tunnelling in multidimensional systems tunnelling is examined from the point of view of analytic continuation of lagrangian manifolds this enables an intrinsically multidimensional approach to many problems we illustrate the ideas by computing energy splittings between congruent tori in a number of integrable systems the examples include an integrable but non separable system which cannot be solved by reduction to one dimensional systems the calculations can all be viewed in a geometrical way that does not make explicit use of separation of coordinates

maximum likelihood estimation of the autoregressive model by relaxation on the reflection coefficients a method for autoregressive parameter estimation which successively maximizes the likelihood with respect to each reflection coefficient while keeping the others fixed is presented the algorithm generalizes the recursive maximum likelihood technique of s m kay 1983 which corresponds to performing only one iteration cycle an interesting application is the estimation of a toeplitz covariance matrix simulations show that the algorithm converges quite fast and provides much better estimates than current procedures for short record length

blind deconvolution of multi input single output systems with binary sources the problem of blind source separation for multi input single output miso systems with binary inputs is treated in this paper our approach exploits the constellation properties of the successor values for each output sample in the absence of noise the successors of each output value form a characteristic finite set of clusters successor constellation the shape of this constellation is invariant of the predecessor value and it only depends on the last filter tap consequently the localization of the successors constellation can lead to the removal of the last filter tap thus reducing the length of the filter a process we call channel deflation based on the successor observation clustering soc we develop two algorithms for blind source separation soc 1 and soc 2 differing mainly on the required size of the data set furthermore the treatment of the system in the presence of noise is described using data clustering and data correction the problem of noise is attacked using a statistical mode based method moreover we correct the problem of misclassified observations using an iterative scheme based on the viterbi algorithm for the decoding of a hidden markov model hmm

discrete approximations of probability distributions practical limits on the size of most probabilistic models require that probability distributions be approximated by a few representative values and associated probabilities this paper demonstrates that methods commonly used to determine discrete approximations of probability distributions systematically underestimate the moments of the original distribution a new procedure based on gaussian quadrature is developed in this paper it can be used to decrease the error in the approximation to any desired level

blind source separation by nonstationarity of variance a cumulant based approach blind separation of source signals usually relies either on the nongaussianity of the signals or on their linear autocorrelations a third approach was introduced by matsuoka et al 1995 who showed that source separation can be performed by using the nonstationarity of the signals in particular the nonstationarity of their variances in this paper we show how to interpret the nonstationarity due to a smoothly changing variance in terms of higher order cross cumulants this is based on the time correlation of the squares energies of the signals and leads to a simple optimization criterion using this criterion we construct a fixed point algorithm that is computationally very efficient

source separation using a criterion based on second order statistics it is often assumed that blind separation of dynamically mixed sources cannot be done with second order statistics it is shown that separation of dynamically mixed sources indeed can be performed using second order statistics only a criterion based on second order statistics for the purpose of separating crosswise mixtures is stated the criterion is used in order to derive a gradient based separation algorithm as well as a newton type separation algorithm the uniqueness of the solution representing the separation is also investigated this reveals that 1 the channel system is parameter identifiable under weak conditions and 2 if the sources have the same color there exists at most two solutions the local convergence behavior of the proposed algorithm is studied and reveals a sufficient condition for local convergence furthermore the estimates of the channel system are shown to be consistent or to locally minimize the criterion

blind source separation in the time frequency domain based on multiple hypothesis testing this paper considers a time frequency t f based approach for blind separation of nonstationary signals in particular we propose a time frequency point selection algorithm based on multiple hypothesis testing which allows automatic selection of auto or cross source locations in the time frequency plane the selected t f points are then used via a joint diagonalization and off diagonalization algorithm to perform source separation the proposed algorithm is developed assuming deterministic signals with additive white complex gaussian noise a performance comparison of the proposed and existing approaches is provided

separation of an instantaneous mixture of gaussian autoregressive sources by the exact maximum likelihood approach this paper deals with the problem of blind separation of an instantaneous mixture of gaussian autoregressive sources without additive noise by the exact maximum likelihood approach the maximization of the likelihood function is divided using relaxation into two suboptimization problems solved by relaxation methods as well the first one consists of the estimation of the separating matrix when the autoregressive structure of the sources is fixed the second one aims at estimating this structure when the separating matrix is fixed we show that the first problem is equivalent to the determinant maximization of the separating matrix under nonlinear constraints we prove the existence and the consistency of the maximum likelihood estimator we also give the expression of fisher s information matrix then we study by computer simulations the performance of our estimator and show the improvement of its achievements w r t both quasimaximum likelihood and second order blind identification sobi estimators

three point approximations for continuous random variables this paper compares a number of approximations used to estimate means and variances of continuous random variables and or to serve as substitutes for the probability distributions of such variables with particular emphasis on three point approximations numerical results from estimating means and variances of a set of beta distributions indicate surprisingly large differences in accuracy among approximations in current use with some of the most popular ones such as the pert and triangular density function approximations faring poorly a simple new three point approximation which is a straightforward extension of earlier work by pearson and tukey outperforms the others significantly in these tests and also performs well in related multivariate tests involving the dirichlet family of distributions it offers an attractive alternative to currently used approximations in a variety of applications

