponds to symmetric convolution in the dct domain when an image is given in terms of its 8 spl times 8 block dct coefficients its resized image is also obtained in 8 spl times 8 block dct coefficients the proposed approach is computationally fast and produces visually fine images with high psnr

symmetric convolution and the discrete sine and cosine transforms this paper discusses the use of symmetric convolution and the discrete sine and cosine transforms dsts and dcts for general digital signal processing the operation of symmetric convolution is a formalized approach to convolving symmetrically extended sequences the result is the same as that obtained by taking an inverse discrete trigonometric transform dtt of the product of the forward dtts of those two sequences there are 16 members in the family of dtts each provides a representation for a corresponding distinct type of symmetric periodic sequence the author defines symmetric convolution relates the dsts and dcts to symmetric periodic sequences and then use these principles to develop simple but powerful convolution multiplication properties for the entire family of dsts and dcts symmetric convolution can be used for discrete linear filtering when the filter is symmetric or antisymmetric the filtering will be efficient because fast algorithms exist for all versions of the dtts conventional linear convolution is possible if one first zero pad the input data symmetric convolution and its fast implementation using dtts are now an alternative to circular convolution and the dft

synchronization of singular complex dynamical networks with time varying delays abstract this paper considers delay dependent synchronizations of singular complex dynamical networks with time varying delays a modified lyapunov krasovskii functional is used to derive a sufficient condition for synchronization in terms of lmis linear matrix inequalities which can be easily solved by various convex optimization algorithms numerical examples show the effectiveness of the proposed method

delay dependent robust stabilization of uncertain state delayed systems this paper concerns a problem of robust stabilization of uncertain state delayed systems a new delay dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities an algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties

pinning control of weighted general complex dynamical networks with time delay abstract time delays commonly exist in the real world in the present work we consider weighted general complex dynamical networks with time delay which are undirected and connected control of such networks by applying local feedback injections to a fraction of network nodes is investigated for both continuous time and discrete time cases both delay independent and delay dependent asymptotical stability criteria for network stabilization are derived it is also shown that the whole network can be stabilized by controlling only one node the efficiency of the derived results was illustrated by numerical examples

synchronization stability of general complex dynamical networks with time varying delays a piecewise analysis method the synchronization problem of some general complex dynamical networks with time varying delays is investigated both time varying delays in the network couplings and time varying delays in the dynamical nodes are considered the delays considered in this paper are assumed to vary in an interval where the lower and upper bounds are known based on a piecewise analysis method the variation interval of the time delay is firstly divided into several subintervals by checking the variation of the derivative of a lyapunov function in every subinterval then the convexity of matrix function method and the free weighting matrix method are fully used in this paper some new delay dependent synchronization stability criteria are derived in the form of linear matrix inequalities two numerical examples show that our method can lead to much less conservative results than those in the existing references

fractional cosine and sine transforms over finite fields abstract in this paper we introduce fractional cosine and sine transforms over finite fields the basis for the definition of such transforms which are respectively referred by the acronyms gfrct and gfrst is the recently proposed fractional fourier transform over finite fields gfrft 1 more specifically we use the eigenvectors of the finite field fourier transform to construct eigenvectors of the finite field cosine and sine transforms such eigenvectors are then used in spectral expansions that allow to compute fractional powers of the finite field cosine and sine transform matrices

synchronization of a complex dynamical network with coupling time varying delays via sampled data control abstract in this paper the synchronization problem of a complex dynamical network with coupling time varying delays via delayed sampled data controller is investigated in order to make full use of the sawtooth structure characteristic of the sampling input delay a discontinuous lyapunov functional is proposed based on the extended wirtinger inequality from a convex representation of the sector restricted nonlinearity in system dynamics the stability condition based on lyapunov stability theory is obtained by utilization of linear matrix inequality formulation to find the controller which achieves the synchronization of a complex dynamical network with coupling time varying delay finally two numerical examples are given to illustrate the effectiveness of the proposed methods

m channel oversampled graph filter banks this paper proposes m channel oversampled filter banks for graph signals the filter set satisfies the perfect reconstruction condition a method of designing oversampled graph filter banks is presented that allows us to design filters with arbitrary parameters unlike the conventional critically sampled graph filter banks the oversampled graph laplacian matrix is also introduced with a discussion of the entire redundancy of the oversampled graph signal processing system the practical performance of the proposed filter banks is validated through graph signal denoising experiments

