new amicable pairs of type 2 2 and type 3 2 a ubasic computer program was developed to implement a method of te riele for finding amicable pairs of type 2 2 hundreds of new pairs were found including a new largest 2 2 pair and several daughter granddaughter and great granddaughter pairs

asymptotic performance of second order algorithms this paper re examines the asymptotic performance analysis of second order methods for parameter estimation in a general context it provides a unifying framework to investigate the asymptotic performance of second order methods under the stochastic model assumption in which both the waveforms and noise signals are possibly temporally correlated possibly non gaussian real or complex possibly noncircular random processes thanks to a functional approach and a matrix valued reformulated central limit theorem about the sample covariance matrix the conditions under which the asymptotic covariance of a parameter estimator are dependent or independent of the distribution of the signal involved are specified finally we demonstrate the application of our general results to direction of arrival doa estimation identification of finite impulse response models sinusoidal frequency estimation for mixed spectra time series and frequency estimation of sinusoidal signal with very lowpass envelope

analytical blind channel identification a novel analytical blind single input single output siso identification algorithm is presented based on the noncircular second order statistics of the output it is shown that statistics of order higher than two are not mandatory to restore identifiability our approach is valid for instance when the channel is excited by phase shift keying psk inputs it is shown that the channel taps need to satisfy a polynomial system of degree 2 and that identification amounts to solving the system we describe the algorithm that is able to solve this particular system entirely analytically thus avoiding local minima computer results eventually show the robustness with respect to noise and to channel length overdetermination identifiability issues are also addressed

operator approach to performance analysis of root music and root min norm the authors carry out a performance analysis of two eigenstructure based direction of arrival estimation algorithms using a series expansion of projection operators or projectors on the signal and noise subspaces in the interest of algebraic simplicity an operator formalism is utilized a perturbation analysis is performed on the projectors the results of which are used to determine the effect on the estimated parameters the approach makes it possible to carry out the analysis to any chosen order of expansion of the projectors by using an original recurrence formula developed for the higher order terms in the series expansion of the projectors this method is used to study the root music and root min norm algorithms and establish the superiority of root music in all cases the analysis has also resulted in insightful asymptotic expressions that describe the statistical behavior of the estimated angles and radii of the signal zeros

asymptotic normality of sample covariance matrix for mixed spectra time series application to sinusoidal frequencies estimation this correspondence addresses the asymptotic normal distribution of the sample mean and the sample covariance matrix of mixed spectra time series containing a sum of sinusoids and a moving average ma process two central limit cl theorems are proved as an application of this result the asymptotic normal distribution of any sinusoidal frequencies estimator of such time series based on second order statistics is deduced

asymptotically minimum variance second order estimation for noncircular signals with application to doa estimation this paper addresses asymptotically minimum variance amv algorithms within the class of algorithms based on second order statistics for estimating direction of arrival doa parameters of possibly spatially correlated even coherent narrowband noncircular sources impinging on arbitrary array structures to reduce the computational complexity due to the nonlinear minimization required by the matching approach the covariance matching estimation technique comet is included in the algorithm numerical examples illustrate the performance of the amv algorithm

on generating new amicable pairs from given amicable pairs ab tract mcthods arc given for constructing new amicable pairs from given amicable pairs by applying thcse methods to 1575 mother pairs known to the author 1782 new amicable pairs were generated so that the average offspring of these mother pairs is greater than 1 by a second much more restricted application of the methods to the 400 smallest daughter pairs 88 new granddaughter pairs were generated

fir channel estimation through generalized cumulant slice weighting we study the problem of linear channel estimation with unknown channel input signals our work stems from the weighted slice algorithm in which cumulant slices of different orders are linearly combined to produce an estimate of a single input single output channel aiming to improve the reliability of estimation the new approach incorporates a certain matrix structure constraint into its weight computation criterion it provides more reliable results for channels with weak leading coefficients this generalized algorithm maintains the advantage of fonollosa and vidal s algorithm in handling the situation with channel order overestimation its natural extension to multiple input multiple output channel estimation is presented along with the channel identifiability conditions required

