measuring the strangeness of strange attractors we study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise the exponent v is closely related to the fractal dimension and the information dimension but its computation is considerably easier its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed algorithms for extracting v from the time series of a single variable are proposed the relations between the various measures of strange attractors and between them and the lyapunov exponents are discussed it is shown that the conjecture of kaplan and yorke for the dimension gives an upper bound for v various examples of finite and infinite dimensional systems are treated both numerically and analytically

filtering and frequency interpretations of singular spectrum analysis new filtering and spectral interpretations of singular spectrum analysis ssa are provided it is shown that the variables reconstructed from diagonal averaging of reduced rank approximations to the trajectory matrix can be obtained from a noncausal convolution filter with zero phase characteristics the reconstructed variables are readily constructed using a two pass filtering algorithm that is well known in the signal processing literature when the number of rows in the trajectory matrix is much larger than number of columns many results reported in the signal processing literature can be used to derive the properties of the resulting filters and their spectra new features of the reconstructed series are revealed using these results two examples are used to illustrate the results derived in this paper

operator theoretic framework for forecasting nonlinear time series with kernel analog techniques abstract kernel analog forecasting kaf alternatively known as kernel principal component regression is a kernel method used for nonparametric statistical forecasting of dynamically generated time series data this paper synthesizes descriptions of kernel methods and koopman operator theory in order to provide a single consistent account of kaf the framework presented here illuminates the property of the kaf method that under measure preserving and ergodic dynamics it consistently approximates the conditional expectation of observables that are acted upon by the koopman operator of the dynamical system and are conditioned on the observed data at forecast initialization more precisely kaf yields optimal predictions in the sense of minimal root mean square error with respect to the invariant measure in the asymptotic limit of large data the presented framework facilitates moreover the analysis of generalization error and quantification of uncertainty extensions of kaf to the construction of conditional variance and conditional probability functions as well as to non symmetric kernels are also shown illustrations of various aspects of kaf are provided with applications to simple examples namely a periodic flow on the circle and the chaotic lorenz 63 system

minimal dynamical systems from pdes using sobolev eigenfunctions abstract a modified karhunen loeve transform is derived using a weighted sobolev norm this approach optimizes the approximation of the higher derivative terms in numerical simulations of partial differential equation and reduces the sizes of the associated system of ordinary differential equations the kuramoto sivashinsky equation is used as an example to demonstrate how a galerkin procedure based on eigenfunctions determined by the sobolev optimality criterion improves the performance of the standard karhunen loeve procedure we present an example of a simulation which required a 19 mode expansion using the k l approach and show how this is reduced to a 7 mode simulation using the sobolev eigenfunctions

breakdown points of affine equivariant estimators of multivariate location and covariance matrices finite sample replacement breakdown points are derived for different types of estimators of multivariate location and covariance matrices the role of various equivariance properties is illustrated the breakdown point is related to a measure of performance based on large deviations probabilities finally we show that one step reweighting preserves the breakdown point

dimension measurement on high dimensional systems abstract using experimental data from a variety of laboratory electrical systems the upper limits on dimension measurement are examined and it is shown that contrary to standard scaling estimates it can be possible to reliably measure correlation dimensions larger than 10 the practical implications of the constraints on such a measurement are examined including the role of statistical errors geometrical artifacts dimension algorithm metric choice and the process power spectrum these ideas are applied to electrical 1 f noise from both macroscopic and microscopic sources to show that it cannot be explained by a deterministic model with fewer than roughly 20 degrees of freedom

convergence of the k 2 entropy for random noises with power law spectra abstract we discuss a counter example to the traditional expectation that stochastic processes lead to a non convergence of the k 2 entropy in computed or measured time series we consider a simple class of colored random noises with power law spectra which have already been shown to generate finite and predictable values of the correlation dimension we show that the k 2 entropy of these random noises converges as well these results imply that the observation of a finite or null value of the k 2 entropy in the analysis of data is not enough to infer that the system is dominated by a deterministic process such as low dimensional chaos

asymptotic behaviour of s estimates of multivariate location parameters and dispersion matrices it is shown under appropriate conditions that rousseeuw s minimum volume estimator and other s estimators of multivariate location and dispersion parameters are consistent under certain differentiability conditions the estimates are asymptotically normally distributed with a norming factor of n 1 2

