the application of generalized diagonal dominance to linear system stability theory abstract this paper shows that the well known diagonal dominance condition associated with rosenbrock s stability theorems is unnecessary and can be replaced by a less restrictive generalized diagonal dominance condition similar results are derived for generalized block diagonally dominant systems whenever possible graphical interpretations are given to facilitate the implementation of these ideas in computer aided design packages

representation of electromagnetic responses in time domain using state space system identification method this paper presents a control system methodology based on system identification si to derive state matrices and system dynamics for the extrapolation of simulated time domain electromagnetic em responses using both input and output data the method is applied to model transient responses for a dielectric resonator and a wideband slot antenna computed by the finite integration method using non gaussian excitation pulses typically employed in digital signals using state space si formulation a compact representation of the output time domain signal is derived including the early time transient responses and its numerical implementation depicts no instability in late time responses plotted well beyond the steady state furthermore all the system poles are found to lie within the unit circle in the complex plane excellent model corroboration is achieved with independently computed frequency domain data or measured results using modest computer resources

horizontal visibility graphs exact results for random time series networks this procedure allows us to apply methods of complex network theory for characterizing time series in this work we present the horizontal visibility algorithm a geometrically simpler and analytically solvable version of our former algorithm focusing on the mapping of random series series of independent identically distributed random variables after presenting some properties of the algorithm we present exact results on the topological properties of graphs associated with random series namely the degree distribution the clustering coefficient and the mean path length we show that the horizontal visibility algorithm stands as a simple method to discriminate randomness in time series since any random series maps to a graph with an exponential degree distribution of the shape pk 1 32 3 k 2 independent of the probability distribution from which the series was generated accordingly visibility graphs with other pk are related to nonrandom series numerical simulations confirm the accuracy of the theorems for finite series in a second part we show that the method is able to distinguish chaotic series from independent and identically distributed i i d theory studying the following situations i noise free low dimensional chaotic series ii low dimensional noisy chaotic series even in the presence of large amounts of noise and iii high dimensional chaotic series coupled map lattice without needs for additional techniques such as surrogate data or noise reduction methods finally heuristic arguments are given to explain the topological properties of chaotic series and several sequences that are conjectured to be random are analyzed

an inclusion region for the eigenvalues of partitioned matrices abstract this note presents a new result which defines disc regions centred on the eigenvalues of the diagonal blocks of a general complex matrix which contain the eigenvalues of the matrix a result of this type is useful in the application of a generalized nyquist type stability criterion to interconnected systems

minimum variance linear estimation of amplitudes for exponential signal models this article presents the minimum variance consistent linear estimator for amplitude parameters in exponential signal models a simple heuristic algorithm is presented to compute the weighting matrix that minimizes error variance the resulting weighted least squares estimator accounts for the statistics of pole estimation errors additionally analysis of binary diagonal weighting matrices demonstrates that for unweighted least squares the amplitude variance is reduced by truncating the vandermonde system of equations

newton algorithms for conditional and unconditional maximum likelihood estimation of the parameters of exponential signals in noise the authors present polynomial based newton algorithms for maximum likelihood estimation mle of the parameters of multiple exponential signals in noise this formulation can be used in the estimation for example of the directions of arrival of multiple noise corrupted narrowband plane waves using uniform linear arrays and the frequencies of multiple noise corrupted complex sine waves the algorithms offer rapid convergence and exhibit the computation efficiency associated with the polynomial approach compact closed form expressions are presented for the gradients and hessians various model assumptions concerning the statistics of the underlying signals are considered numerical simulations are presented to demonstrate the algorithms performance

