nonparametric neural network estimation of lyapunov exponents and a direct test for chaos this paper derives the asymptotic distribution of the nonparametric neural network estimator of the lyapunov exponent in a noisy system positivity of the lyapunov exponent is an operational definition of chaos we introduce a statistical framework for testing the chaotic hypothesis based on the estimated lyapunov exponents and a consistent variance estimator a simulation study to evaluate small sample performance is reported we also apply our procedures to daily stock return data in most cases the hypothesis of chaos in the stock return series is rejected at the 1 level with an exception in some higher power transformed absolute returns

the cramer rao bound for estimating a sparse parameter vector the goal of this contribution is to characterize the best achievable mean squared error mse in estimating a sparse deterministic parameter from measurements corrupted by gaussian noise to this end an appropriate definition of bias in the sparse setting is developed and the constrained cramer rao bound crb is obtained this bound is shown to equal the crb of an estimator with knowledge of the support set for almost all feasible parameter values consequently in the unbiased case our bound is identical to the mse of the oracle estimator combined with the fact that the crb is achieved at high signal to noise ratios signal to noise ratio snrs by the maximum likelihood technique our result provides a new interpretation for the common practice of using the oracle estimator as a gold standard against which practical approaches are compared

on consistent nonparametric order determination and chaos summary we give a brief introduction to deterministic chaos and a link between chaotic deterministic models and stochastic time series models we argue that it is often natural to determine the embedding dimension in a noisy environment first in any systematic study of chaos setting the stochastic models within the framework of non linear autoregression we introduce the notion of a generalized partial autocorrelation and an order we approach the estimation of the embedding dimension via order determination of an unknown non linear autoregression by cross validation and give justification by proving its consistency under global boundedness as a by product we provide a theoretical justification of the final prediction error approach of auestad and tj0stheim some illustrations based on the henon map and several real data sets are given the bias of the residual sum of squares as essentially a noise variance estimator is quantified

a single blind controlled competition among tests for nonlinearity and chaos interest has been growing in testing for nonlinearity or chaos in economic data but much controversy has arisen about the available results this paper explores the reasons for these empirical difficulties we designed and ran a single blind controlled competition among five highly regarded tests for nonlinearity or chaos with ten simulated data series the data generating mechanisms include linear processes chaotic recursions and nonchaotic stochastic processes and both large and small samples were included in the experiment the data series were produced in a single blind manner by the competition manager and sent by e mail without identifying information to the experiment participants each such participant is an acknowledged expert in one of the tests and has a possible vested interest in producing the best possible results with that one test the results of this competition provide much surprising information about the power functions of some of the best regarded tests for nonlinearity or noisy chaos

time delay estimation from low rate samples a union of subspaces approach time delay estimation arises in many applications in which a multipath medium has to be identified from pulses transmitted through the channel previous methods for time delay recovery either operate on the analog received signal or require sampling at the nyquist rate of the transmitted pulse in this paper we develop a unified approach to time delay estimation from low rate samples this problem can be formulated in the broader context of sampling over an infinite union of subspaces although sampling over unions of subspaces has been receiving growing interest previous results either focus on unions of finite dimensional subspaces or finite unions the framework we develop here leads to perfect recovery of the multipath delays from samples of the channel output at the lowest possible rate even in the presence of overlapping transmitted pulses and allows for a variety of different sampling methods the sampling rate depends only on the number of multipath components and the transmission rate but not on the bandwidth of the probing signal this result can be viewed as a sampling theorem over an infinite union of infinite dimensional subspaces by properly manipulating the low rate samples we show that the time delays can be recovered using the well known esprit algorithm combining results from sampling theory with those obtained in the context of direction of arrival estimation we develop sufficient conditions on the transmitted pulse and the sampling functions in order to ensure perfect recovery of the channel parameters at the minimal possible rate

multivariate smoothing spline functions given data z i g t i varepsilon i 1 leqq i leqq n where g is the unknown function the t i are known d dimensional variables in a domain omega and the varepsilon i are i

