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

on the virtual array concept for higher order array processing for about two decades many fourth order fo array processing methods have been developed for both direction finding and blind identification of non gaussian signals one of the main interests in using fo cumulants only instead of second order so ones in array processing applications relies on the increase of both the effective aperture and the number of sensors of the considered array which eventually introduces the fo virtual array concept presented elsewhere and allows in particular a better resolution and the processing of more sources than sensors to still increase the resolution and the number of sources to be processed from a given array of sensors new families of blind identification source separation and direction finding methods at an order m 2q q spl ges 2 only have been developed recently in this context the purpose of this paper is to provide some important insights into the mechanisms and more particularly to both the resolution and the maximal processing capacity of numerous 2qth order array processing methods whose previous methods are part of by extending the virtual array concept to an arbitrary even order for several arrangements of the data statistics and for arrays with space angular and or polarization diversity

icar a tool for blind source separation using fourth order statistics only the problem of blind separation of overdetermined mixtures of sources that is with fewer sources than or as many sources as sensors is addressed in this paper a new method called independent component analysis using redundancies in the quadricovariance icar is proposed in order to process complex data this method without any whitening operation only exploits some redundancies of a particular quadricovariance matrix of the data computer simulations demonstrate that icar offers in general good results and even outperforms classical methods in several situations icar i succeeds in separating sources with low signal to noise ratios ii does not require sources with different second order or and first order spectral densities iii is asymptotically not affected by the presence of a gaussian noise with unknown spatial correlation iv is not sensitive to an over estimation of the number of sources

total blow up versus single point blow up traditional thermal explosion theory is used to describe reaction initiation in condensed explosives and is limited formally to nondeformable materials kassoy and poland 4 significantly extended this theory to develop an ignition model for a reactive gas in a bounded container in order to describe the induction period during this induction period there is a spatially homogeneous pressure rise in the system which causes a com pressive heating effect in the constant volume container mathematically this compressibility of the gas is expressed by means of an integral term in the induction model for the temperature perturbation 0 x t this model is given by e ak 1 j e x t dx y x 2 0 x 0 d x 2 0

joint eigenvalue decomposition of non defective matrices based on the lu factorization with application to ica in this paper we propose a fast and efficient jacobi like approach named jet joint eigenvalue decomposition based on triangular matrices for the joint eigenvalue decomposition jevd of a set of real or complex non defective matrices based on the lu factorization of the matrix of eigenvectors contrarily to classical jacobi like jevd methods the iterative procedure of the jet approach can be reduced to the search for only one of the two triangular matrices involved in the factorization of the matrix of eigenvectors hence decreasing the numerical complexity two variants of the jet technique namely jet u and jet o which correspond to the optimization of two different cost functions are described in detail and these are extended to the complex case numerical simulations show that in many practical cases the jet approach provides more accurate estimation of the matrix of eigenvectors than its competitors and that the lowest numerical complexity is consistently achieved by the jet u algorithm in addition we illustrate in the ica context the interest of being able to solve efficiently the non orthogonal jevd problem more particularly based on our jet u algorithm we propose a more robust version of an existing ica method named micar u the identifiability of the latter is studied and proved under some conditions computer results given in the context of brain interfaces show the better ability of micar u to denoise simulated electrocortical data compared to classical ica techniques for low signal to noise ratio values

blind identification and source separation in 2 spl times 3 under determined mixtures under determined mixtures are characterized by the fact that they have more inputs than outputs or with the antenna array processing terminology more sources than sensors the problem addressed is that of identifying and inverting the mixture which obviously does not admit a linear inverse identification is carried out with the help of tensor canonical decompositions on the other hand the discrete distribution of the sources is utilized for performing the source extraction the under determined mixture being either known or unknown the results presented in this paper are limited to two dimensional 2 d mixtures of three sources

uniform blow up rate for parabolic equations with a weighted nonlocal nonlinear source abstract in this paper the blow up rate of solutions of semi linear reaction diffusion equations with a more complicated source term which is a product of nonlocal or localized source and weight function a x is investigated it is proved that the solutions have global blow up and that the rates of blow up are uniform in all compact subsets of the domain furthermore the blow up rate of u t is precisely determined

uniform blow up rate for diffusion equations with localized nonlinear source abstract in this short paper we investigate blow up rate of solutions of reaction diffusion equations with localized reactions we prove that the solutions have a global blow up and the rate of blow up is uniform in all compact subsets of the domain

concise formulae for the cumulant matrices of a random vector concise formulae are given for the cumulant matrices of a real valued zero mean random vector up to order 6 in addition to usual matrix operations they involve only the kronecker product the vec operator and the commutation matrix orders 5 and 6 are provided here for the first time the same method as provided in the paper can be applied to compute higher orders an immediate consequence of these formulae is to return 1 upper bounds on the rank of the cumulant matrices and 2 the expression of the sixth order moment matrix of a gaussian vector due to their conciseness the proposed formulae also have a computational advantage as compared to the repeated use of leonov and shiryaev formula