a quadratic programming approach to blind equalization and signal separation blind equalization and signal separation are two well established signal processing problems in this paper we present a quadratic programming algorithm for fast blind equalization and signal separation by introducing a special non mean square error mse objective function we reformulate fractionally spaced blind equalization into an equivalent quadratic programming problem based on a clear geometric interpretation and a formal proof we show that a perfect equalization solution is obtained at every local optimum of the quadratic program because blind source separation is by nature and mathematically a closely related problem we also generalize the algorithm for blind signal separation we show that by enforcing source orthogonalization through successive processing the quadratic programming approach can be applied effectively moreover the quadratic program is easily extendible to incorporate additional practical conditions such as jamming suppression constraints we also provide evidence of good performance through computer simulations

chaotic tunneling a remarkable manifestation of complex classical dynamics in non integrable quantum phenomena abstract the tunneling phenomenon in chaotic systems is analyzed in terms of the complex semi classical method in the time domain in contrast to the tunneling paths in integrable systems it is discovered that there exist a tremendous number of candidate complex branches laputa branches which may contribute to the semi classical propagator the origin of a lot of characteristic structures observed in the tunneling tail in chaotic systems which are completely absent in case of integrable systems can fully be interpreted using such complex paths in particular we found a remarkable object forming chain like structures laputa chains which are hidden in the set of initial valuas displayed on the complex plane and they just generate a variety of structures in tunneling tails the relationship between the tunneling tail and the structure of the laputa chain is analyzed in detail the candidate trajectories however contain non physical non contributing part as a manifestation of stokes phenomenon and empirical rules on how to remove such non contributing parts is also discussed on the basis of the whole story constructed here chaotic tunneling is proposed as a universal tunneling mechanism originating in the complicated structure of classical chaotic manifolds in the complex regime several questions arose in the present study but not clarified yet are also listed up in relation to the theories of complex semi classical method and complex dynamical systems

nonorthogonal joint diagonalization by combining givens and hyperbolic rotations a new algorithm for computing the nonorthogonal joint diagonalization of a set of matrices is proposed for independent component analysis and blind source separation applications this algorithm is an extension of the jacobi like algorithm first proposed in the joint approximate diagonalization of eigenmatrices jade method for orthogonal joint diagonalization the improvement consists mainly in computing a mixing matrix of determinant one and columns of equal norm instead of an orthogonal mixing matrix this target matrix is constructed iteratively by successive multiplications of not only givens rotations but also hyperbolic rotations and diagonal matrices the algorithm performance evaluated on synthetic data compares favorably with existing methods in terms of speed of convergence and complexity

blind separation of instantaneous mixture of sources via an independent component analysis in this paper we introduce a procedure for separating a multivariate distribution into nearly independent components based on minimizing a criterion defined in terms of the kullback leibner distance by replacing the unknown density with a kernel estimate we derive useful forms of this criterion when only a sample from that distribution is available we also compute the gradient and hessian of our criteria for use in an iterative minimization setting this gradient to zero yields a set of separating functions similar to the ones considered in the source separation problem except that here these functions are adapted to the observed data finally some simulations are given illustrating the good performance of the method

quick solution of least square equations and inversion of block matrices of low displacement rank a general algorithm for the inversion of block matrices of low displacement rank is proposed it is particularly adapted to the solution of the least squares linear prediction problem some explicit formulas for the inverses of such matrices and a characterization of them are also provided the method is based on the representation of the shift difference of the considered matrix as the difference between two low rank positive matrices

origin of the enhancement of tunneling probability in the nearly integrable system the enhancement of tunneling probability in the nearly integrable system is closely examined focusing on tunneling splittings plotted as a function of the inverse of the planck s constant on the basis of the analysis using the absorber which efficiently suppresses the coupling creating spikes in the plot we found that the splitting curve should be viewed as the staircase shaped skeleton accompanied by spikes we further introduce renormalized integrable hamiltonians and explore the origin of such a staircase structure by investigating the nature of eigenfunctions closely it is found that the origin of the staircase structure could trace back to the anomalous structure in tunneling tail which manifests itself in the representation using renormalized action bases this also explains the reason why the staircase does not appear in the completely integrable system

robust independent component analysis by iterative maximization of the kurtosis contrast with algebraic optimal step size independent component analysis ica aims at decomposing an observed random vector into statistically independent variables deflation based implementations such as the popular one unit fastica algorithm and its variants extract the independent components one after another a novel method for deflationary ica referred to as robustica is put forward in this paper this simple technique consists of performing exact line search optimization of the kurtosis contrast function the step size leading to the global maximum of the contrast along the search direction is found among the roots of a fourth degree polynomial this polynomial rooting can be performed algebraically and thus at low cost at each iteration among other practical benefits robustica can avoid prewhitening and deals with real and complex valued mixtures of possibly noncircular sources alike the absence of prewhitening improves asymptotic performance the algorithm is robust to local extrema and shows a very high convergence speed in terms of the computational cost required to reach a given source extraction quality particularly for short data records these features are demonstrated by a comparative numerical analysis on synthetic data robustica s capabilities in processing real world data involving noncircular complex strongly super gaussian sources are illustrated by the biomedical problem of atrial activity aa extraction in atrial fibrillation af electrocardiograms ecgs where it outperforms an alternative ica based technique

