diffusive limit of a tagged particle in asymmetric simple exclusion processes invariance principles are proved under diffusive scaling for the centered position of a tagged particle in the simple exclusion process with asymmetric nonzero drift jump probabilities in dimensions d 3 the method of proof is by martingale techniques which rely on the fact that symmetric random walks are transient in high dimensions c 2000 john wiley sons inc

the steiglitz mcbride identification algorithm revisited convergence analysis and accuracy aspects the convergence and accuracy properties of the steiglitz and mcbride identification method are examined the analysis is valid for a sufficiently large number of data it is shown that the method can converge to the true parameter vector only when the additive output noise is white in that case the method is proved to be locally convergent to the true parameters the global convergence properties are also investigated it is pointed out that the method is not always globally convergent some sufficient conditions guaranteeing global convergence are given assuming convergence takes place the estimates are shown to be asymptotically gaussian distributed an explicit expression is given for their asymptotic covariance matrix

parameter estimation of exponentially damped sinusoids using higher order statistics a new approach for the estimation of the parameters of exponentially damped sinusoids is introduced based on third or fourth order statistics of the observation signal the method may be seen as an extension of the minimum norm principal eigenvectors method to higher order statistics domains the strong points and limitations of the method are discussed as well as sufficient conditions for the existence of the solution the utilization of the method in the case of finite length signals in the presence of additive gaussian noise white or colored is addressed monte carlo simulations demonstrate the effectiveness of the new method when the additive noise is colored gaussian with unknown autocorrelation sequence for different signal to noise ratios and a single data record the case of an ensemble of data records is studied when the exponentially damped sinusoids are assumed to have random phase

performance of modularity maximization in practical contexts although widely used in practice the behavior and accuracy of the popular module identification technique called modularity maximization is not well understood in practical contexts here we present a broad characterization of its performance in such situations first we revisit and clarify the resolution limit phenomenon for modularity maximization second we show that the modularity function q exhibits extreme degeneracies it typically admits an exponential number of distinct high scoring solutions and typically lacks a clear global maximum third we derive the limiting behavior of the maximum modularity q max for one model of infinitely modular networks showing that it depends strongly both on the size of the network and on the number of modules it contains finally using three real world metabolic networks as examples we show that the degenerate solutions can fundamentally disagree on many but not all partition properties such as the composition of the largest modules and the distribution of module sizes these results imply that the output of any modularity maximization procedure should be interpreted cautiously in scientific contexts they also explain why many heuristics are often successful at finding high scoring partitions in practice and why different heuristics can disagree on the modular structure of the same network we conclude by discussing avenues for mitigating some of these behaviors such as combining information from many degenerate solutions or using generative models

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

linear prediction approach for efficient frequency estimation of multiple real sinusoids algorithms and analyses based on the linear prediction property of sinusoidal signals two constrained weighted least squares frequency estimators for multiple real sinusoids embedded in white noise are proposed in order to achieve accurate frequency estimation the first algorithm uses a generalized unit norm constraint while the second method employs a monic constraint the weighting matrices in both methods are a function of the frequency parameters and are obtained in an iterative manner for the case of a single real tone with sufficiently large data samples both estimators provide nearly identical frequency estimates and their performance approaches crame spl acute r rao lower bound crlb for white gaussian noise before the threshold effect occurs algorithms for closed form single tone frequency estimation are also devised computer simulations are included to corroborate the theoretical development and to contrast the estimator performance with the crlb for different frequencies observation lengths and signal to noise ratio snr conditions

