blind separation of positive sources by globally convergent gradient search the instantaneous noise free linear mixing model in independent component analysis is largely a solved problem under the usual assumption of independent nongaussian sources and full column rank mixing matrix however with some prior information on the sources like positivity new analysis and perhaps simplified solution methods may yet become possible in this letter we consider the task of independent component analysis when the independent sources are known to be nonnegative and well grounded which means that they have a nonzero pdf in the region of zero it can be shown that in this case the solution method is basically very simple an orthogonal rotation of the whitened observation vector into nonnegative outputs will give a positive permutation of the original sources we propose a cost function whose minimum coincides with nonnegativity and derive the gradient algorithm under the whitening constraint under which the separating matrix is orthogonal we further prove that in the stiefel manifold of orthogonal matrices the cost function is a lyapunov function for the matrix gradient flow implying global convergence thus this algorithm is guaranteed to find the nonnegative well grounded independent sources the analysis is complemented by a numerical simulation which illustrates the algorithm

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

vector coherent state theory of the noncompact orthosymplectic superalgebras ii some selected examples for pt i see ibid vol 23 p 5383 1990 the techniques presented in the first paper of the present series for determining the conditions for the existence of star or grade star positive discrete series irreducible representations of osp p 2n r p 2m or 2m 1 and the branching rule for their decomposition into a direct sum of so p sp 2n r irreducible representations as well as for constructing explicit matrix realizations are illustrated with a few selected examples the latter include the most general irreps of osp 1 2n 2 osp 2 2 r osp 3 2 r osp 4 2 r osp 2 4 r and the most degenerate irreps of osp 2 2n r in addition all the information necessary for dealing with other cases amenable to a full analytic treatment is provided

quantal problems with partial algebraization of the spectrum we discuss a new class of spectral problems discovered recently which occupies an intermediate position between the exactly solvable problems e g harmonic oscillator and all others the problems belonging to this class are distinguished by the fact that a part of the eigenvalues and eigenfunctions can be found algebraically but not the whole spectrum the reason explaining the existence of the quasi exactly solvable problems is a hidden dynamical symmetry present in the hamiltonian for one dimensional motion this hidden symmetry issl 2 r it is shown that other groups lead to a partial algebraization in multidimensional quantal problems in particular sl 2 r sl 2 r so 3 andsl 3 r are relevant to two dimensional motion inducing a class of quasi exactly solvable two dimensional hamiltonians typically they correspond to systems in a curved space but sometimes the curvature turns out to be zero graded algebras open the possibility of constructing quasi exactlysolvable hamiltonians acting on multicomponent wave functions for example with a non minimal superextension ofsl 2 r we get a hamiltonian describing the motion of a spinor particle

equivariant adaptive selective transmission in this paper we consider the problem of selective transmission the dual of the blind source separation task in which a set of independent source signals are adaptively premixed prior to a nondispersive physical mixing process so that each source can be independently monitored in the far field following similar procedures for information theoretic blind source separation we derive a stochastic gradient algorithm for iteratively estimating the premixing matrix in the selective transmission problem and through a simple modification we obtain a second algorithm whose performance is equivariant with respect to the channel s mixing characteristics the local stability conditions for the algorithms about any selective transmission solution are shown to be the same as those for similar source separation algorithms practical implementation issues are discussed including the estimation of the combined system matrix and the reordering and scaling of the received signals within the algorithm mean square error based selective transmission algorithms are also derived for performance comparison purposes simulations indicate the useful behavior of the premixing algorithms for selective transmission

emergence of phase and shift invariant features by decomposition of natural images into independent feature subspaces olshausen and field 1996 applied the principle of independence maximization by sparse coding to extract features from natural images this leads to the emergence of oriented linear filters that have simultaneous localization in space and in frequency thus resembling gabor functions and simple cell receptive fields in this article we show that the same principle of independence maximization can explain the emergence of phase and shift invariant features similar to those found in complex cells this new kind of emergence is obtained by maximizing the independence between norms of projections on linear subspaces instead of the independence of simple linear filter outputs the norms of the projections on such independent feature subspaces then indicate the values of invariant features

highest weight representations for gl m n and gl m n it is shown how vector coherent state vcs theory enlightens the simultaneous discussion of representation theory for classical lie algebras and superalgebras and provides an optimal framework for the explanation of the noted similarities and dissimilarities of their representations reducibility atypicality and the positive definitiveness of inner products in vcs representation spaces are discussed the discussion is exemplified through the parallel and explicit construction of highest weight ladder representations of the lie algebra gl m n and superalgebra gl m n in gl m gl n bases

generalized coherent states as eigenstates of linearized quadratic casimir operators it is shown that the generalized coherent states for several groups and a supergroup are eigenstates of the linearized quadratic casimir operator of the associated algebra or superalgebra these operators may be useful in the study of geometrical phases