detecting nonlinear dynamics in spatio temporal systems examples from ecological models mathematical models of marine populations exhibit chaotic dynamics however we hypothesize that in moving water eulerian sampling of spatially heterogeneous populations may obscure any deterministic signal beyond the resolving capabilities of presently available nonlinear signal processing techniques to examine this hypothesis we created two spatio temporal models of population dynamics to caricature actual ocean sampling limitations we sampled the model output in two ways random walks to simulate eulerian sampling and spatial averages to simulate population measurements from finite volumes results indicate that the ability to identify underlying nonlinear dynamics quickly degrades as the step size of a random walk sampling increases on the other hand the analysis techniques used are more robust in the face of spatial averaging

nonuniform sampling and reconstruction in shift invariant spaces this article discusses modern techniques for nonuniform sampling and reconstruction of functions in shift invariant spaces it is a survey as well as a research paper and provides a unified framework for uniform and nonuniform sampling and reconstruction in shift invariant subspaces by bringing together wavelet theory frame theory reproducing kernel hilbert spaces approximation theory amalgam spaces and sampling inspired by applications taken from communication astronomy and medicine the following aspects will be emphasized a the sampling problem is well defined within the setting of shift invariant spaces b the general theory works in arbitrary dimension and for a broad class of generators c the reconstruction of a function from any sufficiently dense nonuniform sampling set is obtained by efficient iterative algorithms these algorithms converge geometrically and are robust in the presence of noise d to model the natural decay conditions of real signals and images the sampling theory is developed in weighted l p spaces

the stability of electricity prices estimation and inference of the lyapunov exponents abstract the aim of this paper is to illustrate how the stability of a stochastic dynamic system is measured using the lyapunov exponents specifically we use a feedforward neural network to estimate these exponents as well as asymptotic results for this estimator to test for unstable chaotic dynamics the data set used is spot electricity prices from the nordic power exchange market nord pool and the dynamic system that generates these prices appears to be chaotic in one case since the null hypothesis of a non positive largest lyapunov exponent is rejected at the 1 per cent level

a compact cramer rao bound expression for parametric estimation of superimposed signals the problem of parameter estimation of superimposed signals in white gaussian noise is considered closed form expressions of the cramer rao bound for real or complex signals with vector parameters are derived extending recent results by p stoica and a nehorai 1989

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

classification of binary textures using the 1 d boolean model the one dimensional 1 d boolean model is used to calculate features for the description of binary textures each two dimensional 2 d texture is converted into several 1 d strings by scanning it according to raster vertical horizontal or hilbert sequences several different probability distributions for the segment lengths created this way are used to model their distribution therefore each texture is described by a set of boolean models classification is performed by calculating the overlapping probability between corresponding models the method is evaluated with the help of 32 different binary textures and the pros and cons of the approach are discussed

pattern generation using likelihood inference for cellular automata cellular automata are discrete dynamical systems which evolve on a discrete grid recent studies have shown that cellular automata with relatively simple rules can produce highly complex patterns we develop likelihood based methods for estimating rules of cellular automata aimed at the re generation of observed regular patterns under noisy data our approach is equivalent to estimating the local map of a stochastic cellular automaton direct computations of the maximum likelihood estimates are possible for regular binary patterns the likelihood formulation of the problem is congenial with the use of the minimum description length principle as a model selection tool we illustrate our method with a series of examples using binary images

looking for systematic approach to select chaos tests abstract this paper will consider the mathematical definition of chaos in sense of devaney in order to select appropriate chaos tests the tests chosen according to investigate the properties mentioned in the definition in fact these are prerequisites of chaoticity either it will be represented that sensitivity dependence on initial conditions is not equivalent to chaos although some researchers considering it hence it is implied that checking all of the properties mentioned in the definition are required to establish chaos as our case study some sample stocks were selected from tehran stock exchange tse and the chosen tests implemented on their returns time series incoming results indicate that the returns series are not chaotic although their largest lyapunov exponent are positive in fact there is no evidence of unstable periodic orbits in the returns series as one of the chaos prerequisites while by using the bds test and some autoregressive models as filters some evidence of nonlinearity has been observed in these series so using chaos mathematical definition prevents us to misleading results about chaoticity