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

unbiased efficient estimator of the fourth order cumulant for random zero mean non i i d signals particular case of ma stochastic process non gaussian processes may require not only the information provided by first two moments but also that given by the higher order statistics in particular by the third and fourth order moments or cumulants this paper addresses a fourth order cumulant estimation problem for real discrete time random non i i d signal that can be approximated as an ma stochastic process an unbiased estimator is proposed studied and compared to two other frequently used estimators of the fourth order cumulant natural estimator and fourth k statistics statistical comparative studies are undertaken from both bias and mse points of view for different distribution laws and ma filters algorithms aiming to reduce computational complexity of the proposed estimator as well as that of the fourth k statistics bias are also provided

applications of cumulants to array processing i aperture extension and array calibration an interpretation for the use of cumulants in narrowband array processing problems is proposed it is shown how fourth order cumulants of multichannel observations increase the directional information compared with second order statistics based on the interpretation it is shown how cumulants can be used to increase the effective aperture of an arbitrary antenna array the amount of partial information necessary to jointly calibrate an arbitrary array and estimate the directions of far field sources is also investigated it is proven that the presence of a doublet and use of fourth order cumulants is sufficient to accomplish this task the proposed approach is computationally efficient and more general than covariance based algorithms that have addressed the calibration problem under constraints a class of beamforming techniques is proposed to recover the source waveforms proposed estimation procedures are based on cumulants which bring insensitivity to the spatial correlation structure of additive gaussian measurement noise simulations are provided to illustrate the use of the proposed algorithms

blind underdetermined mixture identification by joint canonical decomposition of ho cumulants a new family of cumulant based algorithms is proposed in order to blindly identify potentially underdetermined mixtures of statistically independent sources these algorithms perform a joint canonical decomposition cand of several higher order cumulants through a cand of a three way array with special symmetries these techniques are studied in terms of identifiability performance and numerical complexity from a signal processing viewpoint the proposed methods are shown i to have a better estimation resolution and ii to be able to process more sources than the other classical cumulant based techniques second from a numerical analysis viewpoint we deal with the convergence speed of several procedures for three way array decomposition such as the acdc scheme we also show how to accelerate the iterative cand algorithms by using differently the symmetries of the considered three way array next from a multilinear algebra viewpoint the paper aims at giving some insights on the uniqueness of a joint cand of several hermitian multiway arrays compared to the cand of only one array this allows us as a result to extend the concept of virtual array va to the case of combination of several vas

uniform blow up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source in this paper we introduce a new method for investigating the rate and profile of blow up of solutions of diffusion equations with nonlocal nonlinear reaction terms for large classes of equations we prove that the solutions have global blow up and that the rate of blow up is uniform in all compact subsets of the domain this results in a flat blow up profile except for a boundary layer whose thickness vanishes astapproaches the blow up timet in each case the blow up rate of u t is precisely determined furthermore in many cases we derive sharp estimates on the size of the boundary layer and on the asymptotic behavior of the solution in the boundary layer the size of the boundary layer then decays liket t and the solutionu t x behaves like u t d x t tin the boundary layer wheredis the distance to the boundary some fujita type critical exponents results are also given for the cauchy problem

blind source separation using second order cyclostationary statistics this paper studies the blind source separation bss problem with the assumption that the source signals are cyclostationary identifiability and separability criteria based on second order cyclostationary statistics socs alone are derived the identifiability condition is used to define an appropriate contrast function an iterative algorithm ath2 is derived to minimize this contrast function this algorithm separates the sources even when they do not have distinct cycle frequencies

uniform blow up profiles for nonlinear and nonlocal reaction diffusion equations abstract in this paper we investigate the blow up properties of positive solutions to the following integro parabolic equations u t u e u 1 e u d x where 0 and 1 and x r n x r for the radially symmetric and non increasing initial data we give a complete classification in terms of global and single point blow up according to the parameters and moreover the blow up rates are also determined in each case particularly for the special case and n 2 it will be proved that the blow up rate at x 0 is faster than that at the other point x 0 this seems to be a new phenomenon for this kind of problem

total versus single point blow up of solutions of a semilinear parabolic equation with localized reaction abstract in this paper we study the initial boundary value problem of a semilinear parabolic equation with localized reaction p u t u u p u q x t x t b 0 t u x t 0 x t b 0 t u x 0 u 0 x x b where b is a unit ball in r n x b and p q 0 for the case x 0 we completely classify blow up solutions of p into total blow up cases and single point blow up cases according to the values p and q moreover we give the blow up rates of solutions near the blow up time for the other case x 0 we show total blow up and single point blow up of solutions of p in some cases depending on p and q