structural change of the tunneling spectrum with perturbation frequency we investigate in what regime of the frequency the new tunneling mechanism using unstable and stable manifolds of dividing saddle takahashi and ikeda 2008 j phys a math theor 41 095101 takahashi and ikeda 2009 phys rev a 79 052114 works as the leading mechanism of multi dimensional barrier tunneling in the large and small limits of the frequency the tunneling rate is well evaluated based on the instanton picture it is in the intermediate frequency range that the new mechanism dominates the tunneling process the tunneling rate takes the maximum value in this intermediate range

towards a semiclassical theory of the quantum baker s map abstract we develop semiclassical 0 treatments of the quantum baker s map paying special attention to a the discrete and finite nature of its hilbert space and b the asymptotic analysis of the true quantum objects themselves new techniques are described at the theoretical level exact symbolic decomposition of the propagator and at the numerical level color graphics display of operators in the kirkwood representation both of which are of general interest for other quantized chaotic maps periodic orbit theory is tested numerically and we find that log corrections need to be included before an accurate calculation of the spectrum from periodic orbits can be achieved however the asymptotic analysis of the traces of the propagator reveals unexpected departures from standard semiclassical theory those anomalies which we compute explicitly in a few cases are traced ultimately to the discontinuity of the map and to the compactness of the phase space the analysis is far from complete but the results point towards the necessity of careful assessment of semiclassical folklore when applied to chaotic maps

unphysical singularities in semiclassical level density expansions for polygon billiards it is pointed out that the semiclassical periodic orbit expansion for the level density of a bounded quantum system may contain singular structure not found in the exact level density this is illustrated for a particular system a pseudointegrable polygon billiard the author shows that here the periodic orbit expansion has singular structure on all scales of energy and takes on negative as well as positive values however when sufficiently smoothed the expansion bears a good resemblance to the exact smoothed level density

recursive maximum likelihood estimation of autoregressive processes a new method of autoregressive parameter estimation is presented the technique is a closer approximation to the true maximum likelihood estimator than that obtained using linear prediction techniques the advantage of the new algorithm is mainly for short data records and or sharply peaked spectra simulation results indicate that the parameter bias as well as the variance is reduced over the yule walker and the forward backward approaches of linear prediction also spectral estimates exhibit more resolution and less spurious peaks a stable all pole filter estimate is guaranteed the algorithm operates in a recursive model order fashion which allows one to successively fit higher order models to the data

separation of independent sources from correlated inputs the characterization of independent stationary stochastic components sources is generally achieved by using the spectral matrix of partially correlated measurements which are linearly related to the components of interest in the general case where no assumptions are made concerning the way the sources are mixed on the measurements the spectral matrix is not able to extract the true sources while spectral analysis only uses second order properties of independent stochastic sources a procedure based on higher order analysis fourth order cross cumulants is developed this approach leads to a complete identification of the sources

signal separation by symmetric adaptive decorrelation stability convergence and uniqueness the performance of signal enhancement systems based on adaptive filtering is highly dependent on the quality of the noise reference in the lms algorithm signal leakage into the noise reference leads to signal distortion and poor noise cancellation the origin of the problem lies in the fact that lms decorrelates the signal estimate with the noise reference which in the case of signal leakage makes little sense an algorithm is proposed that decorrelates the signal estimate with a signal free noise estimate obtained by adding a symmetric filter to the classical structure the symmetric adaptive decorrelation sad algorithm no longer makes a distinction between signal and noise and is therefore a signal separator rather than a noise canceler stability and convergence are of the utmost importance in adaptive algorithms and hence are carefully studied apart from limitations on the adaptation constants stability around the desired solution can only be guaranteed for a subclass of signal mixtures furthermore the decorrelation criterion does not yield a unique solution and expressions for the phantom solutions are derived simulations with short fir filters confirm the predicted behavior

blind separation of independent sources for virtually any source probability density function the blind source separation bss problem consists of the recovery of a set of statistically independent source signals from a set of measurements that are mixtures of the sources when nothing is known about the sources and the mixture structure in the bss scenario of two noiseless real valued instantaneous linear mixtures of two sources an approximate maximum likelihood ml approach has been suggested in the literature which is only valid under certain constraints on the probability density function pdf of the sources in the present paper the expression for this ml estimator is reviewed and generalized to include virtually any source distribution an intuitive geometrical interpretation of the new estimator is also given in terms of the scatter plots of the signals involved an asymptotic performance analysis is then carried out yielding a closed form expression for the estimator asymptotic pdf simulations illustrate the behavior of the suggested estimator and show the accuracy of the asymptotic analysis in addition an extension of the method to the general bss scenario of more than two sources and two sensors is successfully implemented