signal enhancement a composite property mapping algorithm a signal enhancement algorithm is developed that seeks to recover a signal from noise contaminated distorted measurements made on that signal this object is achieved by utilizing a set of properties which the signal is known or is hypothesized as possessing the measured signal is modified to the smallest degree necessary to sequentially possess each of the individual properties conditions for the algorithm s convergence are established in which the primary requirement is that a composite property mapping be closed this is a relatively unrestricted condition in comparison to that required of most existing signal enhancement algorithms

subspace based channel estimation for code division multiple access communication systems we consider the estimation of channel parameters for code division multiple access cdma communication systems operating over channels with either single or multiple propagation paths the multiuser channel estimation problem is decomposed into a series of single user problems through a subspace based approach by exploiting the eigenstructure of the received signal s sample correlation matrix the observation space can be partitioned into a signal subspace and a noise subspace without prior knowledge of the unknown parameters the channel estimate is formed by projecting a given user s spreading waveform into the estimated noise subspace and then either minimizing the likelihood or minimizing the euclidean norm of this projection both of these approaches yield algorithms which are near far resistant and do not require a preamble

fri sampling on structured nonuniform grids application to super resolved optical imaging the annihilating filter forms the core of many state of the art techniques for finite rate of innovation fri signal reconstruction and spectral estimation in its standard manifestation the annihilating filter is setup in the discrete time domain with uniform sampling and is used to estimate the parameters of a signal that is expressible as a sum of exponentials in this paper we consider annihilation in the continuous domain using translation operators codenamed opera and show that fri signals can be reconstructed using measurements taken on a structured nonuniform sampling sns grid the parameters are estimable uniquely under certain conditions the transition from uniform sampling to sns comes with specific advantages the measurements could be made in bursts from high signal to noise ratio snr regions which directly enhances parameter estimation accuracy the sampling interval could be made larger than in the uniform case which leads to a reduction in the mean squared error mse and closely spaced exponential parameters could be resolved better we present theoretical developments related to the sns grid and demonstrate accurate parameter estimation monte carlo performance analysis in the presence of noise shows that the opera with the sns approach yields a significant decrease in mse up to 10 to 20 db for certain snr ranges compared with the uniform sampling scenario considering an application to frequency domain optical coherence tomography we show that the proposed methodology results in higher resolution and higher reconstruction accuracy than the standard techniques

the asymptotic distribution of nonparametric estimates of the lyapunov exponent for stochastic time series this paper derives the asymptotic distribution of a smoothing based estimator of the lyapunov exponent for a stochastic time series under two general scenarios in the first case we are able to establish root t consistency and asymptotic normality while in the second case which is more relevant for chaotic processes we are only able to establish asymptotic normality at a slower rate of convergence we provide consistent confidence intervals for both cases we apply our procedures to simulated data

sampling moments and reconstructing signals of finite rate of innovation shannon meets strang fix consider the problem of sampling signals which are not bandlimited but still have a finite number of degrees of freedom per unit of time such as for example nonuniform splines or piecewise polynomials and call the number of degrees of freedom per unit of time the rate of innovation classical sampling theory does not enable a perfect reconstruction of such signals since they are not bandlimited recently it was shown that by using an adequate sampling kernel and a sampling rate greater or equal to the rate of innovation it is possible to reconstruct such signals uniquely these sampling schemes however use kernels with infinite support and this leads to complex and potentially unstable reconstruction algorithms in this paper we show that many signals with a finite rate of innovation can be sampled and perfectly reconstructed using physically realizable kernels of compact support and a local reconstruction algorithm the class of kernels that we can use is very rich and includes functions satisfying strang fix conditions exponential splines and functions with rational fourier transform this last class of kernels is quite general and includes for instance any linear electric circuit we thus show with an example how to estimate a signal of finite rate of innovation at the output of an rc circuit the case of noisy measurements is also analyzed and we present a novel algorithm that reduces the effect of noise by oversampling