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

hydrodynamical limit for a hamiltonian system with weak noise starting from a general hamiltonian system with superstable pairwise potential we construct a stochastic dynamics by adding a noise term which exchanges the momenta of nearby particles we prolve that in the scaling limit the time conserved quantities energy momenta and density satisfy the euler equation of conservation laws up to a fixed timet provided that the euler equation has a smooth solution with a given initial data up to timet the strength of the noise term is chosen to be very small but nonvanishing so that it disappears in the scaling limit

algorithms of maximum likelihood data clustering with applications abstract we address the problem of data clustering by introducing an unsupervised parameter free approach based on maximum likelihood principle starting from the observation that data sets belonging to the same cluster share a common information we construct an expression for the likelihood of any possible cluster structure the likelihood in turn depends only on the pearson s coefficient of the data we discuss clustering algorithms that provide a fast and reliable approximation to maximum likelihood configurations compared to standard clustering methods our approach has the advantages that i it is parameter free ii the number of clusters need not be fixed in advance and iii the interpretation of the results is transparent in order to test our approach and compare it with standard clustering algorithms we analyze two very different data sets time series of financial market returns and gene expression data we find that different maximization algorithms produce similar cluster structures whereas the outcome of standard algorithms has a much wider variability

extension of hoshen kopelman algorithm to non lattice environments abstract we extend the hoshen kopelman hk algorithm for cluster labeling to non lattice environments where sites are placed at random at non lattice points this extension is useful for continuum systems and disordered networks our extension of the hk algorithm relies on several data structures that describe network connectivity regardless of its dimensionality just as for the classic hk algorithm on lattices our extension is completed in a single pass through the sites of the network and cluster relabeling operates on a vector whose size is much smaller than the size of the network our extension of the hk algorithm works for any environment lattice or non lattice of any dimensionality type sites bonds or both and with arbitrary connectivity between the sites the proposed extension is illustrated through a simple network consisting of 16 sites and 24 bonds and applied to a complex network extracted from a 3d micro focused x ray ct image of bentheimer sandstone consisting of 3677 sites and 8952 bonds

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

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

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

successive normalization of rectangular arrays standard statistical techniques often require transforming data to have mean 0 and standard deviation 1 typically this process of standardization or normalization is applied across subjects when each subject produces a single number high throughput genomic and financial data often come as rectangular arrays where each coordinate in one direction concerns subjects who might have different status case or control say and each coordinate in the other designates outcome for a specific feature for example gene polymorphic site or some aspect of financial profile it may happen when analyzing data that arrive as a rectangular array that one requires both the subjects and features to be on the same footing thus there may be a need to standardize across rows and columns of the rectangular matrix there arises the question as to how to achieve this double normalization we propose and investigate the convergence of what seems to us a natural approach to successive normalization which we learned from colleague bradley efron we also study the implementation of the method on simulated data and also on data that arose from scientific experimentation

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

toward the fourier law for a weakly interacting anharmonic crystal for a system of weakly interacting anharmonic oscillators perturbed by an energy preserving stochastic dynamics we prove an autonomous stochastic evolution for the energies at large time scale with respect to the coupling parameter it turn out that this macroscopic evolution is given by the so called conservative non gradient ginzburg landau system of stochastic differential equations the proof exploits hypocoercivity and hypoellipticity properties of the uncoupled dynamics

data clustering using a model granular magnet we present a new approach to clustering based on the physical properties of an inhomogeneous ferromagnet no assumption is made regarding the underlying distribution of the data we assign a potts spin to each data point and introduce an interaction between neighboring points whose strength is a decreasing function of the distance between the neighbors this magnetic system exhibits three phases at very low temperatures it is completely ordered all spins are aligned at very high temperatures the system does not exhibit any ordering and in an intermediate regime clusters of relatively strongly coupled spins become ordered whereas different clusters remain uncorrelated this intermediate phase is identified by a jump in the order parameters the spin spin correlation function is used to partition the spins and the corresponding data points into clusters we demonstrate on three synthetic and three real data sets how the method works detailed comparison to the performance of other techniques clearly indicates the relative success of our method