multi input single output nonlinear blind separation of binary sources the problem of blindly separating multiple binary sources from a single nonlinear mixture is addressed through a novel clustering approach without the use of any optimization procedure the method is based on the assumption that the source probabilities are asymmetric in which case the output probability distribution can be expressed as a linear mixture of the sources we are then able to solve the problem by using a known linear multiple input single output miso blind separation method the overall procedure is very fast and in theory it works for any number of independent binary sources and for a wide range of nonlinear functions in practice the accuracy of the method depends on the estimation accuracy of the output probabilities and the cluster centers it can be quite sensitive to noise especially as the number of sources increases or the number of data samples is reduced however in our experiments we have been able to demonstrate successful separation of up to four sources

underdetermined blind source separation based on subspace representation this paper considers the problem of blindly separating sub and super gaussian sources from underdetermined mixtures the underlying sources are assumed to be composed of two orthogonal components one lying in the rowspace and the other in the nullspace of a mixing matrix the mapping from the rowspace component to the mixtures by the mixing matrix is invertible using the pseudo inverse of the mixing matrix the mapping from the nullspace component to zero by the mixing matrix is noninvertible and there are infinitely many solutions to the nullspace component the latent nullspace component which is of lower complexity than the underlying sources is estimated based on a mean square error mse criterion this leads to a source estimator that is optimal in the mse sense in order to characterize and model sub and super gaussian source distributions the parametric generalized gaussian distribution is used the distribution parameters are estimated based on the expectation maximization em algorithm when the mixing matrix is unavailable it must be estimated and a novel algorithm based on a single source detection algorithm which detects time frequency regions of single source occupancy is proposed in our simulations the proposed algorithm compared to other conventional algorithms estimated the mixing matrix with higher accuracy and separated various sources with higher signal to interference ratio

fourth order blind identification of underdetermined mixtures of sources fobium for about two decades numerous methods have been developed to blindly identify overdetermined p spl les n mixtures of p statistically independent narrowband nb sources received by an array of n sensors these methods exploit the information contained in the second order so the fourth order fo or both the so and fo statistics of the data however in practical situations the probability of receiving more sources than sensors increases with the reception bandwidth and the use of blind identification bi methods able to process underdetermined mixtures of sources for which p n may be required although such methods have been developed over the past few years they all present serious limitations in practical situations related to the radiocommunications context for this reason the purpose of this paper is to propose a new attractive bi method exploiting the information contained in the fo data statistics only that is able to process underdetermined mixtures of sources without the main limitations of the existing methods provided that the sources have different trispectrum and nonzero kurtosis with the same sign a new performance criterion that is able to quantify the identification quality of a given source and allowing the quantitative comparison of two bi methods for each source is also proposed in the paper finally an application of the proposed method is presented through the introduction of a powerful direction finding method built from the blindly identified mixture matrix

polynomial diffeomorphisms of ii stable manifolds and recurrence f x y y y ax c the diffeomorphisms in this class have complicated dynamics in particular they have periodic points of infinitely many periods and positive topological entropy see fm s we can distinguish between these classes by considering the growth of the degrees of iterates of the diffeomorphism define deg f to be the maximum of the degrees of the coordinate functions this quantity is not a conjugacy invariant of f hence not a dynamical invariant we can construct a conjugacy invariant which we call the dynamical degree as follows

hybrid linear and nonlinear complexity pursuit for blind source separation blind source separation bss is an increasingly popular data analysis technique with many applications several methods for bss using the statistical properties of original sources have been proposed for a famous case non gaussianity this leads to independent component analysis ica in this paper we propose a hybrid bss method based on linear and nonlinear complexity pursuit which combines three statistical properties of source signals non gaussianity linear predictability and nonlinear predictability a gradient learning algorithm is presented by minimizing a loss function simulations verify the efficient implementation of the proposed method

julia set describes quantum tunnelling in the presence of chaos we find that characteristics of quantum tunnelling in the presence of chaos can be regarded as a manifestation of the julia set of the complex dynamical system several numerical pieces of evidence for the standard map together with a rigorous statement for the henon map are presented demonstrating that the complex classical paths which contribute to the semiclassical propagator are dense in the julia set chaotic tunnelling can thus be characterized by the transitivity of the dynamics and high density of the trajectories on the julia set

operationalizing approximate multiattribute utility functions for use in practice abstract decision analysis provides defensible methods for rank ordering alternatives based on the calculation of expected utility this technique can be quite time consuming and conceptually difficult for the decision maker as many input parameters are needed to be assessed the recognition of such difficulties prompted researchers to call for simplifying approximations which retain the integrity of the original problem but relieve the assessment burden on the decision maker winkler 1982 this call has been answered with the recent development by kirkwood of taylor series approximations to expected utility which have never been applied in practice this paper further addresses the need to simplify decision analysis through the development of a simulation based technique which allows the kirkwood approximations to be used in practice the technique generates confidence intervals for the true but unknown certain equivalents which are used to rank order alternatives