adaptive l estimation for linear models asymptotically efficient adaptive estimators for the slope parameters of the linear regression model are constructed based upon the regression quantile statistics suggested by koenker and bassett the estimators are natural analogues of the adaptive l estimators of location of sacks but employ kernel density type estimators of the optimal l estimator weight function

detecting spatio temporal modes in multivariate data by entropy field decomposition a new data analysis method that addresses a general problem of detecting spatio temporal variations in multivariate data is presented the method utilizes two recent and complimentary general approaches to data analysis information field theory ift and entropy spectrum pathways esp both methods reformulate and incorporate bayesian theory thus use prior information to uncover underlying structure of the unknown signal unification of esp and ift creates an approach that is non gaussian and non linear by construction and is found to produce unique spatio temporal modes of signal behavior that can be ranked according to their significance from which space time trajectories of parameter variations can be constructed and quantified two brief examples of real world applications of the theory to the analysis of data bearing completely different unrelated nature lacking any underlying similarity are also presented the first example provides an analysis of resting state functional magnetic resonance imaging rsfmri data that allowed us to create an efficient and accurate computational method for assessing and categorizing brain activity the second example demonstrates the potential of the method in the application to the analysis of a strong atmospheric storm circulation system during the complicated stage of tornado development and formation using data recorded by a mobile doppler radar reference implementation of the method will be made available as a part of the quest toolkit that is currently under development at the center for scientific computation in imaging

topology from time series we describe methods for the study of topological properties of the invariant manifolds of experimental dynamical systems we explain how to compute such invariants as the euler characteristic and betti numbers using time series data and suggest a number of potential applications

fundamental limitations for estimating dimensions and lyapunov exponents in dynamical systems we show that values of the correlation dimension estimated over a decade from the grassberger procaccia algorithm cannot exceed the value 2 log10n if n is the number of points in the time series when this bound is saturated it is thus not legitimate to conclude that low dimensional dynamics is present the estimation of lyapunov exponents is also discussed

the trimmed mean in the linear model pour le modele lineaire general a erreurs independantes on propose et on examine les proprietes de grands echantillons d un estimateur du parametre de regression

on a geometric notion of quantiles for multivariate data abstract an extension of the concept of quantiles in multidimensions that uses the geometry of multivariate data clouds has been considered the approach is based on blending as well as generalization of the key ideas used in the construction of spatial median and regression quantiles both of which have been extensively studied in the literature these geometric quantiles are potentially useful in constructing trimmed multivariate means as well as many other l estimates of multivariate location and they lead to a directional notion of central and extreme points in a multidimensional setup such quantiles can be defined as meaningful and natural objects even in infinite dimensional hilbert and banach spaces and they yield an effective generalization of quantile regression in multiresponse linear model problems desirable equivariance properties are shown to hold for these multivariate quantiles and issues related to their computation for data in finite dimensional spaces are discussed n 1 2 consistenc

on the relation between s estimators and m estimators of multivariate location and covariance we discuss the relation between s estimators and m estimators of multivariate location and covariance as in the case of the estimation of a multiple regression parameter s estimators are shown to satisfy first order conditions of m estimators we show that the influence function if x s f of s functionals exists and is the same as that of corresponding m functionals also we show that s estimators have a limiting normal distribution which is similar to the limiting normal distribution which is similar to the limiting normal distribution of m estimators finally we compare asymptotic variances and breakdown point of both types of estimators

on the detection of determinism in a time series the nonlinearly scaled distributions of the strengths of the orthogonal modes in the data of a time series are compared with that derived from its surrogate counterpart to assess its chaoticity or the stochastic nature chaoticity manifests in the relatively decreasing strengths of the weaker modes with increasing dimension of the orthogonal spaces mapping the process the distributions of the strengths of the modes for the data and the surrogate are compared statistically singular value decomposition is used for the implementation the ability of the proposed method to distinguish between chaotic and stochastic dynamics is demonstrated through a number of simulated series including linear and nonlinear stochastic noise and processes described by lorenz rossler and mackey glass equations henon map and ecological map and some real life examples

a direct method for solving circulant tridiagonal block systems of linear equations this paper presents a modification of rojo s algorithm comput math appl 20 1990 61 to solve block circulant tridiagonal systems of linear equations which are toeplitz and hermitian this new approach gives us a general direct algorithm for solving the problem we will show how to choose a block matrix as a parameter to describe the method we employ the factorization of block toeplitz tridiagonal matrices as the product of two block toeplitz subdiagonal and superdiagonal matrices the algorithm is based on obtaining the solution of the nonlinear matrix equation email protected b c 1b finally some numerical results will be given