nonequilibrium statistical mechanics of hamiltonian rotators with alternated spins we consider a finite region of a d dimensional lattice of nonlinear hamiltonian rotators where neighbouring rotators have opposite alternated spins and are coupled by a small potential of size varepsilon a a ge 1 2 we weakly stochastically perturb the system in such a way that each rotator interacts with its own stochastic thermostat with a force of order varepsilon then we introduce action angle variables for the system of uncoupled rotators varepsilon 0 and note that the sum of actions over all nodes is conserved by the purely hamiltonian dynamics of the system with varepsilon 0 we investigate the limiting as varepsilon rightarrow 0 dynamics of actions for solutions of the varepsilon perturbed system on time intervals of order varepsilon 1 it turns out that the limiting dynamics is governed by a certain autonomous stochastic equation for the vector of actions this equation has a completely non hamiltonian nature this is a consequence of the fact that the system of rotators with alternated spins do not have resonances of the first order the varepsilon perturbed system has a unique stationary measure widetilde mu varepsilon and is mixing any limiting point of the family widetilde mu varepsilon of stationary measures as varepsilon rightarrow 0 is an invariant measure of the system of uncoupled integrable rotators there are plenty of such measures however it turns out that only one of them describes the limiting dynamics of the varepsilon perturbed system we prove that a limiting point of widetilde mu varepsilon is unique its projection to the space of actions is the unique stationary measure of the autonomous equation above which turns out to be mixing and its projection to the space of angles is the normalized lebesque measure on the torus mathbb t n the results and convergences which concern the behaviour of actions on long time intervals are uniform in the number n of rotators those concerning the stationary measures are uniform in n in some natural cases

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

exact maximum likelihood parameter estimation of superimposed exponential signals in noise a unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise encompassing both the time series and the array problems is presented an exact expression for the ml criterion is derived in terms of the linear prediction polynomial of the signal and an iterative algorithm for the maximization of this criterion is presented the algorithm is equally applicable in the case of signal coherence in the array problem simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques the algorithm is similar to those independently derived by kumaresan et al in addition to its practical value the present formulation is used to interpret previous methods such as prony s pisarenko s and modifications thereof

the most efficient implementation of the iqml algorithm the work by clark and scharf 1992 showed a new implementation of the iqml iterative quadratic maximum likelihood algorithm which requires at each iteration computational flops of order n sup 2 where n is the dimension of signal vector or length of data sequence they also indicated that the implementation of other related algorithms such as the steiglitz mcbride 1965 algorithm would also require order n sup 2 computations the present author gives a better way of implementation which requires computational flops of the order n this better way of implementation is shown in detail for the iqml algorithm following the same idea shown in the present paper one can also straightforwardly design the order n implementation of the steiglitz mcbride algorithm the present implementation is also the most efficient in that no implementation can be made less than order n sup 2

estimation of parameters of exponentially damped sinusoids using fast maximum likelihood estimation with application to nmr spectroscopy data we present fast maximum likelihood fml estimation of parameters of multiple exponentially damped sinusoids the fml algorithm was motivated by the desire to analyze data that have many closely spaced components such as the nmr spectroscopy data of human blood plasma the computational efficiency of fml lies in reducing the multidimensional search involved in ml estimation into multiple 1 d searches this is achieved by using our knowledge of the shape of the compressed likelihood function clf in the parameter space the proposed fml algorithm is an iterative method that decomposes the original data into its constituent signal components and estimates the parameters of the individual components efficiently using our knowledge of the shape of the clf the other striking features of the proposed algorithm are that it provides procedures for initialization has a fast converging iteration stage and makes use of the information extracted in preliminary iterations to segment the data suitably to increase the effective signal to noise ratio snr the computational complexity and the performance of the proposed algorithm are compared with other existing methods such as those based on linear prediction kiss iqml alternating projections ap and expectation maximization em