adaptive quasi newton algorithm for source extraction via cca approach this paper addresses the problem of adaptive source extraction via the canonical correlation analysis cca approach based on liu s analysis of cca approach we propose a new criterion for source extraction which is proved to be equivalent to the cca criterion then a fast and efficient online algorithm using quasi newton iteration is developed the stability of the algorithm is also analyzed using lyapunov s method which shows that the proposed algorithm asymptotically converges to the global minimum of the criterion simulation results are presented to prove our theoretical analysis and demonstrate the merits of the proposed algorithm in terms of convergence speed and successful rate for source extraction

sample partial autocorrelation function a new estimation procedure for a partial autocorrelation coefficient of a stationary time series based on a natural geometrical analysis of the sample data is proposed a method for autoregressive parameter estimation which is midway between the constrained least squares procedure of burg and the unconstrained one given by the for ward backward least squares method is then obtained the method provides a stable filter and operates in a recursive model order fash ion simulation results indicate that the method eliminates some short comings of classical least squares procedures and stays close to the ex act maximum likelihood estimation method

analysis and online realization of the cca approach for blind source separation a critical analysis of the canonical correlation analysis cca approach in blind source separation bss is provided it is proved that by maximizing the autocorrelation functions of the recovered signals we can separate the source signals successfully it is further shown that the cca approach represents the same class of generalized eigenvalue decomposition gevd problems as the matrix pencil method finally online realizations of the cca approach are discussed with a linear predictor based algorithm studied as an example

generalized non orthogonal joint diagonalization with lu decomposition and successive rotations non orthogonal joint diagonalization njd free of prewhitening has been widely studied in the context of blind source separation bss and array signal processing etc however njd is used to retrieve the jointly diagonalizable structure for a single set of target matrices which are mostly formulized with a single dataset and thus is insufficient to handle multiple datasets with inter set dependences a scenario often encountered in joint bss j bss applications as such we present a generalized njd gnjd algorithm to simultaneously perform asymmetric njd upon multiple sets of target matrices with mutually linked loading matrices by using lu decomposition and successive rotations to enable j bss over multiple datasets with indication exploitation of their mutual dependences experiments with synthetic and real world datasets are provided to illustrate the performance of the proposed algorithm

unstable periodic orbits and semiclassical quantisation the bohr sommerfeld quantisation condition has a meaningful extension to classically chaotic systems whose periodic unstable orbits are isolated it provides a semiclassical euler factorisation for the functional determinant of the quantal hamiltonian in contrast to the hadamard infinite product over the eigenvalues by which the exact determinant is defined

weighted rule based adaptive algorithm for simultaneously extracting generalized eigenvectors in this brief we consider extracting generalized eigenvectors in parallel for the generalized eigendecomposition problem the problem is formulated as an optimization problem of minimizing an unconstrained quartic cost function based on the weighted rule it is shown that the proposed weighted cost function has a unique global minimum which corresponds to the principal generalized eigenvectors in order to estimate the principal generalized eigenvector matrix efficiently we simplify the quartic cost function as a quadric one by making an appropriate approximation and then derive a fast algorithm for extracting the principal generalized eigenvector in parallel we also show the application of the proposed algorithm in blind source separation numerical simulations are performed and the results demonstrate the performance of the proposed algorithm

joint blind source separation by multiset canonical correlation analysis in this paper we introduce a simple and effective scheme to achieve joint blind source separation bss of multiple datasets using multiset canonical correlation analysis m cca j r kettenring canonical analysis of several sets of variables biometrika vol 58 pp 433 451 1971 we first propose a generative model of joint bss based on the correlation of latent sources within and between datasets we specify source separability conditions and show that when the conditions are satisfied the group of corresponding sources from each dataset can be jointly extracted by m cca through maximization of correlation among the extracted sources we compare source separation performance of the m cca scheme with other joint bss methods and demonstrate the superior performance of the m cca scheme in achieving joint bss for a large number of datasets group of corresponding sources with heterogeneous correlation values and complex valued sources with circular and non circular distributions we apply m cca to analysis of functional magnetic resonance imaging fmri data from multiple subjects and show its utility in estimating meaningful brain activations from a visuomotor task

group decorrelation enhanced subspace method for identifying fir mimo channels driven by unknown uncorrelated colored sources identification of finite impulse response fir and multiple input multiple output mimo channels driven by unknown uncorrelated colored sources is a challenging problem in this paper a group decorrelation enhanced subspace gdes method is presented the gdes method uses the idea of subspace decomposition and signal decorrelation more effectively than the joint diagonalization enhanced subspace jdes method previously reported in the literature the gdes method has a much better performance than the jdes method the correctness of the gdes method is proved assuming that 1 the channel matrix is irreducible and column reduced and 2 the source spectral matrix has distinct diagonal functions however the gdes method has an inherent ability to trade off between the required condition on the channel matrix and that on the source spectral matrix simulations show that the gdes method yields good results even when the channel matrix is not irreducible which is not possible at all for the jdes method