on the non equivalence of observables in phase space reconstructions from recorded time series in practical problems of phase space reconstruction it is usually the case that the reconstruction is much easier using a particular recorded scalar variable this seems to contradict the general belief that all variables of a dynamical system are equivalent in phase space reconstruction problems this paper will argue that in many cases the choice of a particular scalar time series from which to reconstruct the original dynamics could be critical it is argued that different dynamical variables do not provide the same level of information observability of the underlying dynamics and as a consequence the quality of a global reconstruction critically depends on the recorded variable examples in which the choice of observables is critical are discussed and the level of information contained in a given variable is quantified in the case where the original system is known a clear example of such a situation arises in the r ossler system for which the performance of a global vector field reconstruction technique is investigated using time series of variables x y or z taken one at a time

recognizing chaotic time waveforms in terms of a parametrized family of nonlinear predictors abstract consider a chaotic dynamical system which exhibits a variety of chaotic time waveforms with a change in the bifurcation parameters this paper presents an algorithm for estimating the underlying bifurcation parameters of the chaotic time waveforms in experimental situation in which no a priori analytical knowledge of the dynamical system is available first we construct qualitatively similar parametrized family of nonlinear predictors only from several sets of chaotic time waveforms qualitatively similar parametrized family means that the family of nonlinear predictors exhibits qualitatively similar bifurcation phenomena as the original chaotic time waveforms are then characterized in terms of the qualitatively similar bifurcation parameters of the nonlinear predictors we call the characterization of chaotic time waveforms in terms of the underlying bifurcation parameters chaotic time waveform recognition several numerical experiments using the rossler equations show the efficiency of the algorithm the effect of observational noise included in chaotic time waveforms is also considered

minute ahead stock price forecasting based on singular spectrum analysis and support vector regression abstract time series modeling and forecasting is an essential and hard task in financial engineering and optimization various models have been proposed in the literature and tested on daily data however a limited attention has been given to intraday data in this regard the current work presents a model for intraday stock price prediction that uses singular spectrum analysis ssa and support vector regression svr coupled with particle swarm optimization pso in particular the ssa decomposes stock price time series into a small number of independent components used as predictors the svr is applied to the task of forecasting and pso is employed to optimize svr parameters the performance of our proposed model is compared to the performance of four models widely used in financial prediction the wavelet transform wt coupled with feedforward neural network ffnn autoregressive moving average arma process polynomial regression polyreg and naive model finally the mean absolute error mae mean absolute percentage error mape and the root mean of squared errors rmse are used as main performance metrics by applying all models to six intraday stock price time series the forecasting results from simulations show that the presented ssa pso svr largely outperforms the conventional wt ffnn arma polynomial regression and naive model in terms of mae mape and rmse therefore our proposed predictive system ssa pso svr shows evident potential for noisy financial time series analysis and forecasting

traveling waves in nonequilibrium systems abstract the order parameter equation for the oscillatory instability of a spatially homogeneous state is used to examine traveling wave patterns in large aspect ratio systems with rectangular as well as circular geometries

dimensions and entropies of strange attractors from a fluctuating dynamics approach abstract it is shown that the fluctuations in the divergence of near by trajectories on strictly deterministic strange attractors can be modelled by stochastic concepts in particular we propose kramers moyal type equations for correlation functions between points on the attractor the drift terms are the lyapunov exponents the diffusion terms depend on the above fluctuations from this we obtain bounds on generalized dimensions and entropies numerical results show that in nearly all studied cases henon map zaslavskii map mackey glass eq the attractors are fractal measures in the sense of farmer information dimension hausdorff dimension metric entropy topological entropy

singular value decomposition in attractor reconstruction pitfalls and precautions applicability of singular value decomposition for reconstructing the strange attractor from one dimensional chaotic time series proposed by broomhead and king is extensively tested and discussed previously published doubts about its reliability are confirmed singular value decomposition by nature a linear method can bring distorted and misleading results when nonlinear structures are studied

some extensions of radial basis functions and their applications in artificial intelligence abstract radial basis functions have recently found interesting applications in artificial intelligence and in particular in the problem of learning to perform a particular task from a set of examples however in many practical cases the radial basis functions method cannot be applied in a straight forward manner because it does not take into account some features that are typical of the problem of learning from examples in this paper we show some extensions of the standard theory introduced in order to deal with a large number of examples and with problems in which different variables play very different roles we present some examples and also point out some open problems