the onset and end of the gunn effect in extrinsic semiconductors a hopf bifurcation analysis of the spontaneous current oscillation in direct current dc voltage biased extrinsic semiconductors is given for the classical model of the gunn effect in n gaas for semiconductor lengths l larger than a certain minimal value the steady state is linearly unstable for voltages in an interval phi alpha phi omega as l increases the branch of time periodic solutions bifurcating at simple eigenvalues when phi phi alpha turns from subcritical to supercritical and then back to subcritical again for very long semiconductors a quasi continuum of oscillatory modes bifurcates from the steady state at the onset of the instability the bifurcating branch is then described by a scalar reaction diffusion equation with cubic nonlinearity subject to antiperiodic boundary conditions on a subinterval of 0 l for the electron velocity curve we have considered the bifurcation is subcritical which may agree with experimental observations in n gaas an extension o

non gaussian multivariate adaptive ar estimation using the super exponential algorithm we formulate as a deconvolution problem the causal noncausal non gaussian multichannel autoregressive ar parameter estimation problem the super exponential algorithm presented in a paper by shalvi and weinstein 1993 is generalized to the vector case we present an adaptive implementation that is very attractive since it is higher order statistics hos based but does not present the high computational complexity of methods proposed up to now

on subspace methods for blind identification of single input multiple output fir systems blind identification of single input multiple output simo fir systems based on second order statistics has attracted a great deal of research effort we focus on subspace estimation procedures which exploit the structure of the range space of certain matrix valued statistics constructed by arranging in a prescribed order the covariance coefficients of the observations general subspace identifiability results are obtained based on properties of minimal polynomial bases of rational subspaces several subspace estimation procedures are then derived these estimators are all based on a weighted least square solution of an overdetermined system of linear equations an asymptotic statistical analysis of these estimators is carried out to evaluate the potential of these methods and the impact of the weighting

blind channel estimation using the second order statistics asymptotic performance and limitations we consider the asymptotic performance and fundamental limitations of the class of blind estimators that use second order statistics an achievable lower bound of the asymptotic normalized mean square error anmse is derived it is shown that the achievable anmse is lower bounded by the condition number of the jacobian matrix of the correlation function with respect to the channel parameters it is shown next that the jacobian matrix is singular if and only if the subchannels share common conjugate reciprocal zeros this condition is different from the existing channel identification conditions asymptotic performance of some existing eigenstructure based algorithms is analyzed closed form expressions of anmse and their lower bounds are derived for the least squares ls and the subspace ss blind channel estimators when there are two subchannels asymptotic efficiency of ls ss algorithms is also evaluated showing that significant performance improvement is possible when the information of the source correlation is exploited

connections between the least squares and the subspace approaches to blind channel estimation in this correspondence we study the connections between the least squares and the subspace approaches to blind channel estimation by examining the properties and connections of the so called multichannel filtering and data selection transforms we establish a relationship between the identification equations used in the two approaches next it is shown that the least squares and subspace estimators are identical for the case when there are two subchannels in general the two algorithms are different in their utilization of the noise subspace

performance limits of alphabet diversities for fir siso channel identification finite impulse responses fir of single input single output siso channels can be blindly identified from second order statistics of transformed data for instance when the channel is excited by binary phase shift keying bpsk minimum shift keying msk or quadrature phase shift keying qpsk inputs identifiability conditions are derived by considering that noncircularity induces diversity theoretical performance issues are addressed to evaluate the robustness of standard subspace based estimators with respect to these identifiability conditions then benchmarks such as asymptotically minimum variance amv bounds based on various statistics are presented some illustrative examples are eventually given where monte carlo experiments are compared to theoretical performances these comparisons allow to quantify limits to the use of the alphabet diversities for the identification of fir siso channels and to demonstrate the robustness of algorithms based on high order statistics