a delay dependent stability criterion for systems with uncertain time invariant delays this paper provides a new stability criterion for systems with time invariant uncertain delays based on an improved upper bound for the inner product of two vectors a new delay dependent robust stability criterion is derived which is shown by an example less conservative than existing stability criteria

a time varying complex dynamical network model and its controlled synchronization criteria today complex networks have attracted increasing attention from various fields of science and engineering it has been demonstrated that many complex networks display various synchronization phenomena in this note we introduce a time varying complex dynamical network model we then further investigate its synchronization phenomenon and prove several network synchronization theorems especially we show that synchronization of such a time varying dynamical network is completely determined by the inner coupling matrix and by the eigenvalues and the corresponding eigenvectors of the coupling configuration matrix of the network

synchronization of markovian jumping stochastic complex networks with distributed time delays and probabilistic interval discrete time varying delays the paper investigates the synchronization stability problem for a class of complex dynamical networks with markovian jumping parameters and mixed time delays the complex networks consist of m modes and the networks switch from one mode to another according to a markovian chain with known transition probability the mixed time delays are composed of discrete and distributed delays the discrete time delay is assumed to be random and its probability distribution is known a priori in terms of the probability distribution of the delays the new type of system model with probability distribution dependent parameter matrices is proposed based on the stochastic analysis techniques and the properties of the kronecker product delay dependent synchronization stability criteria in the mean square are derived in the form of linear matrix inequalities which can be readily solved by using the lmi toolbox in matlab the solvability of derived conditions depends on not only the size of the delay but also the probability of the delay taking values in some intervals finally a numerical example is given to illustrate the feasibility and effectiveness of the proposed method

empirical bayes confidence intervals based on bootstrap samples abstract consider the model with data generated by the following two stage process first a parameter is sampled from a prior distribution g and then an observation is sampled from the conditional distribution f y if the prior distribution is known then the bayes estimate under squared error loss is the posterior expectation of conditional on the data y for example if g is gaussian with mean and variance 2 and f y is gaussian with mean and variance 2 then the posterior distribution is gaussian with mean b 1 b y and variance 2 1 b where b 2 2 2 inferences about are based on this distribution we study the application of the bootstrap to situations where the prior must be estimated from the data empirical bayes methods for this model we observe data y t y 1 y k t each independent y k following the compound model described previously as first shown by james and stein 1961 setting each k equal to its estimated posterior mean where and pr

bayesian factor analysis for spatially correlated data with application to summarizing area level material deprivation from census data this article describes a bayesian hierarchical model for factor analysis of spatially correlated multivariate data the first level specifies for each area on a map the distribution of a vector of manifest variables conditional on an underlying latent factor at the second level the area specific latent factors have a joint distribution that incorporates spatial correlation the framework allows for both marginal and conditional e g conditional autoregressive specifications of spatial correlation the model is used to quantify material deprivation at the census tract level using data from the 1990 u s census in rhode island an existing and widely used measure of material deprivation is the townsend index an unweighted sum of four standardized census variables i e z scores corresponding to area level proportions of unemployment car ownership crowding and home ownership the townsend and many related indices are computed as linear combinations of measured census variables which motivates t

two dimensional symmetric and antisymmetric generalizations of exponential and cosine functions the properties of the four families of the recently introduced special functions of two real variables denoted here by e and cos are studied the superscripts and refer to the symmetric and antisymmetric functions respectively the functions are considered in all details required for their exploitation in fourier expansions of digital data sampled on square grids of any density and for general position of the grid in the real plane relative to the lattice defined by the underlying group theory the quality of continuous interpolation resulting from the discrete expansions is studied exemplified and compared for some model functions

a new algorithm to compute the discrete cosine transform a new algorithm is introduced for the 2m point discrete cosine transform this algorithm reduces the number of multiplications to about half of those required by the existing efficient algorithms and it makes the system simpler