non orthogonal joint diagonalization in the least squares sense with application in blind source separation approximate joint diagonalization of a set of matrices is an essential tool in many blind source separation bss algorithms a common measure of the attained diagonalization of the set is the weighted least squares wls criterion however most well known algorithms are restricted to finding an orthogonal diagonalizing matrix relying on a whitening phase for the nonorthogonal factor often such an approach implies unbalanced weighting which can result in degraded performance we propose an iterative alternating directions algorithm for minimizing the wls criterion with respect to a general not necessarily orthogonal diagonalizing matrix under some mild assumptions we prove weak convergence in the sense that the norm of parameters update is guaranteed to fall below any arbitrarily small threshold within a finite number of iterations we distinguish between hermitian and symmetrical problems using bss simulations results we demonstrate the improvement in estimating the mixing matrix resulting from the relaxation of the orthogonality restriction

second order blind separation of first and second order cyclostationary sources application to am fsk cpfsk and deterministic sources most of the second order so and higher order ho blind source separation bss methods developed this last decade aim at blindly separating statistically independent sources that are assumed zero mean stationary and ergodic nevertheless in many situations of practical interest such as in radiocommunications contexts the sources are nonstationary and very often cyclostationary digital modulations the behavior of the current so and fourth order fo cumulant based bss methods in the presence of cyclostationary sources has been analyzed recently in a previous paper by ferre spl acute ol and chevalier assuming zero mean sources however some cyclostationary sources used in practical situations are not zero mean but have a first order fio cyclostationarity property which is in particular the case for some amplitude modulated am signals and for some nonlinearly modulated digital sources such as frequency shift keying fsk or some continuous phase frequency shift keying cpfsk sources for such sources the results presented in the previous paper by ferre spl acute ol and chevalier no longer hold and the purpose of this paper is to analyze the behavior and to propose adaptations of the current so bss methods for sources that are both fio and so cyclostationary and cyclo ergodic an extension for deterministic sources is also proposed in the paper

remarks on certain criteria for detection of number of signals in this paper we derive the asymptotic distribution of the logarithm of the likelihood ratio statistic for testing the hypothesis that the number of signals is equal to q against the alternative that it is equal to k specified for a special case this distribution is not chi square the above statistic also rises in studying consistency property of the mdl criterion and aic for detection of the number of signals

blow up behavior for a nonlinear heat equation with a localized source in a ball in this paper we consider the initial boundary value problem of a semilinear parabolic equation with local and non local localized reactions in a ball ut u up uq x t in b r where p q 0 b r x rn x 1 there exist blow up solutions of this problem for large initial data we treat the radially symmetric and one peak non negative solution u x t u r t r x of this problem we give the complete classification of total blow up phenomena and single point blow up phenomena according to p and q i if q 1 or p q 2 then single point blow up occurs whenever solutions blow up ii if 1 p q both phenomena total blow up and single point blow up occur depending on the initial data iii if p 1 q total blow up occurs whenever solutions blow up iv if max p q 1 every solution exists globally in time

asymptotic analysis for a localized nonlinear diffusion equation in this paper we study a localized nonlinear diffusion equation u t du m l 1u p l 2u q 0 t subject to null dirichlet boundary condition with p q 0 max p q m 1 and l 1 l 2 0 we investigate interactions among the localized and local sources nonlinear diffusion with the zero boundary value condition to establish blow up rates and uniform blow up profiles of solutions under different dominations in addition as results of the interactions of multiple nonlinearities the blow up sets of solutions namely total versus single point blow up of solutions are also determined

a reaction diffusion system with mixed type coupling this paper deals with asymptotic behavior of solutions to a reaction diffusion system coupled via localized and local sources u t du v p x t t v t dv u q both the initial boundary problem with null dirichlet boundary condition and the cauchy problem are considered to study the interaction between the two kinds of sources for the initial boundary problem we prove that the nonglobal solutions blow up everywhere in the bounded domain with uniform blow up profiles in addition it is interesting to observe that the cauchy problem admits an infinity fujita exponent namely the solutions blow up under any nontrivial and nonnegative initial data whenever pq 1 all these imply that the blow up behavior of solutions is governed by the localized source for the two problems with mixed type coupling