bifurcation behavior of a superlattice model we present a complete description of the stationary and dynamical behavior of semiconductor superlattices in the framework of a discrete drift model by means of numerical continuation singular perturbation analysis and bifurcation techniques the control parameters are the applied dc voltage phi and the doping nu in nondimensional units we show that the organizing centers for the long time dynamics are takens bogdanov bifurcation points in a broad range of parameters and we cast our results in a phi nu phase diagram for small values of the doping the system has only one uniform solution where all the variables are almost equal for high doping we find multistability corresponding to domain solutions and the stationary solutions may exhibit chaotic spatial behavior in the intermediate regime of nu the solution can be time periodic depending on the bias the oscillatory regions are related to the appearance and disappearance of hopf bifurcation tongues which can be sub or supercri

breeding amicable numbers in abundance in a first article of this title new procedures were described to compute many amicable numbers by breeding them in several generations an extensive computer search was later performed in 1988 and demonstrated the remarkable effectiveness of this breeding method the number of known amicable pairs was easily quadrupled by this search as we learnt recently 1999 from the internet pederson and te riele have again multiplied that number roughly by ten while they give no information on their method of search we publish here our method and summarize the computations our results provide some evidence for the conjecture that the number of amicable pairs is infinite

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

efficient closed form estimation of multivariate moving average processes using higher order statistics an improved algorithm is proposed for estimation of non gaussian nonminimum phase multivariate moving average ma processes using higher order cumulants this algorithm improves upon earlier results and contains development beyond existing algorithms it provides a closed form solution to estimating the ma parameter matrices up to a post multiplication by a permutation matrix and under certain assumptions eliminates the indeterminacy associated with scaling the algorithm is theoretically derived and tested via computer simulations in addition it is shown that this algorithm is computationally more efficient than the one proposed by tong inouye and liu see ibid vol 40 no 10 p 2547 2558 1992 finally the effect of imperfect input data on our algorithm is tested via simulations

a finite step global convergence algorithm for the parameter estimation of multichannel ma processes an iterative algorithm for the identification of multichannel moving average ma processes using higher order statistics is proposed it is shown that the algorithm has a finite step global convergence property three multichannel ma models including one nonminimum phase ma model are estimated by this algorithm with satisfactory performances

identification of linear systems using input output cumulants a new identification method is proposed for estimating the parameters of a discrete time linear dynamic system excited by non gaussian inputs using kth order k 2 cumulants of input and output signals contaminated by additive possibly coloured gaussian noise the parameter estimates obtained by this method are proved to be consistent under weak conditions this method has an on line algorithm for computing the parameter estimates just like the least squares method a simulation example is included to demonstrate the effectiveness of this method

identification of non minimum phase linear stochastic systems abstract the identification of time invariant non minimum phase stochastic systems driven by non gaussian white noise is considered given only the noisy observations of the system output a two step procedure is proposed in the first step a spectrally equivalent system is estimated using a standard technique that exploits only the second order statistics of the measurements in the second step a partial set of 4th order cumulants of the measurements is exploited to resolve the location of the system zeros knowledge of the probability distribution of the driving noise is not required strong consistency of the proposed estimator is proved under certain sufficient conditions simulation results are also presented in support of the theory

a unifying maximum likelihood view of cumulant and polyspectral measures for non gaussian signal classification and estimation classification and estimation of non gaussian signals observed in additive gaussian noise of unknown covariance are addressed using cumulants or polyspectra by integrating ideas from pattern recognition and model identification asymptotically optimum maximum likelihood classifiers and arma autoregressive moving average parameter estimators are derived without knowledge of the data distribution identifiability of noncausal and nonminimum phase arma models is established using a finite number of cumulant or polyspectral lags of any order greater than two a unifying view of cumulant and polyspectral discriminant measures utilizes these lags and provides a common framework for development and performance analysis of novel and existing estimation and classification algorithms tentative order determination and model validation tests for non gaussian arma processes are described briefly illustrative simulations are also presented