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

reduce and boost recovering arbitrary sets of jointly sparse vectors the rapid developing area of compressed sensing suggests that a sparse vector lying in a high dimensional space can be accurately and efficiently recovered from only a small set of nonadaptive linear measurements under appropriate conditions on the measurement matrix the vector model has been extended both theoretically and practically to a finite set of sparse vectors sharing a common sparsity pattern in this paper we treat a broader framework in which the goal is to recover a possibly infinite set of jointly sparse vectors extending existing algorithms to this model is difficult due to the infinite structure of the sparse vector set instead we prove that the entire infinite set of sparse vectors can be recovered by solving a single reduced size finite dimensional problem corresponding to recovery of a finite set of sparse vectors we then show that the problem can be further reduced to the basic model of a single sparse vector by randomly combining the measurements our approach is exact for both countable and uncountable sets as it does not rely on discretization or heuristic techniques to efficiently find the single sparse vector produced by the last reduction step we suggest an empirical boosting strategy that improves the recovery ability of any given suboptimal method for recovering a sparse vector numerical experiments on random data demonstrate that when applied to infinite sets our strategy outperforms discretization techniques in terms of both run time and empirical recovery rate in the finite model our boosting algorithm has fast run time and much higher recovery rate than known popular methods

bayesian texture classification based on contourlet transform and byy harmony learning of poisson mixtures as a newly developed 2 d extension of the wavelet transform using multiscale and directional filter banks the contourlet transform can effectively capture the intrinsic geometric structures and smooth contours of a texture image that are the dominant features for texture classification in this paper we propose a novel bayesian texture classifier based on the adaptive model selection learning of poisson mixtures on the contourlet features of texture images the adaptive model selection learning of poisson mixtures is carried out by the recently established adaptive gradient bayesian ying yang harmony learning algorithm for poisson mixtures it is demonstrated by the experiments that our proposed bayesian classifier significantly improves the texture classification accuracy in comparison with several current state of the art texture classification approaches

assessing nonlinear structures in real exchange rates using recurrence plot strategies purchasing power parity ppp is an important theory at the basis of a large number of economic models however the implication derived from the theory that real exchange rates must follow stationary processes is not conclusively supported by empirical studies in a recent paper serletis and gogas appl finance econ 10 2000 615 show evidence of deterministic chaos in several oecd exchange rates as a consequence ppp rejections could be spurious in this work we follow a two stage testing procedure to test for nonlinearities and chaos in real exchange rates using a new set of techniques designed by webber and zbilut j appl physiol 76 1994 965 called recurrence quantification analysis rqa our conclusions differ slightly from serletis and gogas appl finance econ 10 2000 615 but they are also supportive of chaos for some exchange rates

on unique localization of multiple sources by passive sensor arrays necessary and sufficient conditions are derived for the unique localization of narrowband sources having the same known center frequency by passive sensor arrays the conditions specify the maximum number of sources that can be uniquely localized by a general array that satisfies some mild geometric constraints the conditions are expressed in terms of the number of sensors and the rank of the correlation matrix of the sources two different conditions are presented the first guarantees uniqueness for every batch of sampled data the second which is weaker guarantees uniqueness for almost every batch of sampled data with the exception of a set of batches of measure zero it is shown that a condition that is slightly weaker than the second one is also necessary

quantifying the influence of initial values on non linear prediction motivated by the m step ahead prediction problem in non linear time series a brief sketch of stochastic chaotic systems is provided the accuracy of the prediction depends on the initial value which is a typical feature of non linear but not necessarily chaotic models however if the model is chaotic small noise can be amplified very quickly through time evolution at some initial values thereby decreasing dramatically the reliability of the prediction further if the model is chaotic small shifts in some initial values can lead to considerable errors in prediction which can be monitored by the newly defined lyapunov like indices for the nonparametric predictor constructed by the locally linear regression method the mean squared error may be decomposed into two parts the conditional variance and the divergence resulting from a small shift in initial values the decomposition also holds for more general predictors a consistent estimator of the lyapunov like index is also constructed by the locally linear regression method both simulated and real data are used as illustrations

estimating a function from ergodic samples with additive noise we study the problem of estimating an unknown function from ergodic samples corrupted by additive noise it is shown that one can consistently recover an unknown measurable function in this setting if the one dimensional 1 d distribution of the samples is comparable to a known reference distribution and the noise is independent of the samples and has known mixing rates the estimates are applied to deterministic sampling schemes in which successive samples are obtained by repeatedly applying a fixed map to a given initial vector and it is then shown how the estimates can be used to reconstruct an ergodic transformation from one of its trajectories