discrete gyrator transforms computational algorithms and applications as an extension of the 2d fractional fourier transform frft and a special case of the 2d linear canonical transform lct the gyrator transform was introduced to produce rotations in twisted space spatial frequency planes it is a useful tool in optics signal processing and image processing in this paper we develop discrete gyrator transforms dgts based on the 2d lct taking the advantage of the additivity property of the 2d lct we propose three kinds of dgts each of which is a cascade of low complexity operators these dgts have different constraints characteristics and properties and are realized by different computational algorithms besides we propose a kind of dgt based on the eigenfunctions of the gyrator transform this dgt is an orthonormal transform and thus its comprehensive properties especially the additivity property make it more useful in many applications we also develop an efficient computational algorithm to significantly reduce the complexity of this dgt at the end a brief review of some important applications of the dgts is presented including mode conversion sampling and reconstruction watermarking and image encryption

generating matrices for the discrete sine transforms in this correspondence we obtain a general form for the generating matrices of the eight types of discrete sine transforms these matrix forms can be used to study the performance of the different discrete sine transforms as substitutes of the karhunen loeve transform and will allow us to show in a very straightforward way that the discrete sine transforms as the discrete cosine transforms are asymptotically optimal for any finite order markov process

on computing the discrete fourier and cosine transforms an efficient algorithm based on real matrix decomposition is developed for computing a class of sinusoidal transforms that include the discrete fourier and cosine transform

symmetric convolution of asymmetric multidimensional sequences using discrete trigonometric transforms this paper uses the fact that the discrete fourier transform diagonalizes a circulant matrix to provide an alternate derivation of the symmetric convolution multiplication property for discrete trigonometric transforms derived in this manner the symmetric convolution multiplication property extends easily to multiple dimensions using the notion of block circulant matrices and generalizes to multidimensional asymmetric sequences the symmetric convolution of multidimensional asymmetric sequences can then be accomplished by taking the product of the trigonometric transforms of the sequences and then applying an inverse trigonometric transform to the result an example is given of how this theory can be used for applying a two dimensional 2 d finite impulse response fir filter with nonlinear phase which models atmospheric turbulence

autoregressive modeling of temporal spectral envelopes with finite length discrete trigonometric transforms the theory of autoregressive ar modeling also known as linear prediction has been established by the fourier analysis of infinite discrete time sequences or continuous time signals nevertheless for various finite length discrete trigonometric transforms dtts including the discrete cosine and sine transforms of different types the theory is not well established several dtts have been used in current audio coding and the ar modeling method can be applied to reduce coding artifacts or exploit data redundancies this paper systematically develops the ar modeling fundamentals of temporal and spectral envelopes for the sixteen members of the dtts this paper first considers the ar modeling in the generalized discrete fourier transforms gdfts then we derive the modeling to all the dtts by introducing the analytic transforms which convert the real valued vectors into complex valued ones through the process we build the compact matrix representations for the ar modeling of the dtts in both time domain and dtt domain these compact forms also illustrate that the ar modeling for the envelopes can be performed through the hilbert envelope and the power envelope these compact forms can be used to develop new coding technologies or examine the possible defects in the existing ar modeling methods for dtts we apply the forms to analyze the current temporal noise shaping tns tool in mpeg 2 4 advanced audio coding aac

multiscale detection of localized anomalous structure in aggregate disease incidence data we present a modelling framework for detection of potentially anomalous structure in aggregate spatial disease incidence data in a manner sensitive to localization at multiple scales and or positions the key technical contribution is the re casting of the components of a multiscale disease mapping methodology recently introduced by the authors in an earlier paper into a form appropriate for hypothesis testing in particular we describe how hypotheses of spatially clustered variations in disease incidence may be linked in one to one correspondence with collections of hypotheses on the values of certain multiscale parameters associated with a user defined hierarchy of nested partitions of an overall spatial region a bayesian hypothesis testing methodology is developed in the context of a standard poisson measurement model over the collection of possible multiscale hypotheses we discuss the specification of hyper parameters and prior distributions on the space of models the methodology is illustrated on both simulated and real data

technical communique robust stabilization of uncertain systems with unknown input delay this paper is concerned with the robust controller design for uncertain input delayed systems the time delay is assumed to be an unknown constant a controller with delay feedback for the robust stabilization of the system is proposed the stability criterion of the closed loop system is derived in terms of linear matrix inequalities lmis examples show that in many cases our method can give less conservative results than those by the existing methods moreover for the same cases our controllers have lower feedback gains than the existing ones