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

efficient wideband source localization using beamforming invariance technique a novel scheme for wideband direction of arrival doa estimation is proposed the technique performs coherent signal subspace transformation by a set of judiciously constructed beamforming matrices the beamformers are chosen to transform each of the narrowband array manifold vectors into the one corresponding to the reference frequency regardless of the actual spatial distribution of the sources the focused data correlation matrix can thus be obtained without any preliminary doa estimation or iteration a simplified version of the beamspace root music algorithm is developed and used in conjunction with the proposed method to efficiently localize multiple wideband sources with a linear equally spaced array numerical simulations are conducted to demonstrate the efficacy of the new scheme

a covariance approximation method for near field direction finding using a uniform linear array most narrowband high resolution bearing estimation algorithms were proposed based on the assumption of a far field source environment when this assumption is violated i e some sources are in the near field these algorithms generally provide unsatisfactory performances a new algorithm is proposed to handle this near field problem using a uniform linear array the received signal covariance matrix for near field sources is viewed as a corrupted measurement of the ideal signal covariance matrix for far field sources located at the same bearings taking this viewpoint the authors reconstruct a far field approximation ffa covariance matrix from the received covariance matrix to reduce the corruptions therefore existing high resolution bearing estimation techniques can be directly applied to estimate the bearings of the near field sources the properties of the proposed approach are investigated in detail simulation results demonstrating the effectiveness of this approach are included

fast maximum likelihood for blind identification of multiple fir channels this paper develops a fast maximum likelihood method for estimating the impulse responses of multiple fir channels driven by an arbitrary unknown input the resulting method consists of two iterative steps where each step minimizes a quadratic function the two step maximum likelihood tsml method is shown to be high snr efficient i e attaining the cramer rao lower bound crb at high snr the tsml method exploits a novel orthogonal complement matrix of the generalized sylvester matrix simulations show that the tsml method significantly outperforms the cross relation cr method and the subspace ss method and attains the crb over a wide range of snr this paper also studies a fisher information fi matrix to reveal the identifiability of the m channel system a strong connection between the fi based identifiability and the cr based identifiability is established

a generalized least squares method for frequency estimation the application of the generalized least squares gls method to the estimation of the frequencies of sinusoids in additive colored noise is discussed an iterative algorithm is proposed starting from the assumption that the parameter vector in the model of the sinusoids is symmetric the algorithm utilizes an adaptive strategy for contracting the poles of the estimated signal model expressions for the probability limit and the asymptotic variance of the estimates are derived for the single sinusoid case possible convergence points and the asymptotic behavior of the algorithm in the case of low snrs signal to noise ratios are analyzed extensive simulation results show that the algorithm represents a simple and reliable tool for practical applications

a characterization of horizontal visibility graphs and combinatorics on words abstract a horizontal visibility graph hvg is defined in association with an ordered set of non negative reals hvgs realize a methodology in the analysis of time series their degree distribution being a good discriminator between randomness and chaos luque et al b luque l lacasa f ballesteros j luque horizontal visibility graphs exact results for random time series phys rev e 80 2009 046103 we prove that a graph is an hvg if and only if it is outerplanar and has a hamilton path therefore an hvg is a noncrossing graph as defined in algebraic combinatorics flajolet and noy p flajolet m noy analytic combinatorics of noncrossing configurations discrete math 204 1999 203 229 our characterization of hvgs implies a linear time recognition algorithm treating ordered sets as words we characterize subfamilies of hvgs highlighting various connections with combinatorial statistics and introducing the notion of a visible pair with this technique we determine asymptotically the average number of edges of hvgs

using the em algorithm to increase the number of signals estimable by 2 d parametric techniques this paper provides an easy method for increasing the number of modes estimable by 2 d parameter estimation schemes which use a single snapshot of the data for data of size m sub 1 spl times m sub 2 few of these techniques allow the number of modes to exceed m sub 1 and or m sub 2 as these restrictions are not inherent to the model but the algorithms themselves this problem is circumvented by treating the observed data as an incomplete version of a larger data set an existing 2 d parameter estimation scheme is then used for the maximization m step of the expectation maximization em algorithm in this way one can increase the number of modes the scheme can estimate without changing the scheme itself

a decoupled approach for optimal estimation of transfer function parameters from input output data a theoretical and algorithmic framework is proposed for optimal identification of rational transfer function parameters of discrete time linear systems from input output io data the nonlinear criterion is theoretically decoupled into a purely linear problem for estimating the optimal numerator and a nonlinear problem for the optimal denominator the proposed decoupled approach has reduced computational requirements when compared with existing algorithms that estimate the parameters simultaneously