new resampling method to assess the accuracy of the maximal lyapunov exponent estimation abstract in this paper we propose a novel method to assess standard errors and confidence intervals for the maximal lyapunov exponent estimated on time continuous chaotic systems the method is based on resampling the original series by means of spline interpolation in the time domain in such a way new time series of increased size are obtained and the sample distribution of the estimators is constructed the method is explained and tested on the basis of computer simulations both for clean and noisy series we give evidence that the distribution of the maximal lyapunov exponent calculated by this method fairly agrees with the one obtained by true series with different initial conditions an empirical criterion for the choice of the parameters of the resampling is also suggested

the structure of finitely generated shift invariant spaces in l2 rd a simple characterization is given of finitely generated subspaces of l2 rd which are invariant under translation by any multi integer and is used to give conditions under which such a space has a particularly nice generating set namely a basis and more than that a basis with desirable properties such as stability orthogonality or linear independence the last property makes sense only for local spaces i e shift invariant spaces generated by finitely many compactly supported functions and special attention is paid to such spaces as an application we prove that the approximation order provided by a given local space is already provided by the shift invariant space generated by just one function with this function constructible as a finite linear combination of the finite generating set for the whole space hence compactly supported this settles a question of some 20 years standing

reduced dimension multiuser detection we present a reduced dimension multiuser detector rd mud structure for synchronous systems that significantly decreases the number of required correlation branches at the receiver front end while still achieving performance similar to that of the conventional matched filter mf bank rd mud exploits the fact that in some wireless systems the number of active users may be small relative to the total number of users in the system hence the ideas of analog compressed sensing may be used to reduce the number of correlators the correlating signals used by each correlator are chosen as an appropriate linear combination of the users spreading waveforms we derive the probability of symbol error when using two methods for recovery of active users and their transmitted symbols the reduced dimension decorrelating rdd detector which combines subspace projection and thresholding to determine active users and sign detection for data recovery and the reduced dimension decision feedback rddf detector which combines decision feedback matching pursuit for active user detection and sign detection for data recovery we derive probability of error bounds for both detectors and show that the number of correlators needed to achieve a small probability of symbol error is on the order of the logarithm of the number of users in the system the theoretical performance results are validated via numerical simulations

sampling signals with finite rate of innovation the authors consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation examples of signals with a finite rate of innovation include streams of diracs e g the poisson process nonuniform splines and piecewise polynomials even though these signals are not bandlimited we show that they can be sampled uniformly at or above the rate of innovation using an appropriate kernel and then be perfectly reconstructed thus we prove sampling theorems for classes of signals and kernels that generalize the classic bandlimited and sinc kernel case in particular we show how to sample and reconstruct periodic and finite length streams of diracs nonuniform splines and piecewise polynomials using sinc and gaussian kernels for infinite length signals with finite local rate of innovation we show local sampling and reconstruction based on spline kernels the key in all constructions is to identify the innovative part of a signal e g time instants and weights of diracs using an annihilating or locator filter a device well known in spectral analysis and error correction coding this leads to standard computational procedures for solving the sampling problem which we show through experimental results applications of these new sampling results can be found in signal processing communications systems and biological systems

paley wiener characterization of kernels for finite rate of innovation sampling exact reconstruction of finite rate of innovation signals can be achieved by employing customized sampling kernels that satisfy certain frequency domain properties we impose compact support in time as an additional constraint considering frequency domain reconstruction we derive conditions for admissible sampling kernels and corresponding sampling rates our constructive kernel design methodology is based on the paley wiener theorem for compactly supported functions the new kernels satisfy generalized strang fix conditions and have specific polynomial modulated exponential reproducing properties unlike exponential splines which have a support that is directly proportional to the number of exponentials they can generate the proposed kernels have a support that is independent of that number to analyze noise robustness we consider a special member of the class that has a sum of modulated splines sms form in the time domain and optimize its parameters to minimize the noise variance the sum of sincs sos kernel reported in the literature is an instance of this construction in noise robustness analysis sms kernels show improvement in mean squared error mse compared with the state of the art alternatives in continuous time noise the improvement in mse is about 2 db for low signal to noise ratio snr and 7 db for high snr in the case of discrete white gaussian noise the mse is lower by as much as 25 db by using a higher order sms kernel compared with the sos kernel for snrs in the range of 10 15 db

