weak solutions of a class of quasilinear hyperbolic integro differential equations describing viscoelastic materials global weak solutions of scalar second order quasilinear hyperbolic integro differential equations with singular kernels are constructed perturbations of rest states are shown to propagate with finite speed smoothing effects of the solution operator are exhibited and conditions for the asymptotic stability of rest states are given the equations arise in viscoelasticity

on the hull of two dimensional percolation clusters a recently proven equivalence between certain random walks with memory and the hull of percolation clusters in two dimensions is used to estimate the fractal dimension of the latter by means of monte carlo simulations the authors calculate the value dh 1 750 or 0 002 in agreement with a recent conjecture that dh 7 4 exactly

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

bi iterative algorithm for extracting independent components from array signals it is well known that the complex valued nonunitary joint diagonalization nujd problem in blind source separation bss can be linked to the trilinear models in this paper by exploring the special structure of the nujd problem in bss we introduce a novel symmetric tri quadratic cost function and then derive a simultaneous bi iterative algorithm s bia for solving the nujd problem finally three experiments are conducted in order to show the comparatively good performance of the proposed bss algorithm

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

a least squares approach to blind beamforming we present a least squares approach to blind beamforming two estimation criteria are derived one turns out to coincide with the comon 1990 1994 criterion whereas the other is a computationally simpler criterion similar in nature to the joint approximate diagonalization of eigenmatrices jade criterion

eden growth on multifractal lattices a modified eden model has been investigated in which the growth probabilities are determined by a fractal measure on the underlying lattice both the spatial distribution and probability distribution of surface sites on the growing clusters have been investigated for the case where the multifractal substrate is constructed using a 2 2 multiplicative generator with the probabilities p1 1 p2 r p3 r3 and p4 r3 the spatial distribution of surface sites and the sites comprising the inner and outer hulls have a fractal geometry which can be described by dimensionalities which depend on r for the total surface this dimensionality converges to a value of about 1 76 or 0 01 as r to 0 for the inner and outer hulls the fractal dimensionality approaches a value of about 1 48 or 0 02

blind separation of mutually correlated sources using precoders this paper studies the problem of blind source separation bss from instantaneous mixtures with the assumption that the source signals are mutually correlated we propose a novel approach to bss by using precoders in transmitters we show that if the precoders are properly designed some cross correlation coefficients of the coded signals can be forced to be zero at certain time lags then the unique correlation properties of the coded signals can be exploited in receiver to achieve source separation based on the proposed precoders a subspace based algorithm is derived for the blind separation of mutually correlated sources the effectiveness of the algorithm is illustrated by simulation examples

a generalization of joint diagonalization criteria for source separation in the field of blind source separation joint diagonalization based approaches constitute an important framework leading to useful algorithms such as the popular joint approximate diagonalization of eigenmatrices jade and simultaneous third order tensor diagonalization stotd algorithms however they are often restricted to the case of cumulants of order four in this paper we extend the results leading to jade and stotd to cumulants of any order greater than or equal to three by exhibiting a new family of contrast functions that constitutes then a unified framework for the above known results this also leads us to generalize some links between contrast functions and joint diagonalization criteria on which these algorithms are based in turn one contrast of the new family allows us to show that a function previously proposed as a separation criterion is also a contrast moreover for the two generalized jade and stotd contrasts the analytical optimal solution in the case of two sources is derived and shown to keep the same simple expression whatever the cumulant order finally some computer simulations illustrate the potential advantage one can take by considering statistics of different orders for the joint diagonalization of cumulant matrices

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

the fractal dimension of percolation cluster hulls large simulations of 2d site percolation on a square lattice provide several estimates of the fractal dimension dh of the hull or outer boundary of percolation clusters close to criticality statistical estimates based on an ensemble of more than 106 clusters with varying sizes yield dh 1 74 or 0 02 geometrical measurements of the hull two point correlation for individual clusters with more than 105 sites give dh 1 76 or 0 01 the observed scaling behaviour is the same both slightly above and below pc

recursive updating the eigenvalue decomposition of a covariance matrix the author addresses the problem of computing the eigensystem of the modified hermitian matrix given the prior knowledge of the eigensystem of the original hermitian matrix specifically an additive rank k modification corresponding to adding and deleting blocks of data to and from the covariance matrix is considered an efficient and parallel algorithm which makes use of a generalized spectrum slicing theorem is derived for computing the eigenvalues the eigenvector can be computed explicitly in terms of the solution of a much reduced k k homogeneous hermitian system the overall computational complexity is shown to be improved by an order of magnitude from o n sup 3 to o n sup 2 k where n n is the size of the covariance matrix it is pointed out that these ideas can be applied to adaptive signal processing applications such as eigen based techniques for frequency or angle of arrival estimation and tracking specifically adaptive versions of the principal eigenvector method and the total least squares method are derived