szego polynomials applied to frequency analysis abstract this paper is concerned with the problem of determining unknown frequencies 1 i using an observed discrete time signal xn xn m arising from a continuous waveform that is the superposition of a finite number of sinusoidal waves with well defined frequencies j periods p j 2 n j n z j 1 i we investigate the wiener levinson method formulated here in terms of szeg polynomials n n z orthogonal on the unit circle with respect to a distribution function n defined by the n observed values of the signal we prove that if n0 denotes the number of critical points eiwj then for every n n0 and n 1 the zeros z j n n of n n z can be arranged so that limn z j n n eiwj for each of the frequencies wj this result confirms one of the main parts of the conjecture given by jones njastad and saff this journal 1990 on the convergence of zeros of the szeg polynomials a related result on the convergence of corresponding two point pade approximants is also given

on the zeros of the linear prediction error filter for deterministic signals the zeros of a linear prediction error filter polynomial for a class of deterministic signals that are a sum of samples of m exponentially damped undamped sinusoids is studied it is assumed that n samples are available for processing and that they are uncorrupted by noise it is shown that the exponent parameters of the m signals can be determined from m zeros called signal zeros of an lth degree prediction error filter polynomial l m if l lies in between m and n m n m 2 in a special case the rest of the l m zeros of the filter polynomial switch are called extraneous zeros are shown to be approximately uniformly distributed with in the unit circle regardless of the type of exponentials in the signal if the prediction filter coefficients are chosen to have minimum euclidean length the results obtained provide insight into the estimation problem with noisy data

on frequency estimation with the iqml algorithm a popular implementation of the kiss iqml algorithm for frequency estimation applies an inappropriate constraint to the parameter vector this results in high thresholds for certain frequency configurations by applying a consistent constraint a better estimator can be obtained

an algorithm for pole zero modeling and spectral analysis an explicit connection between fitting exponential models and pole zero models to observed data is made the fitting problem is formulated as a constrained nonlinear minimization problem this problem is then solved using a simplified iterative algorithm the algorithm is applied to simulated data and the performance of the algorithm is compared to previous results

from the time series to the complex networks the parametric natural visibility graph abstract we present the modification of natural visibility graph nvg algorithm used for the mapping of the time series to the complex networks graphs we propose the parametric natural visibility graph pnvg algorithm the pnvg consists of nvg links which satisfy an additional constraint determined by a newly introduced continuous parameter the view angle the alteration of view angle modifies the pnvg and its properties such as the average node degree average link length of the graph as well as cluster quantity of built graph etc we calculated and analyzed different pnvg properties depending on the view angle for different types of the time series such as the random uncorrelated correlated and fractal and cardiac rhythm time series for healthy and ill patients investigation of different pnvg properties shows that the view angle gives a new approach to characterize the structure of the time series that are invisible in the conventional version of the algorithm it is also shown that the pnvg approach allows us to distinguish identify and describe in detail various time series

asymptotically efficient estimation of spectral moments the article studies parametric estimation of spectral moments of a zero mean complex gaussian stationary process immersed in independent gaussian noise with the merit of the maximum likelihood ml approach as motivation this work exploits a whittle s 1953 type objective function that is able to capture the relevant features of the log likelihood function while being much more manageable the resulting estimates are strongly consistent and asymptotically efficient as an example application to doppler weather radar data is considered

a frequency domain method for decentralized stabilization based on quasi block diagonal dominance in this paper decentralized stabilization of interconnected systems based on quasi block diagonal dominance of transfer function matrices has been examined some previous results are refined and extended to the case where diagonal blocks are not necessarily square it has been shown that the refined stability result leads to a necessary and sufficient condition for robust decentralized stability for a class of additively perturbed interconnected systems some design considerations for decentralized controllers are discussed

statistical properties of visibility graph of energy dissipation rates in three dimensional fully developed turbulence abstract we study the statistical properties of complex networks constructed from time series of energy dissipation rates in three dimensional fully developed turbulence using the visibility algorithm the degree distribution is found to have a power law tail with the tail exponent 3 0 the exponential relation between the number of the boxes n b and the box size l b based on the edge covering box counting method illustrates that the network is not self similar which is also confirmed by the hub hub attraction according to the visibility algorithm in addition it is found that the skeleton of the visibility network exhibits excellent allometric scaling with the scaling exponent 1 163 0 005