a note on noisy chaos summary we prove that under appropriate conditions in a noisy environment an embedded deterministic dynamical system which admits a compact attractor can give rise to an ergodic stochastic system this observation justifies the stochastic set up in the study of deterministic chaos we also clarify a folklore concerning polynomial autoregression chaos and its relationship to statistical non linear time series modelling loosely a chaotic system may be defined as a dynamical system such that starting from points over a certain region all trajectories solutions are uniformly bounded but nearby trajectories initially diverge from each other exponentially and yet the trajec tories have identical statistical properties a trajectory obtained from a chaotic deterministic system thus looks like a realization from some random process the theory of chaos casts the hope that an erratic time series could be fitted with some non linear model so that highly accurate short term forecasts may be available the essential part of the theory of chaos consists of quantifying the chaoticness of a

noisy chaos in intraday financial data evidence from the american index the presence of chaos in financial markets was inconclusive due mainly to test misspecification and data type although noisy chaos was investigated in recent studies it was only explored in daily returns which does not necessary mean that continuous intra daily data will exhibit the same dynamics high level noisy chaos is tested in the standard poor s 500 index returns over 4 different frequencies weekly daily 30 min and 5 min basis the dynamics in all frequencies are non chaotic

nonsingleton fuzzy logic systems theory and application in this paper we present a formal derivation of general nonsingleton fuzzy logic systems nsflss and show how they can be efficiently computed we give examples for special cases of membership functions and inference and we show how an nsfls can be expressed as a nonsingleton fuzzy basis function expansion and present an analytical comparison of the nonsingleton and singleton fuzzy logic systems formulations we prove that an nsfls can uniformly approximate any given continuous function on a compact set and show that our nsfls does a much better job of predicting a noisy chaotic time series than does a singleton fuzzy logic system fls

active high resolution time delay estimation for large bt signals two different high resolution time delay estimation hrtde methods a temporal method and a frequency method specially adapted to large bandwidth duration bt product time resolvent signals are described the performance gain of these methods is shown to be about four times better in comparison with the classical time delay resolution methods the frequency hrtde method is applied to real data obtained from an ocean acoustic experiment although classic methods cannot distinguish close signal components the method presented yields estimates of the delay differences and the attenuation associated with each propagation path

asymmetric pulse modeling for fri sampling we consider sampling and reconstruction of finite rate of innovation fri signals such as a train of pulses where the pulses have varying degrees of asymmetry we address the problem of asymmetry modeling starting from a given symmetric prototype we show that among the class of unitary operators that are linear and invariant to translation and scale the fractional hilbert frh operator is unique for parametrically modeling pulse asymmetry the frh operator is obtained by a trigonometric interpolation between the standard hilbert and identity operators where the interpolation weights are determined by the degree of asymmetry the frh operators are also steerable which allows for estimation of the asymmetry factors in addition to the delays and amplitudes using the high resolution spectral estimation techniques that are used for solving standard fri problems we also develop the discrete counterpart using discrete frh operators and show that all the desirable properties carry over smoothly to the discrete setting as well we derive closed form expressions for the cramer rao bounds and hammersley chapman robbins bound on the variances of the estimators for continuous and discrete parameters respectively experimental results show that the proposed estimators have variances that meet the lower bounds we demonstrate an application of the proposed discrete frh methodology on real electrocardiogram ecg signals in the presence of noise specifically we show how the asymmetry of qrs complexes in various channels of an ecg signal could be modeled accurately

the average posterior variance of a smoothing spline and a consistent estimate of the average squared error a smoothing spline estimator can be interpreted in two ways either as the solution to a variational problem or as the posterior mean when a particular gaussian prior is placed on the unknown regression function the estimate of the average posterior variance of a spline estimate proposed by wahba is shown to converge in probability to a quantity proportional to the expected average squared error this result is established by relating this statistic to a consistent risk estimate based on generalized cross validation

random walk or chaos a formal test on the lyapunov exponent abstract a formal test on the lyapunov exponent is developed to distinguish a random walk model from a chaotic system which is based on the nadaraya watson kernel estimator of the lyapunov exponent the asymptotic null distribution of our test statistic is free of nuisance parameter and simply given by the range of standard brownian motion on the unit interval the test is consistent against the chaotic alternatives a simulation study shows that the test performs reasonably well in finite samples we apply our test to some of the standard macro and financial time series finding no significant empirical evidence of chaos