green kubo formula for weakly coupled systems with noise we study the green kubo formula kappa varepsilon varsigma for the heat conductivity of an infinite chain of d dimensional finite systems cells coupled by a smooth nearest neighbor potential varepsilon v the uncoupled systems evolve according to hamiltonian dynamics perturbed stochastically by an energy conserving noise of strength varsigma noting that kappa varepsilon varsigma exists and is finite whenever varsigma 0 we are interested in what happens when the strength of the noise varsigma to 0 for this we start in this work by formally expanding kappa varepsilon varsigma in a power series in varepsilon kappa varepsilon varsigma varepsilon 2 sum n geq 2 varepsilon n 2 kappa n varsigma and investigating the formal equations satisfied by kappa n varsigma we show in particular that kappa 2 varsigma is well defined when no pinning potential is present and coincides formally with the heat conductivity obtained in the weak coupling van hove limit where time is rescaled as varepsilon 2 t for the cases where the latter has been established liverani and olla in jams 25 555 583 2012 dolgopyat and liverani in commun math phys 308 201 225 2011 for one dimensional systems we investigate kappa 2 varsigma as varsigma to 0 in three cases the disordered harmonic chain the rotor chain and a chain of strongly an harmonic oscillators moreover we formally identify kappa 2 varsigma with the conductivity obtained by having the chain between two reservoirs at temperature t and t delta t in the limit delta t to 0 n to infty varepsilon to 0

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

unsupervised spike detection and sorting with wavelets and superparamagnetic clustering this study introduces a new method for detecting and sorting spikes from multiunit recordings the method combines the wavelet transform which localizes distinctive spike features with superparamagnetic clustering which allows automatic classification of the data without assumptions such as low variance or gaussian distributions moreover an improved method for setting amplitude thresholds for spike detection is proposed we describe several criteria for implementation that render the algorithm unsupervised and fast the algorithm is compared to other conventional methods using several simulated data sets whose characteristics closely resemble those of in vivo recordings for these data sets we found that the proposed algorithm outperformed conventional methods

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

model for correlations in stock markets we propose a group model for correlations in stock markets in the group model the markets are composed of several groups within which the stock price fluctuations are correlated the spectral properties of empirical correlation matrices reported recently are well understood from the model it provides the connection between the spectral properties of the empirical correlation matrix and the structure of correlations in stock markets

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

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

existence of nonequilibrium steady state for a simple model of heat conduction this paper contains rigorous results for a simple stochastic model of heat conduction similar to the kmp knipnis marchiori presutti model but with possibly energy dependent interaction rates we prove the existence and uniqueness of nonequilibrium steady states their relation to lebesgue measure and exponential convergence to steady states from suitable initial conditions

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

an efficient approach for two dimensional parameter estimation of a single tone in this paper parameter estimation of a two dimensional 2 d single damped real complex tone in the presence of additive white gaussian noise is addressed by utilizing the rank one property of the 2 d noise free data matrix the damping factor and frequency for each dimension are estimated in a separable manner from the principal left and right singular vectors according to an iterative weighted least squares procedure the remaining parameters are then obtained straightforwardly using standard least squares the biases as well as variances of the damping factor and frequency estimates are also derived which show that they are approximately unbiased and their performance achieves crame r rao lower bound crlb at sufficiently large signal to noise ratio snr and or data size conditions we refer the proposed approach to as principal singular vector utilization for modal analysis puma which performs estimation in a fast and accurate manner the development and analysis can easily be adapted for a tone which is undamped in at least one dimension furthermore comparative simulation results with several conventional 2 d estimators and crlb are included to corroborate the theoretical development of the puma approach as well as to demonstrate its superiority