two dimensional angle of arrival estimation in the presence of finite distance sources when sources are a finite distance away from an array system most high resolution bearing estimation techniques exhibit unsatisfactory performance due to the invalidity of the planar wavefront assumption this problem has been addressed by a far field approximation ffa method based on a preprocessing scheme by exploiting favorable characteristics of a uniform linear array the method constructs a ffa covariance matrix which is toeplitz and approximates to the far field data covariance matrix from the observed data covariance matrix then eigenstructure methods can be applied to perform bearing estimation without revising the planar wavefront assumption this method is extended to the problem of two dimensional angle of arrival aoa estimation using a uniform planar array in the presence of finite distance sources a procedure is derived for reconstructing the 2 d ffa covariance matrix with block toeplitz structure using the 2 d ffa covariance matrix eigenstructure methods can be applied in conjunction with a 2 d aoa search to solve the problem simulation results confirm the theoretical work

maximum likelihood estimation of multiple frequencies with constraints to guarantee unit circle roots an approximate maximum likelihood estimator mle of multiple exponentials converts the frequency estimation problem into a problem of estimating the coefficients of a z polynomial with roots at the desired frequencies theoretically the roots of the estimated polynomial should fall on the unit circle but mle as originally proposed does not guarantee unit circle roots this drawback sometimes causes merged frequency estimates especially at low snr if all the sufficient conditions for the z polynomial to have unit circle roots are incorporated the optimization problem becomes too nonlinear and it loses the desirable weighted quadratic structure of mle in the present paper the exact constraints are imposed on each of the first order factors corresponding to individual frequencies for ensuring unit circle roots the constraints are applied during optimization alternately for each frequency in the absence of any merged frequency estimates the rms values more closely approach the theoretical cramer rao cr bound at low snr levels

estimating the bearings of near field cyclostationary signals by exploiting favorable characteristics of a uniform linear array ula the far field approximation ffa method reduces the deterioration of most high resolution bearing estimation techniques due to the invalidity of the planar wavefront assumption when near field sources exist we first present a new technique that provides better performance than existing bearing estimation techniques for cyclostationary signals then the proposed technique incorporating with the ffa method is proposed to estimate signal bearings in the presence of near field sources without revising the planar wavefront assumption several simulation examples confirm the theoretical work and show the effectiveness of the proposed technique

visibility graph analysis of economy policy uncertainty indices abstract uncertainty plays an important role in the global economy in this paper the economic policy uncertainty epu indices of the united states and china are selected as the proxy variable corresponding to the uncertainty of national economic policy by adopting the visibility graph algorithm the four economic policy uncertainty indices of the united states and china are mapped into complex networks and the topological properties of the corresponding networks are studied the hurst exponents of all the four indices are within 0 5 1 which implies that the economic policy uncertainty is persistent the degree distributions of the epu networks have power law tails and thus the networks are scale free the average clustering coefficients of the four epu networks are high and close to each other while these networks exhibit weak assortative mixing we also find that the epu network in united states based on daily data shows the small world feature since the average shortest path length increases logarithmically with the network size such that l n 0 626 ln n 0 405 our research highlights the possibility to study the epu from the view angle of complex networks

superresolution by structured matrix approximation the bearing estimation problem is formulated as a matrix approximation problem the columns of a matrix x are formed by the snapshot vectors from an n element array the matrix x is then approximated by a matrix in the least square sense the rank as well as the partial structure of the space spanned by the columns of the approximated x matrix are prespecified after the approximated x matrix is computed the bearings of the sources and consequently the spatial correlation of the source signals are estimated the performance of the proposed technique is compared with two existing methods using simulation the comparison is made in terms of bias mean squared error failure rates and confidence intervals for the mean and the variance estimates for all three methods at different signal to noise ratios when the sources are moving slowly and the number of snapshot vectors available for processing is large a simple online adaptive algorithm is suggested