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

performance analysis of the total least squares esprit algorithm the asymptotic distribution of the estimation error for the total least squares tls version of esprit is derived the application to a uniform linear array is treated in some detail and a generalization of esprit to include row weighting is discussed the cramer rao bound crb for the esprit problem formulation is derived and found to coincide with the asymptotic variance of the tls esprit estimates through numerical examples a comparison of this method to least squares esprit music and root music as well as to the crb for a calibrated array is also presented tls esprit is found to be competitive with the other methods and the performance is close to the calibrated crb for many cases of practical interest for highly correlated signals however the performance deviates significantly from the calibrated crb simulations are included to illustrate the applicability of the theoretical results to a finite number of data

small scale turbulence in the plankton low order deterministic chaos or high order stochasticity abstract almost all regions of the oceans are heavily influenced by the effects of physical processes such as turbulence which in turn influence the distribution and ecology of organisms that occupy these regions there is a real need for additional focus placed on the precise knowledge of both physical and biological processes which is often difficult using basic time series analysis in that way we applied nonlinear analysis techniques to high frequency time series of temperature salinity and phytoplankton concentrations recorded in different hydrodynamical regimes related to tidal forcing in a tidally mixed coastal ecosystem techniques devoted to the identification of low order deterministic chaos cannot find evidence of chaos while a lower dimensionality was identified in low hydrodynamic conditions the results rather suggest stochastic time series with many degrees of freedom no obvious attractor in phase space trajectory lle indistinguishable from zero absence of convergence of the correlation integral we then applied to these data specific multifractal analysis techniques and showed that these time series clearly exhibit high order stochasticity in addition the stochastic structure of purely passive scalars i e temperature and salinity remained invariant while the one of phytoplankton biomass must be regarded as highly structured in time by both hydrodynamic and advective processes

estimation of sparse mimo channels with common support we consider the problem of estimating sparse communication channels in the mimo context in small to medium bandwidth communications as in the current standards for ofdm and cdma communication systems with bandwidth up to 20 mhz such channels are individually sparse and at the same time share a common support set since the underlying physical channels are inherently continuous time we propose a parametric sparse estimation technique based on finite rate of innovation fri principles parametric estimation is especially relevant to mimo communications as it allows for a robust estimation and concise description of the channels the core of the algorithm is a generalization of conventional spectral estimation methods to multiple input signals with common support we show the application of our technique for channel estimation in ofdm uniformly contiguous dft pilots and cdma downlink walsh hadamard coded schemes in the presence of additive white gaussian noise theoretical lower bounds on the estimation of sparse common support scs channel parameters in rayleigh fading conditions are derived finally an analytical spatial channel model is derived and simulations on this model in the ofdm setting show the symbol error rate ser is reduced by a factor 2 0 db of snr to 5 high snr compared to standard non parametric methods e g lowpass interpolation

choosing a range for the amount of smoothing in nonparametric regression abstract most nonparametric regression estimates smooth the observed data in the process of generating a suitable estimate the resulting curve estimate is sensitive to the amount of smoothing introduced and it is important to examine the estimate over a range of smoothing choices an objective way to specify such a range is to estimate the optimal value of the smoothing parameter bandwidth with respect to some loss function and then report a confidence interval for this parameter estimate this interval suggests examining three regression estimates an undersmoothed curve evaluated at the lower endpoint of the confidence interval an oversmoothed curve evaluated at the upper endpoint and also an optimal curve chosen by the data based method this article describes two strategies for constructing such confidence intervals using asymptotic approximations and simulation techniques suppose that data are observed from the model yk f tk ek 1 k n where f is a function that is twice differentia