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

inhomogeneous differential realization boson fermion realization of lie superalgebras and their indecomposable representations an inhomogeneous differential realization ihdr of lie superalgebras which plays an important role in the search for quasi exactly solvable problems qesp of quantum mechanics is studied the corresponding inhomogeneous boson fermion realization ihbfr of lie superalgebras is obtained by making use of the ihbfr a new kind of indecomposable and irreducible representations of lie superalgebras is studied on the universal enveloping algebra of heisenberg weyl superalgebra and on its subspaces and quotient spaces the finite dimensional representations of lie superalgebras are naturally obtained on the subspaces of fock space as examples the ihdr of lie superalgebra spl m 1 is given and the indecomposable and irreducible representations of lie superalgebra su 2 1 are studied in detail

inhomogeneous boson realization of indecomposable representations of lie algebras by making use of the differential realization of lie algebras in the space of inhomogeneous polynomials of a certain number of variables the corresponding inhomogeneous boson realization of lie algebras is given a new kind of indecomposable representations of lie algebras are studied on the universal enveloping algebra of heisenberg weyl algebra its subspaces and its quotient spaces the finite dimensional representations are naturally obtained on the subspaces of fock space as an example the indecomposable and irreducible representations of the lie algebra su 2 are discussed in detail

a constrained em algorithm for independent component analysis we introduce a novel way of performing independent component analysis using a constrained version of the expectation maximization em algorithm the source distributions are modeled as d one dimensional mixtures of gaussians the observed data are modeled as linear mixtures of the sources with additive isotropic noise this generative model is fit to the data using constrained em the simpler soft switching approach is introduced which uses only one parameter to decide on the sub or supergaussian nature of the sources we explain how our approach relates to independent factor analysis

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

independent vector analysis identification conditions and performance bounds recently an extension of independent component analysis ica from one to multiple datasets termed independent vector analysis iva has been a subject of significant research interest iva has also been shown to be a generalization of hotelling s canonical correlation analysis in this paper we provide the identification conditions for a general iva formulation which accounts for linear nonlinear and sample to sample dependencies the identification conditions are a generalization of previous results for ica and for iva when samples are independently and identically distributed furthermore a principal aim of iva is identification of dependent sources between datasets thus we provide additional conditions for when the arbitrary ordering of the estimated sources can be common across datasets performance bounds in terms of the cramer rao lower bound are also provided for demixing matrices and interference to source ratio the performance of two iva algorithms are compared to the theoretical bounds

vector coherent state representation theory a vector coherent state theory is formulated as a natural extension of standard coherent state theory it is shown that the godement representations and the coherent state representations of the sp n r groups of rowe and of deenen and quesne are special cases of this more general theory

rvccc a new variational network of cube connected cycles and its topological properties abstract the ccc r n network is an extension of the hypercube which replaces each vertex with a cycle of length n providing that the hypercube is r dimensional when n r the ccc r n network contains more vertices than that of ccc r r which makes it more useful in the construction of a large scale interconnection network however the ccc r n is irregular when n r which makes their properties difficult to be analyzed in this paper we propose a new variational network of the cube connected cycles rvccc the rvccc networks have the properties of regularity vertex symmetry and low diameter compared with the general ccc networks the rvccc networks are more suitable for constructing a large scale interconnection network after the shortest internode distance between any two vertices in the rvccc was determined the exact diameter of this network was calculated and the communication algorithms including the routing algorithm and the broadcasting algorithm were also developed

a generalized contrast function and stability analysis for overdetermined blind separation of instantaneous mixtures in this letter the problem of blind separation of n independent sources from their m linear instantaneous mixtures is considered first a generalized contrast function is defined as a valuable extension of the existing classical and nonsymmetrical contrast functions it is applicable to the overdetermined blind separation m n with an unknown number of sources because not only independent components but also redundant ones are allowed in the outputs of a separation system second a natural gradient learning algorithm developed primarily for the complete case m n is shown to work as well with an n m or m m separating matrix for each optimizes a certain mutual information contrast function finally we present stability analysis for a newly proposed generalized orthogonal natural gradient algorithm which can perform the overdetermined blind separation when n is unknown obtaining an expectable result that its local stability conditions are slightly stricter than those of the conventional natural gradient algorithm using an invertible mixing matrix m n