geometric methods for determining system poles from transient response the problem treated is that of identifying the poles of a finite order system by observing its transient decay after cessation of input for a limited time using possibly multiple observation points and experimental repetition various approaches are studied having the common characteristic that a homogeneous matrix equation must be solved several techniques that have been given scant attention in the literature are consolidated by a geometric treatment together with new results including an analytical treatment of the consequences of assuming an excessively high system order derivation of a statistically unbiased estimate for an intermediate parameter in the solution new theorems on error effects a recipe for effective use of the singular value decomposition and a new method for suppression of extraneous poles

arma based time signature estimator for analyzing resonant structures by the fdtd method we propose an algorithm for estimation of the optimal system parameters of time sequences tss computed by the finite difference time domain fdtd method with the goal of accurate representation of the time signature using low order models the fdtd method requires computation of very long time sequences to accurately characterize the slowly decaying transient behavior of resonant structures therefore it becomes critical to investigate methods of reducing the computational time for such objects several researchers have argued that the fdtd ts can be modeled as the impulse response ir of an autoregressive moving average arma transfer function however it is known that determination of arma parameters by ir matching is a complex nonlinear optimization problem hence many existing methods in em literature tend to use prony based linear predictor type spectrum estimation algorithms which minimize a linearized equation error criterion that approximates the true nonlinear model fitting error criterion as a result significantly high model orders are needed by these methods to achieve good corroboration in the frequency domain especially when a magnitude spectrum has deep nulls or notches we propose to use a deterministic arma approach which minimizes the true nonlinear criterion iteratively and attains significantly improved ir fit over prony s 1795 method using fewer arma model parameters for a given time sequence of an analyzed circuit the issues of model order selection and choice of decimation factor are also addressed systematically the improved performance of the proposed algorithm is demonstrated with transient simulation and signal analysis of microstrip structures which manifest deep nulls in the frequency domain

full newton and constraint methods for semilinear signal modeling the authors derive an expression for the hessian matrix of the variable projection functional vpf and implement the hessian using qr factorization this is incorporated into a full newton variable projection fnvp algorithm for estimating parameters in semilinear signals they introduce a deflation technique for constraining the vpf to contain known basis vectors for modeling exponential signals the computational cost of the fnvp algorithm is shown to vary linearly with n the size of the data vector while other algorithms vary as n sup 2 or n log sub 2 n

music maximum likelihood and cramer rao bound further results and comparisons the problem of determining the direction of arrival of narrowband plane waves using sensor arrays and the related problem of estimating the parameters of superimposed signals from noisy measurements are studied a number of results have been recently presented by the authors on the statistical performance of the multiple signal characterization music and the maximum likelihood ml estimators for the above problems this work extends those results in several directions first it establishes that in the class of weighted music estimators the unweighted music achieves the best performance i e the minimum variance of estimation errors in large samples next it derives the covariance matrix of the ml estimator and presents detailed analytic studies of the statistical efficiency of music and ml estimators these studies include performance comparisons of music and mle with each other as well as with the ultimate performance corresponding to the cramer rao bound finally some numerical examples are given which provide a more quantitative study of performance for the problem of finding two directions with uniform linear sensor arrays

detecting chaos in pseudoperiodic time series without embedding a different method is proposed to detect deterministic structure from a pseudoperiodic time series by using the correlation coefficient as a measure of the distance between cycles we are exempt from phase space reconstruction and further construct a hierarchy of pseudocycle series that in turn preserve less determinism than the original time series appropriate statistics are then devised to reveal the temporal and spatial correlation encoded in this hierarchy of the pseudocycle series which allows for a reliable detection of determinism and chaos in the original time series we demonstrate that this method can reliably identify chaos in the presence of noise of different sources for both artificial data and experimental time series