blind parafac receivers for ds cdma systems this paper links the direct sequence code division multiple access ds cdma multiuser separation equalization detection problem to the parallel factor parafac model which is an analysis tool rooted in psychometrics and chemometrics exploiting this link it derives a deterministic blind parafac ds cdma receiver with performance close to non blind minimum mean squared error mmse the proposed parafac receiver capitalizes on code spatial and temporal diversity combining thereby supporting small sample sizes more users than sensors and or less spreading than users interestingly parafac does not require knowledge of spreading codes the specifics of multipath interchip interference doa calibration information finite alphabet constant modulus or statistical independence whiteness to recover the information bearing signals instead parafac relies on a fundamental result regarding the uniqueness of low rank three way array decomposition due to kruskal 1977 1988 and generalized herein to the complex valued case that guarantees identifiability of all relevant signals and propagation parameters these and other issues are also demonstrated in pertinent simulation experiments

a case study for homoclinic chaos in an autonomous electronic circuit a trip taken from takens bogdanov to hopf sbil nikov abstract the dynamics of an autonomous electronic oscillator is analysed both theoretical study with methods of local bifurcation theory and numerical simulation by using continuation methods to detect global behaviours are carried out comment is made on the presence of homoclinic connections which organise the periodic and nonperiodic behaviour the richness and complexity of the periodic oscillations are described and the presence of isolated branches of odd period orbits are emphasized further attention is paid to the chaotic attractor coexisting with sil nikov homoclinicity even in the presence of a hopf degeneracy the hopf sil nikov singularity

identification of nonminimum phase systems using higher order statistics a method is presented for identification of linear time variant nonminimum phase systems when only output data are available the input sequence need not be independent but it must be non gaussian with some special properties described in the test the authors model a finite dimensional system as an arma autoregressive moving average rational function of known orders but the special cases of ar ma and all pass models are also considered to estimate the parameters of their model the authors utilize both second and higher order statistics of the output which may be contaminated by additive zero mean gaussian white noise of unknown variance the parameter estimators obtained are proved under mild conditions to be consistent simulations verify the performance of the proposed method in the case of relatively low signal to noise ratios and when there is a model order mismatch

widely linear versus conventional subspace based estimation of simo flat fading channels mean squared error analysis we analyze the mean squared error mse performance of widely linear wl and conventional subspace based channel estimation for single input multiple output simo flat fading channels employing binary phase shift keying bpsk modulation when the covariance matrix is estimated using a finite number of samples the conventional estimator suffers from a phase ambiguity that reduces to a sign ambiguity for the wl estimator we derive accurate closed form expressions for the mse of the two estimators under four ambiguity resolution scenarios in the first three scenarios the receiver resolves the ambiguity using some clairvoyant knowledge about the channel the first scenario used as a reference is the ideal case of optimal resolution the second scenario assumes that one of the channel coefficients is known and the third assumes knowledge of the coefficient with the largest magnitude the fourth scenario considers the more realistic case where pilot symbols are employed for ambiguity resolution our work demonstrates that there is a strong relationship between the accuracy of ambiguity resolution and the relative performance of wl and conventional subspace based estimators showing that the wl estimator performs better when partial or inaccurate channel information is employed for ambiguity resolution

regression to the mean for nonnormal populations summary regression to the mean is the term used to describe the effect by which individuals selected on the basis of an initial measurement which is particularly high or low compared with other members of the population have upon remeasurement values nearer to the population mean for the normal distribution simple expressions for estimates of the magnitude of this effect are available many biological variables however are not normally distributed estimates for regression to the mean for nonnormal data are given based on edgeworth series and saddlepoint approximations