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

algorithms for complex ml ica and their stability analysis using wirtinger calculus we derive a class of algorithms for independent component analysis ica based on maximum likelihood ml estimation and perform stability analysis of natural gradient ml ica with and without the constraint for unitary demixing matrix in the process we demonstrate how wirtinger calculus facilitates derivations and most importantly performing second order analysis in the complex domain and eliminates the need for making simplifying assumptions we derive natural gradient complex ml ica update rule and its variant with a unitary constraint as well as a newton algorithm for better convergence behavior the conditions for local stability are derived and studied using a generalized gaussian density ggd source model when the sources are circular and non gaussian we show analytically that both the ml and ml unitary ica update rules converge to the inverse of mixing matrix subject to a phase shift when the sources are noncircular and non gaussian we show that the nonunitary ml ica update rule is more stable than the ml unitary ica update rule when the sources are noncircular gaussians both update rules are stable only when the sources have distinct noncircularity indices simulation results are given to support these results

statistical dynamics of on line independent component analysis the learning dynamics of on line independent component analysis is analysed in the limit of large data dimension we study a simple hebbian learning algorithm that can be used to separate out a small number of non gaussian components from a high dimensional data set the de mixing matrix parameters are confined to a stiefel manifold of tall orthogonal matrices and we introduce a natural gradient variant of the algorithm which is appropriate to learning on this manifold for large input dimension the parameter trajectory of both algorithms passes through a sequence of unstable fixed points each described by a diffusion process in a polynomial potential choosing the learning rate too large increases the escape time from each of these fixed points effectively trapping the learning in a sub optimal state in order to avoid these trapping states a very low learning rate must be chosen during the learning transient resulting in learning time scales of o n2 or o n3 iterations where n is the data dimension escape from each sub optimal state results in a sequence of symmetry breaking events as the algorithm learns each source in turn this is in marked contrast to the learning dynamics displayed by related on line learning algorithms for multilayer neural networks and principal component analysis although the natural gradient variant of the algorithm has nice asymptotic convergence properties it has an equivalent transient dynamics to the standard hebbian algorithm

the multicomponent q coherent states of the quantum algebra slq 3 the multicomponent q coherent states associated with the quantum algebra slq 3 are presented the expansions are discussed for arbitrary operators in terms of the multicomponent q coherent states of slq 3 an inhomogeneous differential realization of slq 3 in this multicomponent q coherent state space is obtained

path integral for new coherent states of lie superalgebra osp 1 2 r a path integral formulation in the representation of new coherent states for the lie superalgebra osp l 2 r is introduced by the use of the completeness relation of the new coherent states a path integral expression for the transition amplitude between two osp l 2 r new coherent states for a hamiltonian which is linear in the generators of the superalgebra are obtained in the classical limit the equations of motion for the system are derived

linear multilayer ica generating hierarchical edge detectors in this letter a new ica algorithm linear multilayer ica lmica is proposed there are two phases in each layer of lmica one is the mapping phase where a two dimensional mapping is formed by moving more highly correlated nonindependent signals closer with the stochastic multidimensional scaling network another is the local ica phase where each neighbor namely highly correlated pair of signals in the mapping is separated by maxkurt algorithm because in lmica only a small number of highly correlated pairs have to be separated it can extract edge detectors efficiently from natural scenes we conducted numerical experiments and verified that lmica generates hierarchical edge detectors from large size natural scenes

vector coherent states of non compact orthosymplectic lie supergroups vector coherent states are defined for the generic lowest weight ladder irreducible representations of the non compact orthosymplectic lie supergroups osp 2m 2n r and osp 2m 1 2n r their simultaneous use with k matrix theory is shown to provide a powerful tool for the study of such representations this is illustrated with the detailed example of osp 1 2n r

waveform preserving blind estimation of multiple independent sources the problem of blind estimation of source signals is to estimate the source signals without knowing the characteristics of the transmission channel it is shown that the minimum variance unbiased estimates can be obtained if and only if the transmission channel can be identified blindly it is shown that the channel can be blindly identified if and only if there is not more than one gaussian source this condition suggests that waveform preserving blind estimation can be achieved over a wide range of signal processing applications including those cases in which the source signals have identical nongaussian distributions the constructive proof of the necessary and sufficient condition serves as a foundation for the development of waveform preserving blind signal estimation algorithms examples are presented to demonstrate the applications of the theoretical results

superfield and matrix realizations of highest weight representations for osp m 2n a differential representation of the classical lie superalgebra osp m 2n acting on superfield functions is given this representation is used to construct matrix representations of the finite dimensional irreducible representations of the algebra inner products on the irreducible spaces are discussed and classes of star and grade star equivalent representations are identified