an experimental observation of a new type of intermittency abstract a novel hysteretic form of regular intermittency has been observed experimentally in a variant of the taylor couette problem where the fluid flow is confined between a stationary outer cylinder and a rotating inner cylinder and end plates the results cannot all be explained within the standard pomeau manneville classification of intermittency and an extension to this theory is proposed to account for the observed phenomena a satisfactory agreement is found between experiment and theory both for the reinjection burst frequency scaling law and the influence of noise on the regularity of the bursts

statistical analysis of geopotential height gh timeseries based on tsallis non extensive statistical mechanics abstract in this paper we perform statistical analysis of time series deriving from earth s climate the time series are concerned with geopotential height gh and correspond to temporal and spatial components of the global distribution of month average values during the period 1948 2012 the analysis is based on tsallis non extensive statistical mechanics and in particular on the estimation of tsallis q triplet namely q stat q sens q rel the reconstructed phase space and the estimation of correlation dimension and the hurst exponent of rescaled range analysis r s the deviation of tsallis q triplet from unity indicates non gaussian tsallis q gaussian non extensive character with heavy tails probability density functions pdfs multifractal behavior and long range dependences for all timeseries considered also noticeable differences of the q triplet estimation found in the timeseries at distinct local or temporal regions moreover in the reconstructive phase space revealed a lower dimensional fractal set in the gh dynamical phase space strong self organization and the estimation of hurst exponent indicated multifractality non gaussianity and persistence the analysis is giving significant information identifying and characterizing the dynamical characteristics of the earth s climate

statistical uses of the spatial median the spatial median called the mediancentre in an earlier paper by j c gower is defined as the bivariate location measure to minimize the sum of absolute distances to observations its asymptotic efficiency relative to the sample mean vector with normal data is shown to exceed the usual univariate 2 ir 0 637 its estimating equations have an angular aspect and are used to develop angle tests which are analogues of sign tests in one dimension

on band matrices and their inverses abstract structural properties of the inverses of band matrices are discussed the definition of semiseparable matrices is given and the theorem is proved that the inverse of a strict band matrix is a semiseparable matrix and vice versa finally a recurrence algorithm is recommended for computing the blocks of the inverses of strict band matrices

a derivation of a macroscopic field theory of the brain from the quasi microscopic neural dynamics abstract the purpose of this paper is twofold first we present a semi quantitative nonlinear field theory of the brain under realistic anatomical connectivity conditions describing the interaction between functional units within the brain this macroscopic field theory is derived from the quasi microscopic conversion properties of neural populations occurring at synapses and somas the quasi microscopic models by wilson cowan 1972 1973 and nunez 1974 can be derived from these functional units are treated as inhomogeneities within a nonlinear one dimensional neural tissue second for the case of the kelso experiment the field equation is treated analytically and numerically and can be reduced to a set of ordinary differential equations which corresponds to a model by jirsa et al 1994 1995 this phenomenological model reproduces the spatio temporal phenomena experimentally observed here the most prominent property of the neural tissue is the parametric excitation the macroscopic field parameters can be expressed by quasi microscopic neural parameters

extracting qualitative dynamics from experimental data abstract we consider the notion of qualitative information and the practicalities of extracting it from experimental data our approach based on a theorem of takens draws on ideas from the generalized theory of information known as singular system analysis due to bertero pike and co workers we illustrate our technique with numerical data from the chaotic regime of the lorenz model

the reduction of complex dynamical systems using principal interaction patterns abstract a method of constructing low dimensional nonlinear models capturing the main features of complex dynamical systems with many degrees of freedom is described the system is projected onto a linear subspace spanned by only a few characteristic spatial structures called principal interaction patterns pips the expansion coefficients are assumed to be governed by a nonlinear dynamical system the optimal low dimensional model is determined by identifying spatial modes and interaction coefficients describing their time evolution simultaneously according to a nonlinear variational principle the algorithm is applied to a two dimensional geophysical fluid system on the sphere the models based on principal interaction patterns are compared to models using empirical orthogonal functions eofs as basis functions a pip model using 12 patterns is capable of capturing the long term behaviour of the complete system monitored by second order statistics while in the case of eofs 17 modes are necessary