estimating the lyapunov exponent of a chaotic system with nonparametric regression abstract we discuss procedures based on nonparametric regression for estimating the dominant lyapunov exponent 1 from time series data generated by a nonlinear autoregressive system with additive noise for systems with bounded fluctuations 1 0 is the defining feature of chaos thus our procedures can be used to examine time series data for evidence of chaotic dynamics we show that a consistent estimator of the partial derivatives of the autoregression function can be used to obtain a consistent estimator of 1 the rate of convergence we establish is quite slow a better rate of convergence is derived heuristically and supported by simulations simulation results from several implementations one local thin plate splines and three global neural nets radial basis functions and projection pursuit are presented for two deterministic chaotic systems local splines and neural nets yield accurate estimates of the lyapunov exponent however the spline method is sensitive to the choice of the emb

a theory for sampling signals from a union of subspaces one of the fundamental assumptions in traditional sampling theorems is that the signals to be sampled come from a single vector space e g bandlimited functions however in many cases of practical interest the sampled signals actually live in a union of subspaces examples include piecewise polynomials sparse representations nonuniform splines signals with unknown spectral support overlapping echoes with unknown delay and amplitude and so on for these signals traditional sampling schemes based on the single subspace assumption can be either inapplicable or highly inefficient in this paper we study a general sampling framework where sampled signals come from a known union of subspaces and the sampling operator is linear geometrically the sampling operator can be viewed as projecting sampled signals into a lower dimensional space while still preserving all the information we derive necessary and sufficient conditions for invertible and stable sampling operators in this framework and show that these conditions are applicable in many cases furthermore we find the minimum sampling requirements for several classes of signals which indicates the power of the framework the results in this paper can serve as a guideline for designing new algorithms for various applications in signal processing and inverse problems

spatial size distributions applications to shape and texture analysis this paper proposes new descriptors for binary and gray scale images based on newly defined spatial size distributions ssd the main idea consists of combining a granulometric analysis of the image with a comparison between the geometric covariograms for binary images or the auto correlation function for gray scale images of the original image and its granulometric transformation the usual granulometric size distribution then arises as a particular case of this formulation examples are given to show that in those cases in which a finer description of the image is required the more complex descriptors generated from the ssd could be advantageously used it is also shown that the new descriptors are probability distributions so their intuitive interpretation and properties can be appropriately studied from the probabilistic point of view the usefulness of these descriptors in shape analysis is illustrated by some synthetic examples and their use in texture analysis is studied various cases of ssd and several former methods for texture classification are compared

false determinations of chaos in short noisy time series a method nemg proposed in 1992 for diagnosing chaos in noisy time series with 50 or fewer observations entails fitting the time series with an empirical function which predicts an observation in the series from previous observations and then estimating the rate of divergence or convergence of two nearby trajectories of the function sensitive dependence on initial conditions workers applying nemg have concluded that chaos exists in some natural biological populations however there are insufficient published tests of the reliability of nemg using time series from biologically realistic models with numerous 4 state variables also there are unresolved technical issues for nemg whether or not the data should be detrended removal of linear or quadratic trends before analysis and how long a sampling interval should be used to define the time series we addressed these issues by applying nemg to time series of 50 observations generated by four different chaotic models ranging from simple models of physical systems to a complex ecosystem model we also analyzed output from non chaotic versions of each model previously recommended guidelines for specifying parameters affecting nemg diagnoses of chaos were often ineffective for the models we examined nemg produced high incidences of false determinations of chaos in non chaotic time series and of the absence of chaos in chaotic time series thus the method appears to be unreliable for the circumstances we examined

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

svd based modeling for image texture classification using wavelet transformation this paper introduces a new model for image texture classification based on wavelet transformation and singular value decomposition the probability density function of the singular values of wavelet transformation coefficients of image textures is modeled as an exponential function the model parameter of the exponential function is estimated using maximum likelihood estimation technique truncation of lower singular values is employed to classify textures in the presence of noise kullback leibler distance kld between estimated model parameters of image textures is used as a similarity metric to perform the classification using minimum distance classifier the exponential function permits us to have closed form expressions for the estimate of the model parameter and computation of the kld these closed form expressions reduce the computational complexity of the proposed approach experimental results are presented to demonstrate the effectiveness of this approach on the entire 111 textures from brodatz database the experimental results demonstrate that the proposed approach improves recognition rates using a lower number of parameters on large databases the proposed approach achieves higher recognition rates compared to the traditional subband energy based approach the hybrid imm svm approach and the ggd based approach