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

sensor array processing based on subspace fitting algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem the methods considered are the deterministic maximum likelihood method ml esprit and a recently proposed multidimensional signal subspace method these methods are formulated in a subspace fitting based framework which provides insight into their algebraic and asymptotic relations it is shown that by introducing a specific weighting matrix the multidimensional signal subspace method can achieve the same asymptotic properties as the ml method the asymptotic distribution of the estimation error is derived for a general subspace weighting and the weighting that provides minimum variance estimates is identified the resulting optimal technique is termed the weighted subspace fitting wsf method numerical examples indicate that the asymptotic variance of the wsf estimates coincides with the cramer rao bound the performance improvement compared to the other techniques is found to be most prominent for highly correlated signals

the blowup property of solutions to some diffusion equations with localized nonlinear reactions abstract in this paper we investigate the blowup property of solutions to the equation u t u u x 0 t where x0 is a fixed point in the domain we show that under certain conditions the solution blows up in finite time moreover we prove that the set of all blowup points is the whole region furthermore the growth rate of solutions near the blowup time is also derived finally the results are generalized to the following nonlocal reaction diffusion equation u t u u dx

beyond fcm graph theoretic post processing algorithms for learning and representing the data structure we show that when fuzzy c means fcm algorithm is used in an over partitioning mode the resulting membership values can be further utilized for building a connectivity graph that represents the relative distribution of the computed centroids standard graph theoretic procedures and recent algorithms from manifold learning theory are subsequently applied to this graph this facilitates the accomplishment of a great variety of data analysis tasks the definition of optimal cluster number c o the detection of intrinsic geometrical constraints within the data and the faithful low dimensional representation of the original structure are all performed efficiently by working with just a down sampled version comprised of the centroids of the data our approach is extensively demonstrated using synthetic data and actual brain signals

asymptotic analysis to a parabolic equation with a weighted localized source abstract this paper deals with a nonlinear parabolic equation with a more complicated source term which is a product of localized source u q 0 t local source u p x t and weight function a x we investigate how the three factors influence the asymptotic behavior of solutions it is shown that the blow up set consists of single point x 0 if p 1 when 0 p 1 with p q 1 the blow up take place everywhere in b moreover the blow up rate estimate is established with more precise coefficients determined

uniform blow up rate for diffusion equations with nonlocal nonlinear source abstract in this paper we investigate the blow up rate of solutions of diffusion equations with nonlocal nonlinear reaction terms for large classes of equations we prove that the solutions have global blow up and that the rate of blow up is uniform in all compact subsets of the domain in each case the blow up rate of u t is precisely determined

on the behavior of current second and higher order blind source separation methods for cyclostationary sources most of the second order so and higher order ho blind source separation methods developed in the 1990s aim at blindly separating statistically independent sources that are assumed zero mean stationary and ergodic nevertheless in many situations of practical interest such as in radiocommunication contexts the sources are nonstationary and very often quasi cyclostationary digital modulations in these conditions it becomes important to wonder whether the performance of these current so and ho blind source separation methods which have been developed for stationary sources may be affected by the potential nonstationarity of the latter limiting the analysis to the so and fourth order fo cumulant based blind source separation methods the purpose of this paper is to bring some answers to this important question through the behavior analysis of the empirical so and fo cumulants estimator in the presence of zero mean quasi cyclostationary sources

single point blow up for a semilinear initial value problem abstract the initial value problem on r r is considered u t t x u xx t x u t x u t r 0 u 0 x x where 0 and is a fixed large number it is known that for some initial values the solution u t x exists only up to some finite time t and that u t as t t for the specific initial value k where 0 xx 0 r 0 k is sufficiently large it is shown that if x 0 then lim t t u t x and lim t t u x t x exist and are finite in other words blow up occurs only at the point x 0

blow up properties for a degenerate parabolic system with nonlinear localized sources in this paper we investigate the initial boundary problem of a degenerate parabolic system with nonlinear localized sources we classify the blow up solutions into global blow up cases and single point blow up cases according to the values of m n p i q i furthermore we obtain the uniform blow up profiles of solutions for the global blow up case finally we give some numerical examples to verify the results these extend and generalize a recent work of one of the authors l du blow up for a degenerate reaction diffusion systems with nonlinear localized sources j math anal appl 324 2006 304 320 which only considered uniform blow up profiles under the special case p 1 p 2 0

critical exponents for non simultaneous blow up in a localized parabolic system abstract the paper deals with the radially symmetric solutions of u t u u m x t v n 0 t v t v u p 0 t v q x t subject to null dirichlet boundary conditions for the blow up classical solutions we propose the critical exponents for non simultaneous blow up by determining the complete and optimal classification for all the non negative exponents i there exist initial data such that u v blows up alone if and only if m p 1 q n 1 which means that any blow up is simultaneous if and only if m p 1 q n 1 ii any blow up is u v blowing up with v u remaining bounded if and only if m p 1 q n 1 m p 1 q n 1 iii both non simultaneous and simultaneous blow up may occur if and only if m p 1 q n 1 moreover we consider the blow up rate and set estimates which were not obtained in the previously known work for the same model