dynamical approach study of spurious steady state numerical solutions of nonlinear differential equations i the dynamics of time discretization and its implications for algorithm development in computational fluid dynamics abstract the goal of this paper is to utilize the theory of nonlinear dynamics approach to investigate the possible sources of errors and slow convergence and nonconvergence of steady state numerical solutions when using the time dependent approach for nonlinear hyperbolic and parabolic partial differential equations terms this interdisciplinary research belongs to a subset of a new field of study in numerical analysis sometimes referred to as the dynamics of numerics and the numerics of dynamics at the present time this new interdisciplinary topic is still the property of an isolated discipline with all too little effort spent in pointing out an underlying generality that could make it adaptable to diverse fields of applications this is the first of a series of research papers under the same topic our hope is to reach researchers in the fields of computational fluid dynamics cfd and in particular hypersonic and combustion related cfd by simple examples in which the exact solutions of the governing equations are known the application of the apparently straightforward numerical technique to genuinely nonlinear problems can be shown to lead to incorrect or misleading results one striking phenomenon is that with the same initial data the continuum and its discretized counterpart can asymptotically approach different stable solutions this behavior is especially important for employing a time dependent approach to the steady state since the initial data are usually not known and a freestream condition or an intelligent guess for the initial conditions is often used with the unique property of the different dependence of the solution on initial data for the partial differential equation and the discretized counterpart it is not easy to delineate the true physics from numerical artifacts when numerical methods are the sole source of solution procedure for the continuum part i concentrates on the dynamical behavior of time discretization for scalar nonlinear ordinary differential equations in order to motivate this new yet unconventional approach to algorithm development in cfd and to serve as an introduction for parts 11 and iii of the same series of research papers

factoring integers with elliptic curves this paper is devoted to the description and analysis of a new algorithm to factor positive integers it depends on the use of elliptic curves the new method is obtained from pollard s p 1 method proc cambridge philos soc 76 1974 521 528 by replacing the multiplicative group by the group of points on a random elliptic curve it is conjectured that the algorithm determines a non trivial divisor of a composite number n in expected time at most k p log n 2 where p is the least prime dividing n and k is a function for which log k x 2 o 1 log x log log x for x x o in the worst case when n is the product of two primes of the same order of magnitude this is

blind mimo system identification based on cumulant subspace decomposition blind identification of multiple input multiple output mimo linear systems can be achieved by utilizing higher order statistics of the output signals we study the blind identification of mimo systems whose inputs are mutually independent temporally white non gaussian source signals based on sub space analysis we develop a new linear batch algorithm to identify mimo systems from the common nullspace of a set of fourth order cumulant matrices of the channel outputs given knowledge of the channel orders the identifiability conditions required by the proposed algorithm are properly established like most subspace based approaches this new algorithm remains sensitive to channel order overestimation simulation results illustrate its performance for various channel models

ica based on asymmetry we build a new approach to ica which is based on the data asymmetry instead of densities with heavy tails we use asymmetric ones split gaussians we verified our approach on images sound and eeg data in the case of source signal reconstructing our approach gives better results independent component analysis ica one of the basic tools in data analysis aims to find a coordinate system in which the components of the data are independent most of existing methods are based on the minimization of the function of fourth order moment kurtosis skewness third order moment has received much less attention in this paper we present a competitive approach to ica based on the split gaussian distribution which is well adapted to asymmetric data consequently we obtain a method which works better than the classical approaches especially in the case when the underlying density is not symmetric which is a typical situation in the color distribution in images

a least squares approach to blind channel identification conventional blind channel identification algorithms are based on channel outputs and knowledge of the probabilistic model of channel input in some practical applications however the input statistical model may not be known or there may not be sufficient data to obtain accurate enough estimates of certain statistics in this paper we consider the system input to be an unknown deterministic signal and study the problem of blind identification of multichannel fir systems without requiring the knowledge of the input statistical model a new blind identification algorithm based solely on the system outputs is proposed necessary and sufficient identifiability conditions in terms of the multichannel systems and the deterministic input signal are also presented