ordered phase ab diffusive growth ordered phase ab formation and diffusive growth and its boundary evolution on a square lattice are investigated by computer simulation it is found that the boundary is a self similar fractal d 7 4 and its width and length grow as a power law with exponents 1 3 and 1 4 correspondingly the phase is found to exist over the 0 31 0 69 concentration range it is shown that a phase formed via a second order phase transition may have a boundary if the physical properties of the system have a gradient

a matrix pencil approach to blind separation of colored nonstationary signals for many signal sources such as speech with distinct nonwhite power spectral densities second order statistics of the received signal mixture can be exploited for signal separation without knowledge of the noise correlation matrix we propose a simple and yet effective signal extraction method for signal source separation under unknown temporally white noise this new and unbiased signal extractor is derived from the matrix pencil formed between output autocorrelation matrices at different delays based on the matrix pencil an esprit type algorithm is derived to get an optimal solution in the least square sense our method is well suited for systems with colored sensor noises and for nonstationary signals

existence of periodic weak solutions to the three dimensional nonlinear viscoelastic system in this paper we discuss the time periodic solutions to a general three dimensional nonlinear viscoelastic system with dirichlet boundary condition employing the singularity of the integral kernel we obtain the energy estimates in sobolev spaces with fractional index and then show the existence of time periodic solutions to the problem for viscoelastic solid and liquid models respectively

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

plane rotation based evd updating schemes for efficient subspace tracking we present new algorithms based on plane rotations for tracking the eigenvalue decomposition evd of a time varying data covariance matrix these algorithms directly produce eigenvectors in orthonormal form and are well suited for the application of subspace methods to nonstationary data after recasting evd tracking as a simplified rank one evd update problem computationally efficient solutions are obtained in two steps first a new kind of parametric perturbation approach is used to express the eigenvector update as an unimodular orthogonal transform which is represented in exponential matrix form in terms of a reduced set of small unconstrained parameters second two approximate decompositions of this exponential matrix into products of plane or givens rotations are derived one of which being previously unknown these decompositions lead to new plane rotation based evd updating schemes proteus whose main feature is the use of plane rotations for updating the eigenvectors thereby preserving orthonormality finally the proteus schemes are used to derive new evd trackers whose convergence and numerical stability are investigated via simulations one algorithm can track all the signal subspace evd components in only o lm operations where l and m respectively denote the data vector and signal subspace dimensions while achieving a performance comparable to an exact evd approach and maintaining perfect orthonormality of the eigenvectors the new algorithms show no signs of error buildup

adaptive eigensubspace algorithms for direction or frequency estimation and tracking the authors present an adaptive estimator of the complete noise or signal subspace of a sample covariance matrix as well as the estimator s practical implementations the general formulation of the proposed estimator results from an asymptotic argument which shows the signal or noise subspace computation to be equivalent to a constrained gradient search procedure a highly parallel algorithm denoted the inflation method is introduced for the estimation of the noise subspace the simulation results of these adaptive estimators show that the adaptive subspace algorithms perform substantially better than p a thompson s 1980 adaptive version of v f pisarenko s technique 1973 in estimating frequencies or directions of arrival doa of plane waves for tracking nonstationary parameters the simulation results also show that the adaptive subspace algorithms are better than direct eigendecomposition methods for which computational complexity is much higher than the adaptive versions

a neural network learning for adaptively extracting cross correlation features between two high dimensional data streams this paper proposes a novel cross correlation neural network cnn model for finding the principal singular subspace of a cross correlation matrix between two high dimensional data streams we introduce a novel nonquadratic criterion nqc for searching the optimum weights of two linear neural networks lnn the nqc exhibits a single global minimum attained if and only if the weight matrices of the left and right neural networks span the left and right principal singular subspace of a cross correlation matrix respectively the other stationary points of the nqc are unstable saddle points we develop an adaptive algorithm based on the nqc for tracking the principal singular subspace of a cross correlation matrix between two high dimensional vector sequences the nqc algorithm provides a fast online learning of the optimum weights for two lnn the global asymptotic stability of the nqc algorithm is analyzed the nqc algorithm has several key advantages such as faster convergence which is illustrated through simulations