on the use of discrete cosine transforms for multicarrier communications in this correspondence the conditions to use any kind of discrete cosine transform dct for multicarrier data transmission are derived the symmetric convolution multiplication property of each dct implies that when symmetric convolution is performed in the time domain an element by element multiplication is performed in the corresponding discrete trigonometric domain therefore appending symmetric redundancy as prefix and suffix into each data symbol to be transmitted and also enforcing symmetry for the equivalent channel impulse response the linear convolution performed in the transmission channel becomes a symmetric convolution in those samples of interest furthermore the channel equalization can be carried out by means of a bank of scalars in the corresponding discrete cosine transform domain the expressions for obtaining the value of each scalar corresponding to these one tap per subcarrier equalizers are presented this study is completed with several computer simulations in mobile broadband wireless communication scenarios considering the presence of carrier frequency offset cfo the obtained results indicate that the proposed systems outperform the standardized ones based on the dft

dct dst alternate transform image coding an image coding method for low bit rates is proposed it is based on alternate use of the discrete cosine transform dct and the discrete sine transform dst on image blocks this procedure achieves the removal of redundancies in the correlation between neighboring blocks as well as the preservation of continuity across the block boundaries an outline of the mathematical justification of the method assuming a certain first order gauss markov model is given the resulting coding method is then adapted to nonstationary real images by locally adapting the model parameters and improving the block classification technique simulation results are shown and compared with the performance of related previous methods namely adaptive dct and fast karhunen loeve transform fklt

fast unified computation of the multi dimensional discrete sinusoidal transforms based on a one to one index mapping approach conversions of two types of m dimensional discrete w transforms into the multiple sums involving a number of one dimensional discrete w transforms 1 d dwts are first presented a unified fast m 1 dimensional polynomial transform m 1 d pt and 1 d dwts algorithm for computing these two types of m d dwts are then proposed by revealing the relationships among the m dimensional discrete w transforms m d dwts the m dimensional generalized discrete fourier transforms m d gdfts the m dimensional discrete cosine transforms m d dcts and the m dimensional discrete sine transforms m d dsts the generalized fast algorithms for 14 types of the m d discrete sinusoidal transforms including four types of m d dwts and the same number of types of m d gdfts and three types of m d dcts and the same number of types of m d dsts are presented the number of multiplications for all 14 types of the m d discrete sinusoidal transforms needed by the proposed algorithm is only 1 m times that of the widely used corresponding row column methods the number of additions required by the proposed algorithm is also reduced considerably finally with the help of the software platform visual c 6 0 for windows 98 the computation time comparisons between the proposed and the reported algorithms are given the numerical experiments show that the proposed algorithms are not only highly efficient but are also very simple in computational structure

the discrete cosine transform each discrete cosine transform dct uses n real basis vectors whose components are cosines in the dct 4 for example the j th component of boldv k is cos j frac 1 2 k frac 1 2 frac pi n these basis vectors are orthogonal and the transform is extremely useful in image processing if the vector boldx gives the intensities along a row of pixels its cosine series sum c k boldv k has the coefficients c k boldx boldv k n they are quickly computed from a fast fourier transform but a direct proof of orthogonality by calculating inner products does not reveal how natural these cosine vectors are we prove orthogonality in a different way each dct basis contains the eigenvectors of a symmetric second difference matrix by varying the boundary conditions we get the established transforms dct 1 through dct 4 other combinations lead to four additional cosine transforms the type of boundary condition dirichlet or neumann centered at a meshpoint or a midpoint determines the applications that are appropriate for each transform the centering also determines the period n 1 or n in the established transforms n frac 1 2 or n frac 1 2 in the other four the key point is that all these eigenvectors of cosines come from simple and familiar matrices

analysis of the structured perturbation for the bsccb linear system abstract in this paper based on block style spectral decomposition of the block skew circulant with circulant blocks bsccb matrix the structure perturbation is discussed which includes the condition number and relative error of the bsccb linear system then the optimal backward perturbation bound of the bsccb linear system is analyzed simultaneously the algorithm for the optimal backward perturbation bound is presented at the end of the paper a numerical example is provided to verify the effectiveness of the algorithm

bayesian estimates of disease maps how important are priors in the fully bayesian fb approach to disease mapping the choice of the hyperprior distribution of the dispersion parameter is a key issue in this context we investigated the sensitivity of the rate ratio estimates to the choice of the hyperprior via a simulation study we also compared the performance of the fb approach to mapping disease risk to the conventional approach of mapping maximum likelihood ml estimates and p values the study was modelled on the incidence data of insulin dependent diabetes mellitus iddm as observed in the communes of sardinia