total least squares for affinely structured matrices and the noisy realization problem structured rank deficient matrices arise in many applications in signal processing system identification and control theory the author discusses the structured total least squares stls problem which is the problem of approximating affinely structured matrices i e matrices affine in the parameters by similarly structured rank deficient ones while minimizing an l sub 2 error criterion it is shown that the optimality conditions lead to a nonlinear generalized singular value decomposition which can be solved via an algorithm that is inspired by inverse iteration next the author concentrates on the so called l sub 2 optimal noisy realization problem which is equivalent with approximating a given data sequence by the impulse response of a finite dimensional time invariant linear system of a given order this can be solved as a structured total least squares problem it is shown with some simple counter examples that classical algorithms such as the steiglitz mcbride 1965 iterative quadratic maximum likelihood and cadzow s 1988 iteration do not converge to the optimal l sub 2 solution despite misleading claims in the literature

spatiotemporal dynamics analysis and systemic risk measurement of energy price system based on complex network abstract multivariate time series contain rich information of corresponding complex systems this paper proposes a new method to characterize the evolution and transition characteristics of the correlation modes for multivariate time series etccmmts based on etccmmts the characteristics of energy price systems are analyzed the results show that energy price correlated modes exhibit co movement group occurrence and the small world property the results prove that futures prices have the leading role the crude oil futures price affects the stability of an energy price system and the crude oil spot price has the highest clustering coefficient whereas the heating oil futures price has the largest betweenness coefficient the topological absorptive is introduced to measure the systemic risk and the risk hopping phenomenon is revealed the recursive graph indicates that the fluctuations of energy price display not only short range correlation for 1 2 months but also long range correlation for 7 8 years additionally the long range correlation will lead to high systematic risk in the course of energy price fluctuations there is a total of 41 different types of correlation modes the cumulative time of different correlation modes may result in a cumulative time jump and shows a linear growth in general in addition the topological structure of energy price correlated modal transition network epcmtn is revealed

maximum likelihood estimation of superimposed complex sinusoids in white gaussian noise by reduced effort coarse search recs an efficient implementation for the maximum likelihood estimator for the frequencies of superimposed complex sinusoids in white gaussian noise is presented the algorithm uses one dimensional searches and classical optimization techniques and produces data that can be used for model order selection its convergence and statistical properties are verified through simulation the method does not require polynomial rooting frequent manipulation of large matrices or the use of approximate constraints

fast iterative algorithm for real time array processing an online iterative conjugate gradient algorithm for array processing is presented the basic idea is to recast the array processing problem into a form so that the iterative method can be applied to compute the array weights vector recursively to speed up the rate of convergence of the iterative process the conjugate gradient method is used under moderate signal to noise ratios the algorithm converges to the minimum euclidean norm least squares solution in p iterations for p number of signals it does not require eigendecomposition of the covariance matrix and prior information regarding the number of signals it is capable of handling fully coherent sources and is effective for a small number of snapshots numerical examples are presented to illustrate the performance achievable

topological properties of the limited penetrable horizontal visibility graph family the limited penetrable horizontal visibility graph algorithm was recently introduced to map time series in complex networks in this work we extend this algorithm to create a directed limited penetrable horizontal visibility graph and an image limited penetrable horizontal visibility graph we define two algorithms and provide theoretical results on the topological properties of these graphs associated with different types of real value series we perform several numerical simulations to check the accuracy of our theoretical results finally we present an application of the directed limited penetrable horizontal visibility graph to measure real value time series irreversibility and an application of the image limited penetrable horizontal visibility graph that discriminates noise from chaos we also propose a method to measure the systematic risk using the image limited penetrable horizontal visibility graph and the empirical results show the effectiveness of our proposed algorithms

ambiguities in recurrence based complex network representations of time series recently different approaches have been proposed for studying basic properties of time series from a complex network perspective in this work the corresponding potentials and limitations of networks based on recurrences in phase space are investigated in some detail we discuss the main requirements that permit a feasible system theoretic interpretation of network topology in terms of dynamically invariant phase space properties possible artifacts induced by disregarding these requirements are pointed out and systematically studied finally a rigorous interpretation of the clustering coefficient and the betweenness centrality in terms of invariant objects is proposed