independent component analysis over galois fields of prime order we consider the framework of independent component analysis ica for the case where the independent sources and their linear mixtures all reside in a galois field of prime order p similarities and differences from the classical ica framework over the real field are explored we show that a necessary and sufficient identifiability condition is that none of the sources should have a uniform distribution we also show that pairwise independence of the mixtures implies their full mutual independence namely a nonmixing condition in the binary p 2 and ternary p 3 cases but not necessarily in higher order p 3 cases we propose two different iterative separation or identification algorithms one is based on sequential identification of the smallest entropy linear combinations of the mixtures and is shown to be equivariant with respect to the mixing matrix the other is based on sequential minimization of the pairwise mutual information measures we provide some basic performance analysis for the binary p 2 case supplemented by simulation results for higher orders demonstrating advantages and disadvantages of the proposed separation approaches

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

estimating the impact of uncertainty on a deterministic multiattribute evaluation a method is presented to estimate the impact of uncertainty on the results of a multiattribute evaluation prior to conducting a complete probabilistic multiattribute utility analysis the method assumes that a deterministic analysis has been completed using a weighted additive multiattribute value evaluation function and that either an additive or multiplicative utility function is appropriate for the multiattribute utility analysis an approximation procedure is developed to estimate whether uncertainty about attribute levels could change the deterministic evaluation results an illustrative application investigates the accuracy of the procedure and its use to simplify analysis of the effects of uncertainty

independent component analysis by entropy bound minimization a novel differential entropy estimator is introduced where the maximum entropy bound is used to approximate the entropy given the observations and is computed using a numerical procedure thus resulting in accurate estimates for the entropy we show that such an estimator exists for a wide class of measuring functions and provide a number of design examples to demonstrate its flexible nature we then derive a novel independent component analysis ica algorithm that uses the entropy estimate thus obtained ica by entropy bound minimization ica ebm the algorithm adopts a line search procedure and initially uses updates that constrain the demixing matrix to be orthogonal for robust performance we demonstrate the superior performance of ica ebm and its ability to match sources that come from a wide range of distributions using simulated and real world data

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

penalty function based joint diagonalization approach for convolutive blind separation of nonstationary sources a new approach for convolutive blind source separation bss by explicitly exploiting the second order nonstationarity of signals and operating in the frequency domain is proposed the algorithm accommodates a penalty function within the cross power spectrum based cost function and thereby converts the separation problem into a joint diagonalization problem with unconstrained optimization this leads to a new member of the family of joint diagonalization criteria and a modification of the search direction of the gradient based descent algorithm using this approach not only can the degenerate solution induced by a null unmixing matrix and the effect of large errors within the elements of covariance matrices at low frequency bins be automatically removed but in addition a unifying view to joint diagonalization with unitary or nonunitary constraint is provided numerical experiments are presented to verify the performance of the new method which show that a suitable penalty function may lead the algorithm to a faster convergence and a better performance for the separation of convolved speech signals in particular in terms of shape preservation and amplitude ambiguity reduction as compared with the conventional second order based algorithms for convolutive mixtures that exploit signal nonstationarity

second order blind separation of sources based on canonical partial innovations this paper is devoted to the study of the second order properties using partial autocorrelations of an instantaneous mixture of colored sources without additive noise we introduce the notion of symmetric recursive canonical partial innovation then their components for the observation process meet exactly with those of the source process from the order for which the autoregressive models underlying the sources are distinct this property leads to a new separation method based on the sample counterpart of partial autocorrelation matrices associated with these innovations simulation results show a notable improvement of the achievements of such an approach with respect to those of similar methods two other separation methods related to partial autocorrelation are also discussed

perturbation free prediction of resonance assisted tunneling in mixed regular chaotic systems for generic hamiltonian systems we derive predictions for dynamical tunneling from regular to chaotic phase space regions in contrast to previous approaches we account for the resonance assisted enhancement of regular to chaotic tunneling in a nonperturbative way this provides the foundation for future semiclassical complex path evaluations of resonance assisted regular to chaotic tunneling our approach is based on a new class of integrable approximations which mimic the regular phase space region and its dominant nonlinear resonance chain in a mixed regular chaotic system we illustrate the method for the standard map

adaptive modal identification of structures with equivariant adaptive separation via independence approach abstract an efficient output only blind source separation bss method was recently introduced for the modal identification of structures bss procedures recover a set of independent sources from their unknown linear mixtures when only mixtures are observed batch data is required for the separation in traditional blind source separation methods these algorithms are however unfavorable as some sets of data are observed one after another in this paper an adaptive blind source separation technique equivariant adaptive separation via independence easi is introduced to overcome the mentioned disadvantage within the structures the easi algorithm is beneficial as it can provide solutions to real time problems while also update the un mixing matrix for each step easi not only avoids increases in size of the relevant matrices and vectors but also decreases the analysis time a synthetic example and a benchmark structure have been used in this paper to better investigate the efficiency of the proposed method the simulation results demonstrate the effectiveness of the easi algorithm in on line identification of modal parameters of structures