a fast fixed point algorithm for independent component analysis we introduce a novel fast algorithm for independent component analysis which can be used for blind source separation and feature extraction we show how a neural network learning rule can be transformed into a fixedpoint iteration which provides an algorithm that is very simple does not depend on any user defined parameters and is fast to converge to the most accurate solution allowed by the data the algorithm finds one at a time all nongaussian independent components regardless of their probability distributions the computations can be performed in either batch mode or a semiadaptive manner the convergence of the algorithm is rigorously proved and the convergence speed is shown to be cubic some comparisons to gradient based algorithms are made showing that the new algorithm is usually 10 to 100 times faster sometimes giving the solution in just a few iterations

stationary points of a kurtosis maximization algorithm for blind signal separation and antenna beamforming blind source separation has been the subject of extensive research in particular blind antenna beamforming is an effective signal separation technique for communication systems to combat co channel interference among many potential candidate approaches the simple constant modulus algorithm cma has been widely studied and used in practice the cma is designed to capture and separate signals with negative kurtosis however when some signals have positive kurtoses the cma is unable to capture and separate these sources we show that the kurtosis maximum algorithm kma can capture signals with both the positive and negative kurtoses its global convergence proof is presented for noiseless systems with multiple signals sources and for systems with a single source and zero kurtosis such as gaussian additive noise

fast and robust fixed point algorithms for independent component analysis independent component analysis ica is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible we use a combination of two different approaches for linear ica comon s information theoretic approach and the projection pursuit approach using maximum entropy approximations of differential entropy we introduce a family of new contrast functions for ica these contrast functions enable both the estimation of the whole decomposition by minimizing mutual information and estimation of individual independent components as projection pursuit directions the statistical properties of the estimators based on such contrast functions are analyzed under the assumption of the linear mixture model and it is shown how to choose contrast functions that are robust and or of minimum variance finally we introduce simple fixed point algorithms for practical optimization of the contrast functions

matrix group algorithm via improved whitening process for extracting statistically independent sources from array signals this paper addresses the problem of blind separation of multiple independent sources from observed array output signals the main contributions in this paper include an improved whitening scheme for estimation of signal subspace a novel biquadratic contrast function for extraction of independent sources and an efficient alterative method for joint implementation of a set of approximate diagonalization structural matrices specifically an improved whitening scheme is first developed by estimating the signal subspace jointly from a set of diagonalization structural matrices based on the proposed cyclic maximizer of an interesting cost function moreover the globally asymptotical convergence of the proposed cyclic maximizer is analyzed and proved next a novel biquadratic contrast function is proposed for extracting one single independent component from a slice matrix group of any order cumulant of the array signals in the presence of temporally white noise a fast fixed point algorithm that is a cyclic minimizer is constructed for searching a minimum point of the proposed contrast function the globally asymptotical convergence of the proposed fixed point algorithm is analyzed then multiple independent components are obtained by using repeatedly the proposed fixed point algorithm for extracting one single independent component and the orthogonality among them is achieved by the well known qr factorization the performance of the proposed algorithms is illustrated by simulation results and is compared with three related blind source separation algorithms

possibly exact fractal dimensions from conformal invariance based on an equivalence between the q state potts model and conformally invariant field theories the author speculates that all fractal dimensionalities of two dimensional percolation are given by the formula d 100 x2 48 where x is an integer the same formula should also apply to self avoiding walks and lattice animals this approach is extended to cluster weighted percolation his conjecture seems to agree with previous exact and numerical results except for the backbone exponent and possibly for lattice animals

interdiffusion fractal structures scaling size effect interdiffusion that proceeds via the vacancy mechanism with formation of an ideal substitutional solid solution is investigated by monte carlo simulation on a square lattice the produced stochastic structures studied are the percolation diffusion front and the total boundary of the clusters it is shown that they have a fractal geometry and that their evolution is characterized by a number of critical exponents a conclusion is made that the fractal nature of the diffusion front leads to diffusion size effect in thin films the approach used permits description of propagation of superconducting conducting magnetic and other phases during interdiffusion

a blind source separation technique using second order statistics separation of sources consists of recovering a set of signals of which only instantaneous linear mixtures are observed in many situations no a priori information on the mixing matrix is available the linear mixture should be blindly processed this typically occurs in narrowband array processing applications when the array manifold is unknown or distorted this paper introduces a new source separation technique exploiting the time coherence of the source signals in contrast with other previously reported techniques the proposed approach relies only on stationary second order statistics that are based on a joint diagonalization of a set of covariance matrices asymptotic performance analysis of this method is carried out some numerical simulations are provided to illustrate the effectiveness of the proposed method