a deconvolution approach to source localization due to its low resolution the conventional beamformer cbf has generally been neglected in the recent literature on array processing and considerable attention devoted to the high resolution hr techniques applying a deconvolution approach to the output of the cbf the authors obtain a source localization procedure whose performances are comparable to those of the most efficient hr techniques the scheme moreover also furnishes estimates of the source powers and comprises a test that detects the number of sources present it can indeed be seen as a means to obtain maximum likelihood estimates mle when the cbf output is taken as the observed data

multiscale entropy analysis of complex physiologic time series there has been considerable interest in quantifying the complexity of physiologic time series such as heart rate however traditional algorithms indicate higher complexity for certain pathologic processes associated with random outputs than for healthy dynamics exhibiting long range correlations this paradox may be due to the fact that conventional algorithms fail to account for the multiple time scales inherent in healthy physiologic dynamics we introduce a method to calculate multiscale entropy mse for complex time series we find that mse robustly separates healthy and pathologic groups and consistently yields higher values for simulated long range correlated noise compared to uncorrelated noise

time dependent limited penetrable visibility graph analysis of nonstationary time series abstract recent years have witnessed the development of visibility graph theory which allows us to analyze a time series from the perspective of complex network we in this paper develop a novel time dependent limited penetrable visibility graph tdlpvg two examples using nonstationary time series from rr intervals and gas liquid flows are provided to demonstrate the effectiveness of our approach the results of the first example suggest that our tdlpvg method allows characterizing the time varying behaviors and classifying heart states of healthy congestive heart failure and atrial fibrillation from rr interval time series for the second example we infer tdlpvgs from gas liquid flow signals and interestingly find that the deviation of node degree of tdlpvgs enables to effectively uncover the time varying dynamical flow behaviors of gas liquid slug and bubble flow patterns all these results render our tdlpvg method particularly powerful for characterizing the time varying features underlying realistic complex systems from time series

optimal identification of discrete time systems from impulse response data an optimal method om for estimation of the parameters of rational transfer functions from prescribed impulse response data is presented the multidimensional nonlinear fitting error minimization problem has been theoretically decoupled into two subproblems of reduced computational complexities the proposed approach is applicable for identifying rational models with arbitrary numbers of poles and zeros the nonlinear denominator subproblem possesses weighted quadratic structure which is utilized to formulate an efficient iterative minimization algorithm the optimal numerator is found noniteratively with a linear least squares approach that utilizes the optimized denominator both the decoupled subcriteria of om posses global optimality properties the steiglitz mcbride 1960 sm method is also decoupled for arbitrary numbers of poles and zeros dsm g it is demonstrated that the denominator subproblem of dsm g is theoretically optimal for another existing decoupled sm method dsm j it has been shown that only the numerator is theoretically optimal

matrix pencil method for estimating parameters of exponentially damped undamped sinusoids in noise a study of a matrix pencil method for estimating frequencies and damping factors of exponentially damped and or undamped sinusoids in noise is presented comparison of this method to a polynomial method svd prony method shows that the matrix pencil method and the polynomial method are two special cases of a matrix prediction approach and that the pencil method is more efficient in computation and less restrictive about signal probes it is found through perturbation analysis and simulation that for signals with unknown damping factors the pencil method is less sensitive to noise than the polynomial method an expression of the cramer rao bound for the exponential signals is presented

universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices the investigations of financial markets from a complex network perspective have unveiled many phenomenological properties in which the majority of these studies map the financial markets into one complex network in this work we investigate 30 world stock market indices through their visibility graphs by adopting the visibility algorithm to convert each single stock index into one visibility graph a universal allometric scaling law is uncovered in the minimal spanning trees whose scaling exponent is independent of the stock market and the length of the stock index in contrast the maximal spanning trees and the random spanning trees do not exhibit universal allometric scaling behaviors there are marked discrepancies in the allometric scaling behaviors between the stock indices and the brownian motions using surrogate time series we find that these discrepancies are caused by the fat tailedness of the return distribution and the nonlinear long term correlation