the magnitude of errors in proximal multiattribute decision analysis with probabilistically dependent attributes this paper investigates the accuracy of an approximation procedure for evaluating alternatives under uncertainty with multiple evaluation attributes this approximation uses only the first two moments of the probability distributions for the alternatives and hence it can substantially reduce the amount of information which must be collected in order to evaluate alternatives when evaluation attributes are probabilistically dependent the accuracy of the approximation is investigated by comparing results from using it with exact calculations for a variety of situations representative of those found in decision analysis practice this investigation shows that the approximation is accurate for situations representative of many decision analysis applications however caution is needed in applying the approximation in some situations where it may give inaccurate results characteristics of cases where the approximation is less accurate are presented

blind separation of mixture of independent sources through a quasi maximum likelihood approach we propose two methods for separating mixture of independent sources without any precise knowledge of their probability distribution they are obtained by considering a maximum likelihood ml solution corresponding to some given distributions of the sources and relaxing this assumption afterward the first method is specially adapted to temporally independent non gaussian sources and is based on the use of nonlinear separating functions the second method is specially adapted to correlated sources with distinct spectra and is based on the use of linear separating filters a theoretical analysis of the performance of the methods has been made a simple procedure for optimally choosing the separating functions is proposed further in the second method a simple implementation based on the simultaneous diagonalization of two symmetric matrices is provided finally some numerical and simulation results are given illustrating the performance of the method and the good agreement between the experiments and the theory

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

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

sequential blind source separation based exclusively on second order statistics developed for a class of periodic signals a sequential algorithm for the blind separation of a class of periodic source signals is introduced in this paper the algorithm is based only on second order statistical information and exploits the assumption that the source signals have distinct periods separation is performed by sequentially converging to a solution which in effect diagonalizes the output covariance matrix constructed at a lag corresponding to the fundamental period of the source we select the one with the smallest period simulation results for synthetic signals and real electrocardiogram recordings show that the proposed algorithm has the ability to restore statistical independence and its performance is comparable to that of the equivariant adaptive source separation easi algorithm a benchmark high order statistics based sequential algorithm with similar computational complexity the proposed algorithm is also shown to mitigate the limitation that the easi algorithm can separate at most one gaussian distributed source furthermore the steady state performance of the proposed algorithm is compared with that of easi and the block based second order blind identification sobi method

markovian source separation a maximum likelihood ml approach is used to separate the instantaneous mixtures of temporally correlated independent sources with neither preliminary transformation nor a priori assumption about the probability distribution of the sources a markov model is used to represent the joint probability density of successive samples of each source the joint probability density functions are estimated from the observations using a kernel method for the special case of autoregressive models the theoretical performance of the algorithm is computed and compared with the performance of second order algorithms and i i d based separation algorithms

blind source separation by sparse decomposition in a signal dictionary the blind source separation problem is to extract the underlying source signals from a set of linear mixtures where the mixing matrix is unknown this situation is common in acoustics radio medical signal and image processing hyperspectral imaging and other areas we suggest a two stage separation process a priori selection of a possibly overcomplete signal dictionary for instance a wavelet frame or a learned dictionary in which the sources are assumed to be sparsely representable followed by unmixing the sources by exploiting the their sparse representability we consider the general case of more sources than mixtures but also derive a more efficient algorithm in the case of a nonovercomplete dictionary and an equal numbers of sources and mixtures experiments with artificial signals and musical sounds demonstrate significantly better separation than other known techniques

blind separation of sound sources from the principle of least spatial entropy abstract the aim of the paper is to offer a method for separating incoherent and compact sound sources which may overlap in both the space and frequency domains this is found of interest in acoustical applications involving the identification and ranking of sound sources stemming from different physical origins the principle proceeds in two steps the first one being reminiscent to source reconstruction e g as in near field acoustical holography and the second one to blind source separation specifically the source mixture is first expanded into a linear combination of spatial basis functions whose coefficients are set by backpropagating the pressures measured by an array of microphones to the source domain this leads to a formulation similar but no identical to blind source separation in the second step these coefficients are blindly separated into uncorrelated latent variables assigned to incoherent virtual sources these are shown to be defined up to an arbitrary rotation a unique set of sound sources is finally recovered by searching for that rotation by conjugate gradient descent in the stiefel manifold of unitary matrices which maximizes their spatial compactness as measured either by their spatial variance or their spatial entropy this results in the proposal of two separation criteria coined least spatial variance and least spatial entropy respectively the same concept of spatial entropy which is central to the paper is also exploited in defining a new criterion the entropic l curve dedicated to determining the number of active sound sources the idea consists in considering the number of sources that achieves the best compromise between a low spatial entropy as expected from compact sources and a low statistical entropy as expected from a low residual error the proposed methodology is validated on both laboratory experiments and numerical data and illustrated on an industrial example concerned with the ranking of sound sources on a diesel engine at the same time its robustness to the estimated number of active sources is demonstrated