array processing in correlated noise fields based on instrumental variables and subspace fitting accurate signal parameter estimation from sensor array data is a problem which has received much attention in the last decade a number of parametric estimation techniques have been proposed in the literature in general these methods require knowledge of the sensor to sensor correlation of the noise which constitutes a significant drawback this difficulty can be overcome only by introducing alternative assumptions that enable separating the signals from the noise in some applications the raw sensor outputs can be preprocessed so that the emitter signals are temporally correlated with correlation length longer than that of the noise an instrumental variable iv approach can then be used for estimating the signal parameters without knowledge of the spatial color of the noise a computationally simple iv approach has recently been proposed by the authors herein a refined technique that can give significantly better performance is derived a statistical analysis of the parameter estimates is performed enabling optimal selection of certain user specified quantities a lower bound on the attainable error variance is also presented the proposed optimal iv method is shown to attain the bound if the signals have a quasideterministic character

equivariant adaptive source separation source separation consists of recovering a set of independent signals when only mixtures with unknown coefficients are observed this paper introduces a class of adaptive algorithms for source separation that implements an adaptive version of equivariant estimation and is henceforth called equivariant adaptive separation via independence easi the easi algorithms are based on the idea of serial updating this specific form of matrix updates systematically yields algorithms with a simple structure for both real and complex mixtures most importantly the performance of an easi algorithm does not depend on the mixing matrix in particular convergence rates stability conditions and interference rejection levels depend only on the normalized distributions of the source signals closed form expressions of these quantities are given via an asymptotic performance analysis the theme of equivariance is stressed throughout the paper the source separation problem has an underlying multiplicative structure the parameter space forms a matrix multiplicative group we explore the favorable consequences of this fact on implementation performance and optimization of easi algorithms

kinetic growth walks and trails on oriented square lattices hull percolation and percolation hulls the authors have studied kinetic growth walks on the manhattan lattice and kinetic growth trails on the l lattice they find that the directional properties of these lattices prevent the kinetic growth walks from being trapped except at the origin as a consequence kgws are found to be in the skw universality class for these lattices extensive numerical calculations support this fact moreover it has been shown that the recently introduced hull percolation is equivalent to the kinetic growth walks on the manhattan lattice and the bond percolation hull on the square lattice at the percolation threshold is equivalent to the kinetic growth trails on the l lattice their numerical estimates agree nicely with the original estimates and thus support the equivalence

globally convergent blind source separation based on a multiuser kurtosis maximization criterion we consider the problem of recovering blindly i e without the use of training sequences a number of independent and identically distributed source user signals that are transmitted simultaneously through a linear instantaneous mixing channel the received signals are hence corrupted by interuser interference iui and we can model them as the outputs of a linear multiple input multiple output mimo memoryless system assuming the transmitted signals to be mutually independent i i d and to share the same non gaussian distribution a set of necessary and sufficient conditions for the perfect blind recovery up to scalar phase ambiguities of all the signals exists and involves the kurtosis as well as the covariance of the output signals we focus on a straightforward blind constrained criterion stemming from these conditions from this criterion we derive an adaptive algorithm for blind source separation which we call the multiuser kurtosis muk algorithm at each iteration the algorithm combines a stochastic gradient update and a gram schmidt orthogonalization procedure in order to satisfy the criterion s whiteness constraints a performance analysis of its stationary points reveals that the muk algorithm is free of any stable undesired local stationary points for any number of sources hence it is globally convergent to a setting that recovers them all

projection approximation subspace tracking subspace estimation plays an important role in a variety of modern signal processing applications we present a new approach for tracking the signal subspace recursively it is based on a novel interpretation of the signal subspace as the solution of a projection like unconstrained minimization problem we show that recursive least squares techniques can be applied to solve this problem by making an appropriate projection approximation the resulting algorithms have a computational complexity of o nr where n is the input vector dimension and r is the number of desired eigencomponents simulation results demonstrate that the tracking capability of these algorithms is similar to and in some cases more robust than the computationally expensive batch eigenvalue decomposition relations of the new algorithms to other subspace tracking methods and numerical issues are also discussed

site percolation threshold for honeycomb and square lattices a new method of estimating the critical percolation threshold is proposed based on stauffer s cluster number scaling hypothesis and the universality with respect to lattice structure of the corresponding stauffer scaling function this method is illustrated by obtaining estimates of the site percolation threshold for the honeycomb lattice pc 0 6962 or 0 0006 and for the square lattice pc 0 5923 or 0 0007 the error bars or confidence limits of our estimates are substantially smaller than previous series estimates and for the honeycomb lattice would have to be multiplied by the factor 18 to include the value pc 2 12 recently proposed by kondor 1980 to be exact an additional result is r 4 95 or 0 15 where r lims to infinity rs and rs is the ratio of the cluster number scaling function at its maximum to its value at pc for clusters of size s