cumulant based blind identification of linear multi input multi output systems driven by colored inputs the blind identification problem of a linear multi input multi output mimo system is widely noticed by many researchers in diverse fields due to its relevance to blind signal separation however such a problem is ill posed and has no unique solution therefore we can only find a solution of the problem within an equivalence class we address the blind identification problem of the linear mimo system driven by unobservable colored inputs using higher order statistics hos particularly the fourth order cumulants of the outputs where the unobservable inputs are mutually independent but temporally colored linear processes we first define the set which is denoted by s of stable scalar transfer functions and then define the notion of a generalized permutation matrix which is abbreviated by a g matrix over s then it is shown that the transfer function matrix of an unknown system is identified only up to post multiplication by a g matrix this result is applied to identifying fir systems for blind signal separation

multichannel arma processes parametric modeling of multichannel time series is accomplished by using higher than second order statistics hos of the observed nongaussian data cumulants of vector processes are defined using a kronecker product formulation and consistency of their sample estimators is addressed identifiability results in connection with the hos based parameter estimation of causal and noncausal multivariate arma processes are established estimates of the parameters of causal arma models are obtained as the solution to a set of linear equations whereas those of noncausal arma models are obtained as the solution to a cumulant matching algorithm conventional approaches based on second order statistics can identify a multichannel system only to within post multiplication by a unimodular matrix hos based methods yield solutions that are unique to within post multiplication by an extended permutation matrix additionally the multiminimum phase assumption can be relaxed and the observations may be contaminated with colored gaussian noise frequency domain methods for nonparametric system identification are discussed briefly simulations results validating the multichannel parameter estimation algorithms are provided

blind identification of volterra hammerstein systems this paper is concerned with the blind identification of volterra hammerstein systems two identification scenarios are covered the first scenario assumes that although the input is not available the statistics of the input are a priori known this case appears in communication applications where the input statistics of the transmitter are known to the receiver the second scenario assumes that the input statistics are unknown in the case of known input statistics the input is stationary higher order white noise with arbitrary probability density function under the scenario of unknown input statistics the input is restricted to gaussian white process new cumulant based identification methods are described for the above scenarios the problem is converted into a linear multivariable form and the output cumulants are calculated using kronecker products first initial conditions are determined by a linear system of equations these correspond to the boundary values of the volterra kernels the remaining kernel coefficients can be determined under both identification schemes from a possibly overdetermined system of linear equations

parameter identifiability of multichannel arma models of linear non gaussian signals via cumulant matching the problem of estimating the parameters of a vector stationary arma p q signal model driven by an i i d vector non gaussian sequence is considered the focus of the paper is the problem of parameter identifiability of multichannel arma models given the higher order cumulants of the signal on a finite set of lags the authors specify the finite lag set for general arma p q models the approach is to first derive the basic results via a diagonal canonical form and then to extend the parameter identifiability results to other more parsimonious canonical forms

the cross bicepstrum definition properties and application for simultaneous reconstruction of three nonminimum phase signals the recovery of three signals from their cross bispectrum or the identification of the impulse responses of three parallel linear time invariant lti systems from the cross bispectrum of their system outputs by computing the complex cepstrum of the cross bispectrum as long as the signals or impulse responses have no zeros on the unit circle is discussed it is shown that the three signals can be separated completely and approximately recovered in the cross bicepstrum domain except for their magnitude and linear phase factors the computation of the cross bicepstrum can be seen as a method for the simultaneous computation of the ordinary complex cepstra of three nonminimum phase signals without the need for phase unwrapping both least squares and fast fourier transform fft based methods for computing the bicepstral coefficients are presented simulation examples of signal reconstruction in gaussian white and nongaussian colored noise and of system identification are included the results are extended to nth order cross spectra and the factorization problem for these spectra is discussed