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

identification of clusters of companies in stock indices via potts super paramagnetic transitions the clustering of companies within a specic stock market index is studied by means of super paramagnetic transitions of an appropriate q state potts model where the spins correspond to companies and the interactions are functions of the correlation coecients determined from the time dependence of the companies individual stock prices the method is a generalization of the clustering algorithm by domany et al to the case of anti ferromagnetic interactions corresponding to anti correlations for the dow jones industrial average where no anti correlations were observed in the investigated time period the previous results obtained by dierent tools were well reproduced for the standard poor s 500 where anti correlations occur repulsion between stocks modify the cluster structure c 2000 elsevier science b v all rights reserved stock market indices like the dow jones dj or standard poor s 500 s p 500 are used as indicators of the status of the markets they are averaged values of a dierent number of selected companies indicative of the economy of a given market it is of both theoretical and practical importance to analyze how individual contributions to the average behave the customary approach in the nancial literature focuses on the investigation of the properties of the covariance matrix here we take a dierent approach aiming to identify the presence of a hierarchical structure inside the set of stocks simultaneously traded in a market the identication of the hierarchy of clusters is of central importance both from the point of view of understanding the dynamics of

nonlinear diffusion limit for a system with nearest neighbor interactions we consider a system of interacting diffusions the variables are to be thought of as charges at sites indexed by a periodic one dimensional lattice the diffusion preserves the total charge and the interaction is of nearest neighbor type with the appropriate scaling of lattice spacing and time a nonlinear diffusion equation is derived for the time evolution of the macroscopic charge density

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

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

fast super paramagnetic clustering abstract we map stock market interactions to spin models to recover their hierarchical structure using a simulated annealing based super paramagnetic clustering spc algorithm this is directly compared to a modified implementation of a maximum likelihood approach we call fast super paramagnetic clustering f spc the methods are first applied to standard toy test case problems and then to a data set of 447 stocks traded on the new york stock exchange nyse over 1249 days the signal to noise ratio of stock market correlation matrices is briefly considered our result recover approximately clusters representative of standard economic sectors and mixed ones whose dynamics shine light on the adaptive nature of financial markets and raise concerns relating to the effectiveness of industry based static financial market classification in the world of real time data analytics a key result is that we show that f spc maximum likelihood solutions converge to ones found within the super paramagnetic phase where the entropy is maximum and those solutions are qualitatively better for high dimensionality data sets

limits of random differential equations on manifolds consider a family of random ordinary differential equations on a manifold driven by vector fields of the form sum ky k alpha k z t epsilon omega where y k are vector fields epsilon is a positive number z t epsilon is a 1 over epsilon mathcal l 0 diffusion process taking values in possibly a different manifold alpha k are annihilators of mathrm ker mathcal l 0 under hormander type conditions on mathcal l 0 we prove that as epsilon approaches zero the stochastic processes y t over epsilon epsilon converge weakly and in the wasserstein topologies we describe this limit and give an upper bound for the rate of the convergence

a combined order selection and parameter estimation algorithm for undamped exponentials we propose an approximate maximum likelihood parameter estimation algorithm combined with a model order estimator for superimposed undamped exponentials in noise the algorithm combines the robustness of fourier based estimators and the high resolution capabilities of parametric methods we use a combination of a wald 1945 statistic and a map test for order selection and initialize an iterative maximum likelihood descent algorithm recursively based on estimates at higher candidate model orders experiments using simulated data and synthetic radar data demonstrate improved performance over mdl map and aic in places of practical interest

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

on the complexity of iqml algorithms the authors study the computational complexity of two methods for solving least squares and maximum likelihood modal analysis problems in particular they consider the steiglitz mcbride and iterative quadratic maximum likelihood iqml algorithms j h mcclellan and d lee ibid vol 39 no 2 p 509 12 1991 have shown the iterations of the two methods to be equivalent however they suggest that the steiglitz mcbride algorithm may be computationally preferable a method for reducing the dimension of the matrix inversion required at each iteration of iqml is provided the resulting reduction in the computation makes the computational complexity of iqml commensurate with that of the steiglitz mcbride algorithm

employing symmetry constraints for improved frequency estimation by eigenanalysis methods the problem of extracting sinusoid signals from noisy observations made at equally spaced times is considered eigenanalysis methods such as pisarenko s method and the extended prony method find the eigenvector with minimum eigenvalue of a suitably chosen matrix and then obtain the complex sinusoids as the roots of the polynomial that has the components of the eigenvector as coefficients for the sinusoids to be undamped it is necessary that the roots lie on the unit circle and hence that the eigenvector be conjugate symmetric it is shown how this symmetry constraint can be incorporated into eigenanalysis estimation methods in a routine way the practical importance of the constraint is investigated by cramer rao variance bound calculations and by simulation the following conclusions are made 1 the symmetry constraint is straightforward to implement and reduces the amount of computation required 2 the relative reduction in variance of the constrained over the unconstrained frequency estimators