the cramer rao bound on frequency estimates of signals closely spaced in frequency unconditional case the paper analyzes the cramer rao cr bound on frequency estimation covariance for the unconditional or stochastic signal model it addresses the problem of n signals closely spaced in temporal or spatial frequency the main result is that for this regime the cr bound decomposes into a product of simple scalar factors that individually reflect frequency separation signal powers and covariances data sampling grid and sample size the factored expression provides useful insight into the behavior of the bound for closely spaced frequencies the result also leads to a new formula for the signal to noise snr threshold at which an unbiased frequency estimator can resolve signals closely spaced in frequency interestingly with a simple modification the formulae are identical to those recently obtained for the conditional or deterministic signal model

exact equivalence of the steiglitz mcbride iteration and iqml the exact equivalence of the steiglitz mcbride mode 1 algorithm and the iterative quadratic maximum likelihood algorithm iqml is demonstrated other methods published earlier by l l scharf et al 1986 and by a g evans and r fischl 1973 are also known to give the same equations and answer as iqml hence all these methods are equivalent to the steiglitz mcbride iteration since the iqml method was originally formulated to solve a multiple measurement case an extended version of the steiglitz mcbride mode 1 algorithm applicable to the multiple measurement case is also stated and shown to be equivalent to the general form of iqml

characterizing pseudoperiodic time series through the complex network approach recently a new framework has been proposed to explore the dynamics of pseudoperiodic time series by constructing a complex network j zhang m small phys rev lett 96 2006 238701 essentially this is a transformation from the time domain to the network domain which allows for the dynamics of the time series to be studied via organization of the network in this paper we focus on the deterministic chaotic rossler time series and stochastic noisy periodic data that yield substantially different structures of networks in particular we test an extensive range of network topology statistics which have not been discussed in previous work but which are capable of providing a comprehensive statistical characterization of the dynamics from different angles our goal is to find out how they reflect and quantify different aspects of specific dynamics and how they can be used to distinguish different dynamical regimes for example we find that the joint degree distribution appears to fundamentally characterize spatial organizations of cycles in phase space and this is quantified via an assortativity coefficient we applied network statistics to electrocardiograms of a healthy individual and an arrythmia patient such time series are typically pseudoperiodic but are noisy and nonstationary and degrade traditional phase space based methods these time series are however better differentiated by our network based statistics

estimation of structural wave numbers from spatially sparse response measurements a method is presented for estimating the complex wave numbers and amplitudes of waves that propagate in damped structures such as beams plates and shells the analytical basis of the method is a wave field that approximates response measurements in an aperture where no excitations are applied at each frequency the method iteratively adjusts wave numbers to best approximate response measurements using wave numbers at neighboring frequencies as initial estimates in the search in comparison to existing methods the method generally requires far fewer measurement locations and does not require evenly spaced locations the number of locations required by the method scales with the number of waves that propagate in the structure whereas the number of locations required by existing methods scales with the minimum wavelength in addition the method allows convenient inclusion of the analytic relationships between wave numbers that exist for flexural vibrations of beams and plates advantages of the method are illustrated by an example in which a beam is excited by a transverse force at one end using analytic data and experimental measurements the method produces a wave field that matches response measurements to within 1 percent one interesting feature of the new method is that when applied to analytic data it supplies more robust wave number estimates using responses at unevenly spaced locations

an l shaped array for estimating 2 d directions of wave arrival a simple structured 2 d array the l shaped array is presented the l shaped array consists of two uniform linear arrays ula connected orthogonally at one end of each ula it is shown that the cramer rao bounds crb of the estimated wave directions based on the l shaped array are about 37 smaller than those for the cross array the crb indicates the accuracy potential because it is the reachable lower bound on the variance of any unbiased estimate an efficient maximum likelihood algorithm is developed utilizing the ula structure inherent in the l shaped array

decentralized control using quasi block diagonal dominance of transfer function matrices the purpose of this paper is to present a generalization of the nyquist array method to blockwise decompositions which is based upon a new version of block diagonal dominance an additional flexibility of the proposed method is in partitioning of the system matrices into disjoint as well as overlapping submatrices which increases considerably the class of control systems which can be designed via block diagonal dominance within this framework the controllers for individual subsystems can be designed independently of each other so that their union represents a decentralized controller for the overall system