cumulant based identification of multichannel moving average models given cumulants of a stationary perhaps noisy non gaussian r variate moving average ma q process identifiability conditions are studied under which the ma coefficient matrices the input statistics and the order q can be uniquely determined the selection of a unique representative from the equivalence class corresponding to a given cumulant structure involves fewer restrictions than that corresponding to a given covariance structure two algorithms are derived for estimating the possibly nonminimum phase ma coefficient matrices

on the identifiability of non gaussian arma models using cumulants a fixed set of output cumulants of order greater than two guarantees unique identification of known order causal arma autoregressive moving average models which are driven by unobservable non gaussian i i d noise the models are allowed to be non minimum phase and their outputs may be corrupted by additive colored gaussian noise of unknown covariance the arma parameters can be estimated either by means of linear equations and closed form expressions or by minimizing quadratic cumulant matching criteria the latter approach requires computation of cumulants in terms of the arma parameters which is carried out in the state space using kronecker products

extension of the matrix bartlett s formula to the third and fourth order and to noisy linear models with application to parameter estimation this paper focuses on the extension of the asymptotic covariance of the sample covariance denoted bartlett s formula of linear processes to thirdand fourth order sample cumulant and to noisy linear processes closed form expressions of the asymptotic covariance and cross covariance of the sample second third and fourth order cumulants are derived in a relatively straightforward manner thanks to a matrix polyspectral representation and a symbolic calculus akin to a high level language as an application of these extended formulae we underscore the sensitivity of the asymptotic performance of estimated arma parameters by an arbitrary third or fourth order based algorithm with respect to the signal to noise ratio the spectra of the linear process and the colored additive noise

on estimating noncausal nonminimum phase arma models of non gaussian processes the authors address the problem of estimating the parameters of non gaussian arma autoregressive moving average processes using only the cumulants of the noisy observation the measurement noise is allowed to be colored gaussian or independent and identically non gaussian distributed the arma model is not restricted to be causal or minimum phase and may even contain all pass factors the unique parameter estimates of both the ma and ar parts are obtained by linear equations the structure of the proposed algorithm facilitates asymptotic performance evaluation of the parameter estimators and model order selection using cumulant statistics the method is computationally simple and can be viewed as the least squares solution to a quadratic model fitting of a sampled cumulant sequence identifiability issues are addressed simulations are presented to illustrate the proposed algorithm

general approach to blind source separation this paper identifies and studies two major issues in the blind source separation problem separability and separation principles we show that separability is an intrinsic property of the measured signals and can be described by the concept of m row decomposability introduced in this paper we also show that separation principles can be developed by using the structure characterization theory of random variables in particular we show that these principles can be derived concisely and intuitively by applying the darmois skitovich theorem which is well known in statistical inference theory and psychology some new insights are gained for designing blind source separation filters

information geometric measure for neural spikes this study introduces information geometric measures to analyze neural firing patterns by taking not only the second order but also higher order interactions among neurons into account information geometry provides useful tools and concepts for this purpose including the orthogonality of coordinate parameters and the pythagoras relation in the kullback leibler divergence based on this orthogonality we show a novel method for analyzing spike firing patterns by decomposing the interactions of neurons of various orders as a result purely pairwise triple wise and higher order interactions are singled out we also demonstrate the benefits of our proposal by using several examples

a cumulant based hankel approach to direction of arrival estimation a new cumulant based approach to doa estimation for independent nongaussian sources and a uniform linear array is presented the doas are obtained by finding the eigenvalues of a matrix made up from cumulants of the data as with other cumulant based methods the present method does not need the characteristics of the noise when the noise is gaussian this algorithm is developed using an approach that leads to a general relation between the cumulant functions and the parameters to be estimated this general relation gives a common framework for developing other algorithms for doa estimation computer simulation results show the effectiveness of this new method