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

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

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

boson representations of the real symplectic group and their applications to the nuclear collective model both non hermitian dyson and hermitian holstein primakoff representations of the sp 2d r algebra are obtained when the latter is restricted to a positive discrete series irreducible representation d n 2 1 n 2 for such purposes some results for boson representations recently deduced from a study of the sp 2d r partially coherent states are combined with some standard techniques of boson expansion theories the introduction of usui operators enables the establishment of useful relations between the various boson representations two dyson representations of the sp 2d r algebra are obtained in compact form in terms of d d 1 2 pairs of boson creation and annihilation operators and of an extra u d spin characterized by the irreducible representation 1 d in contrast to what happens when 1 d it is shown that the holstein primakoff representation of the sp 2d r algebra cannot be written in such a compact form for a generic irreducible representation explicit expansions are

edge disjoint hamiltonian cycles in k ary n cubes and hypercubes solutions for decomposing a higher dimensional torus to edge disjoint lower dimensional tori in particular edge disjoint hamiltonian cycles are obtained based on the coding theory approach first lee distance gray codes in z sub k sup n are presented and then it is shown how these codes can directly be used to generate edge disjoint hamiltonian cycles in k ary n cubes further some new classes of binary gray codes are designed from these lee distance gray codes and using these new classes of binary gray codes edge disjoint hamiltonian cycles in hypercubes are generated

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 linear non gaussian acyclic model for causal discovery in recent years several methods have been proposed for the discovery of causal structure from non experimental data such methods make various assumptions on the data generating process to facilitate its identification from purely observational data continuing this line of research we show how to discover the complete causal structure of continuous valued data under the assumptions that a the data generating process is linear b there are no unobserved confounders and c disturbance variables have non gaussian distributions of non zero variances the solution relies on the use of the statistical method known as independent component analysis and does not require any pre specified time ordering of the variables we provide a complete matlab package for performing this lingam analysis short for linear non gaussian acyclic model and demonstrate the effectiveness of the method using artificially generated data and real world data

new coherent states and inhomogeneous differential realization of lie superalgebra b 0 1 new coherent states for the lie superalgebra b 0 1 are presented an inhomogeneous differential realization ihdr of the lie superalgebra is obtained this ihdr may be useful for the study of quasi exactly solvable problems of quantum mechanics

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

independent factor analysis we introduce the independent factor analysis ifa method for recovering independent hidden sources from their observed mixtures ifa generalizes and unifies ordinary factor analysis fa principal component analysis pca and independent component analysis ica and can handle not only square noiseless mixing but also the general case where the number of mixtures differs from the number of sources and the data are noisy ifa is a two step procedure in the first step the source densities mixing matrix and noise covariance are estimated from the observed data by maximum likelihood for this purpose we present an expectation maximization em algorithm which performs unsupervised learning of an associated probabilistic model of the mixing situation each source in our model is described by a mixture of gaussians thus all the probabilistic calculations can be performed analytically in the second step the sources are reconstructed from the observed data by an optimal nonlinear estimator a variational approximation of this algorithm is derived for cases with a large number of sources where the exact algorithm becomes intractable our ifa algorithm reduces to the one for ordinary fa when the sources become gaussian and to an em algorithm for pca in the zero noise limit we derive an additional em algorithm specifically for noiseless ifa this algorithm is shown to be superior to ica since it can learn arbitrary source densities from the data beyond blind separation ifa can be used for modeling multidimensional data by a highly constrained mixture of gaussians and as a tool for nonlinear signal encoding

path integral formalism for osp 1 2 r coherent states a path integral formulation in the representation of coherent states for the non compact supergroup osp 1 2 r is introduced an expression for the transition amplitude connecting two osp 1 2 r coherent states is constructed and the corresponding canonical equations of motion derived a set of generalized poisson brackets is introduced and interpreted

vector coherent state theory of the noncompact orthosymplectic superalgebras i general theory vector coherent states are defined for the positive discrete series irreducible representations of the non compact orthosymplectic superalgebras osp p 2n r where p 2m or 2m 1 an orthonormal bargmann berezin basis symmetry adapted to osp p 2n r so p sp 2n r so p u n is constructed and used to develop the k matrix theory for osp p 2n r a general method is provided for determining the conditions of existence of star representations and of grade star representations in the osp 2 2n r case and the branching rule for their decomposition into a direct sum of so p sp 2n r irreducible representations as a by product it also enables the matrix elements of the odd generators between basis states of lowest weight so p u n irreducible representations to be calculated in a straightforward way