underdetermined blind modal identification of structures by earthquake and ambient vibration measurements via sparse component analysis abstract sparse component analysis sca approach was adopted to handle underdetermined blind modal identification of structures where the number of sensors is less than the number of active modes to exploit the sparsity of structural responses in time frequency domain short time fourier transform stft was used in this study the proposed sca based approach has two main stages modal matrix estimation and modal displacement estimation in the first stage hierarchical clustering algorithm was used to estimate the modal matrix the clustering algorithm was preceded by a preprocessing step to select the points in time frequency domain that only one mode makes contribution in the responses these points were fed to the clustering algorithm as an input performing this analysis enhanced the modal matrix estimation accuracy and reduced the computational cost while conducting clustering analysis having estimated mixing matrix the complex valued modal responses in the transformed domain were recovered via smoothed zero norm sl 0 algorithm in a broad sense using the sl 0 algorithm permits researchers to use any kind of transform in seeking sparsity regardless of obtaining real valued or complex valued signals in transformed domain natural frequencies and damping ratios were extracted from the recovered modal responses performance of the proposed method was investigated using a synthetic example and a benchmark structure with earthquake and ambient excitation respectively

a coordinate descent algorithm for complex joint diagonalization under hermitian and transpose congruences abstract this paper deals with the problem of joint complexmatrix diagonalization by considering both the hermitian andtranspose congruences we address the general case where thesearched diagonalizing matrix is apriori nonunitary based onthe minimization of a quadratic criterion we propose a ex ible algorithm in the sense that it allows to directly consider arectangular diagonalizing matrix and to take into considerationboth the hermitian and transpose congruences within the sameframework the proposed algorithm is a coordinate descentalgorithm that is based on an approximate criterion leading to theanalytical derivation of the minima arguments computer simu lations are drawn to illustrate the usefulness and performancesof the algorithm and a comparison to state of the art algorithmsis presented finally an application to independent componentanalysis based on fourth order statistics is also presented index terms blind source separation complex symmetric ma trices hermitian matrices independent component analysis jointdiagonalization

a sequential subspace method for blind identification of general fir mimo channels this correspondence addresses the problem of blindly identifying multiple input multiple output mimo finite impulse response fir channels without the conventional assumption of identical column degrees a subspace based algorithm is developed that identifies the channel s columns sequentially from the lowest degree columns to the highest degree ones compared with the previous generalized subspace method by gorokhov and loubaton 1997 the new method is simpler and more accurate

efficient computation of autoregressive estimates through a sufficient statistic it is shown that various time reversible methods in particular burg s algorithm for autoregressive model estimation may be performed through the use of a simple sufficient statistic this provides more efficient computation of the estimators

certainty equivalents for three point discrete distribution approximations three point discrete distribution approximations are often used in decision and risk analyses to represent probability distributions for continuous random variables e g as probability nodes in decision or probability trees performance evaluations of such approximations have generally been based on their accuracies in estimating moments for the underlying distributions however moment based comparisons for recently proposed approximations have been limited moreover very little research has addressed the accuracies of any such approximations in representing expected utilities or certainty equivalents of the underlying distributions this is of potential concern since recent research shows three point discrete distribution approximations exist that match the first several moments of an underlying distribution exactly while counterintuitively approximating its certainty equivalents poorly this paper compares the best two approximations for estimating means and variances identified in an earlier study with promising approximations proposed more recently specifically it examines how accurately six simple general purpose three point approximations represent certainty equivalents for continuous random variables as the level of risk aversion is varied as well as how accurately they estimate means and variances the results show that several of these are quite accurate over a variety of test distributions when the level of risk aversion and the characteristics of the distributions are within reasonable bounds their robust performance is significant for decision analysis practice

statistical inference for independent component analysis application to structural var models abstract the well known problem of non identifiability of structural var models disappears if the structural shocks are independent and if at most one of them is gaussian in that case the relevant estimation technique is the independent component analysis ica since the introduction of ica by comon 1994 various semi parametric estimation methods have been proposed for orthogonalizing the error terms these methods include pseudo maximum likelihood pml approaches and recursive pml the aim of our paper is to derive the asymptotic properties of the pml approaches in particular to study their consistency we conduct monte carlo studies exploring the relative performances of these methods finally an application based on real data shows that structural var models can be estimated without additional identification restrictions in the non gaussian case and that the usual restrictions can be tested

regularized spectral matching for blind source separation application to fmri imaging the main contribution of this paper is to present a bayesian approach for solving the noisy instantaneous blind source separation problem based on second order statistics of the time varying spectrum the success of the blind estimation relies on the nonstationarity of the second order statistics and their intersource diversity choosing the time frequency domain as the signal representation space and transforming the data by a short time fourier transform stft our method presents a simple em algorithm that can efficiently deal with the time varying spectrum diversity of the sources the estimation variance of the stft is reduced by averaging across time frequency subdomains the algorithm is demonstrated on a standard functional resonance imaging fmri experiment involving visual stimuli in a block design explicitly taking into account the noise in the model the proposed algorithm has the advantage of extracting only relevant task related components and considers the remaining components artifacts to be noise