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

parametric identification using weighted null space fitting in identification of dynamical systems the prediction error method with a quadratic cost function provides asymptotically efficient estimates under gaussian noise but in general it requires solving a nonconvex optimization problem which may imply convergence to nonglobal minima an alternative class of methods uses a nonparametric model as intermediate step to obtain the model of interest weighted null space fitting wnsf belongs to this class starting with the estimate of a nonparametric arx model with least squares then the reduction to a parametric model is a multistep procedure where each step consists of the solution of a quadratic optimization problem which can be obtained with weighted least squares the method is suitable for both open and closed loop data and can be applied to many common parametric model structures including output error armax and box jenkins the price to pay is the increase of dimensionality in the nonparametric model which needs to tend to infinity as function of the sample size for certain asymptotic statistical properties to hold in this paper we conduct a rigorous analysis of these properties namely consistency and asymptotic efficiency also we perform a simulation study illustrating the performance of wnsf and identify scenarios where it can be particularly advantageous compared with state of the art methods

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

comparative study of iqml and mode direction of arrival estimators we present a comparative study of using the iterative quadratic maximum likelihood iqml and the method of direction estimation mode for direction of arrival doa estimation of narrowband incident signals with a uniform linear array the conditions for local convergence and the theoretical performance of iqml are derived although the doa estimates obtained via mode are asymptotically statistically efficient we show that those obtained via iqml are almost always inconsistent and have much larger mean squared errors we also show that the amount of computations required by iqml is usually much larger than that required by mode especially for low signal to noise ratio snr and a large number of snapshots

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

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

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

asymptotic localization of energy in nondisordered oscillator chains we study two popular one dimensional chains of classical anharmonic oscillators the rotor chain and a version of the discrete nonlinear schrodinger chain we assume that the interaction between neighboring oscillators controlled by the parameter 0 is small we rigorously establish that the thermal conductivity of the chains has a nonperturbative origin with respect to the coupling constant and we provide strong evidence that it decays faster than any power law in as 0 the weak coupling regime also translates into a high temperature regime suggesting that the conductivity vanishes faster than any power of the inverse temperature to our knowledge it is the first time that a clear connection has been established between kam like phenomena and thermal conductivity 2015 wiley periodicals inc

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 analysis of cross correlations in an emerging market abstract we apply random matrix theory to compare correlation matrix estimators c obtained from emerging market data the correlation matrices are constructed from 10 years of daily data for stocks listed on the johannesburg stock exchange jse from january 1993 to december 2002 we test the spectral properties of c against random matrix predictions and find some agreement between the distributions of eigenvalues nearest neighbour spacings distributions of eigenvector components and the inverse participation ratios for eigenvectors we show that interpolating both missing data and illiquid trading days with a zero order hold increases agreement with rmt predictions for the more realistic estimation of correlations in an emerging market we suggest a pairwise measured data correlation matrix for the data set used this approach suggests greater temporal stability for the leading eigenvectors an interpretation of eigenvectors in terms of trading strategies is given as opposed to classification by economic sectors

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

data clustering and noise undressing of correlation matrices we discuss an approach to data clustering we find that maximum likelihood leads naturally to an hamiltonian of potts variables that depends on the correlation matrix and whose low temperature behavior describes the correlation structure of the data for random uncorrelated data sets no correlation structure emerges on the other hand for data sets with a built in cluster structure the method is able to detect and recover efficiently that structure finally we apply the method to financial time series where the low temperature behavior reveals a nontrivial clustering