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

quasi exactly solvable problems and sl 2 algebra recently discovered quasi exactly solvable problems of quantum mechanics are shown to be related to the existence of the finite dimensional representations of the groupsl 2 q whereq r c it is proven that the bilinear formh a j j b j stand for the generators allows one to generate a set of quasi exactly solvable problems of different types including those that are already known we get in particular problems in which the spectral riemannian surface containing an infinite number of sheets is split off one or two finite sheet pieces in the general case the transitionh h d2 dx2 v x is realized with the aim of the elliptic functions all known exactly solvable quantum problems with known spectrum and factorized riemannian surface can be obtained in this approach

coherent states for the harmonic oscillator representations of the orthosymplectic supergroup osp 1 2n r coherent states for the harmonic oscillator representations of the noncompact supergroup osp 1 2n r are introduced and the invariant integration measure is calculated by studying transformation properties of supercoset variables the generalized bogoliubov transformation for mixed systems of bosons and fermions is also obtained an example for the simple harmonic oscillator is given

partially coherent states of the real symplectic group in the present paper we introduce partially coherent states for the positive discrete series irreducible representations d n 2 1 n 2 of sp 2d r encountered in physical applications these states are characterized by both continuous and discrete labels the latter specify the row of the irreducible representation 1 2 d of the maximal compact subgroup u d while the former parametrize an element of the factor space sp 2d r h where h is the sp 2d r subgroup leaving the 1 2 d representation space invariant we consider three classes of partially coherent states respectively generalizing the perelomov and barut girardello coherent states as well as some recently introduced intermediate coherent states we prove that each family of partially coherent states forms an overcomplete set in the representation space of d n 2 1 n 2 and study its generating function properties we show that it leads to a representation of the sp 2d r generators in the form of differential operato

faster independent component analysis by preconditioning with hessian approximations independent component analysis ica is a technique for unsupervised exploration of multichannel data that is widely used in observational sciences in its classic form ica relies on modeling the data as linear mixtures of nongaussian independent sources the maximization of the corresponding likelihood is a challenging problem if it has to be completed quickly and accurately on large sets of real data this problem has been addressed by resorting to quasi newton methods which rely on sparse approximations of the hessian of the log likelihood however those approximations are not accurate when the ica model does not hold exactly as is often the case for real datasets we propose a new algorithm dubbed picard which makes use of sparse approximate hessians only as a preconditioner to the l bfgs algorithm refining the hessian approximation from a memory of the past iterates extensive numerical comparisons to several algorithms of the same class demonstrate the superior performance of the proposed technique especially on real data

stochastic trapping in a solvable model of on line independent component analysis previous analytical studies of on line independent component analysis ica learning rules have focused on asymptotic stability and efficiency in practice the transient stages of learning are often more significant in determining the success of an algorithm this is demonstrated here with an analysis of a hebbian ica algorithm which can find a small number of nongaussian components given data composed of a linear mixture of independent source signals an idealized data model is considered in which the sources comprise a number of nongaussian and gaussian sources and a solution to the dynamics is obtained in the limit where the number of gaussian sources is infinite previous stability results are confirmed by expanding around optimal fixed points where a closed form solution to the learning dynamics is obtained however stochastic effects are shown to stabilize otherwise unstable suboptimal fixed points conditions required to destabilize one such fixed point are obtained for the case of a single nongaussian component indicating that the initial learning rate required to escape successfully is very low o n 2 where n is the data dimension resulting in very slow learning typically requiring o n3 iterations simulations confirm that this picture holds for a finite system

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

generalized hypercubes edge disjoint hamiltonian cycles and gray codes some new classes of hamming metric gray codes over zpn where p is a prime and n is an integer power of 2 are described then how these gray codes can be used to generate the maximum number of edge disjoint hamiltonian cycles in an n dimensional generalized hypercube ghc qpn is shown for qpn the number of edge disjoint hamiltonian cycles generated using these methods is n p 1 2 which is the maximum possible since the degree of each node in qpn is n p 1 in addition for any integers p and n p not necessarily a prime and n not necessarily a power of 2 how to generate the maximum number of edge disjoint hamiltonian cycles in qnp is also described

high order contrasts for independent component analysis this article considers high order measures of independence for the independent component analysis problem and discusses the class of jacobi algorithms for their optimization several implementations are discussed we compare the proposed approaches with gradient based techniques from the algorithmic point of view and also on a set of biomedical data