multidimensional trimming based on projection depth as estimators of location parameters univariate trimmed means are well known for their robustness and efficiency they can serve as robust alternatives to the sample mean while possessing high efficiencies at normal as well as heavy tailed models this paper introduces multidimensional trimmed means based on projection depth induced regions robustness of these depth trimmed means is investigated in terms of the influence function and finite sample breakdown point the influence function captures the local robustness whereas the breakdown point measures the global robustness of estimators it is found that the projection depth trimmed means are highly robust locally as well as globally asymptotics of the depth trimmed means are investigated via those of the directional radius of the depth induced regions the strong consistency asymptotic representation and limiting distribution of the depth trimmed means are obtained relative to the mean and other leading competitors the depth trimmed means are highly efficient at normal or symmetric models and overwhelmingly more efficient when these models are contaminated simulation studies confirm the validity of the asymptotic efficiency results at finite samples

epidemic spreading by indirect transmission in a compartmental farm abstract in this paper we present a discrete dynamic system which describes an epidemic spreading within a single farm where animals are separated into batches in this model we consider an indirect transmission of the disease coming from the bacteria remaining in the reservoir and taking into account the transfer of bacteria between adjacent compartments in our model tridiagonal matrices of non negative blocks are involved the development of the matrix spectral properties allows us to improve our understanding of the epidemic spreading within a farm with the above mentioned characteristics based on the results obtained we have determined some bounds to obtain the maximum number of batches and the maximum population in each batch to ensure that the disease dies out

dynamic multiscale modes of resting state brain activity detected by entropy field decomposition the ability of functional magnetic resonance imaging fmri to noninvasively measure fluctuations in brain activity in the absence of an applied stimulus offers the possibility of discerning functional networks in the resting state of the brain however the reconstruction of brain networks from these signal fluctuations poses a significant challenge because they are generally nonlinear and nongaussian and can overlap in both their spatial and temporal extent moreover because there is no explicit input stimulus there is no signal model with which to compare the brain responses a variety of techniques have been devised to address this problem but the predominant approaches are based on the presupposition of statistical properties of complex brain signal parameters which are unprovable but facilitate the analysis in this article we address this problem with a new method entropy field decomposition for estimating structure within spatiotemporal data this method is based on a general information field theoretic formulation of bayesian probability theory incorporating prior coupling information that allows the enumeration of the most probable parameter configurations without the need for unjustified statistical assumptions this approach facilitates the construction of brain activation modes directly from the spatial temporal correlation structure of the data these modes and their associated spatial temporal correlation structure can then be used to generate space time activity probability trajectories called functional connectivity pathways which provide a characterization of functional brain networks

unmasking multivariate outliers and leverage points abstract detecting outliers in a multivariate point cloud is not trivial especially when there are several outliers the classical identification method does not always find them because it is based on the sample mean and covariance matrix which are themselves affected by the outliers that is how the outliers get masked to avoid the masking effect we propose to compute distances based on very robust estimates of location and covariance these robust distances are better suited to expose the outliers in the case of regression data the classical least squares approach masks outliers in a similar way also here the outliers may be unmasked by using a highly robust regression method finally a new display is proposed in which the robust regression residuals are plotted versus the robust distances this plot classifies the data into regular observations vertical outliers good leverage points and bad leverage points several examples are discussed

construction and analysis of differential equations from experimental time series of oscillatory systems abstract we propose a novel method to derive an autonomous system of ordinary differential equations from an experimental time series this model describe quantitatively transient behaviour of a system with limit cycle dynamics and is simplified to an evolution equation for the amplitude and frequency the landau equation in addition the model is used for a qualitative prediction of the influence of periodic excitation on the experimental system using the van der pol transformation and floquet theory in particular the instability of the locking solution including the hopf bifurcation the intermittency scenario and the period doubling cascade is considered the method of constructing a differential equation from an experimental time signal is successfully applied to a velocity fluctuation of the laminar periodic wake behind a circular cylinder

an approximate analytic solution of the lorenz equations multiple time perturbation theory is applied to the lorenz equations to obtain approximate solutions these solutions are used to obtain the form of the mapping relating two successive maxima of one of the variables of the equations good agreement is obtained with the numerical results presented by lorenz

faint phase synchronization detection through structured orthomax rotations in singular spectrum analysis multivariate singular spectrum analysis m ssa with a structured varimax rotation is a method that allows a deep characterization of phase synchronization ps phenomena in an almost automatic fashion it has been increasingly used in the study of ps in networks of nonlinear real world and numeric systems this paper investigates the impact of the other recently developed structured orthomax rotations on the m ssa ability to characterize ps the results show that by using the structured quartimax rotation a very faint and intermittent ps regime can be detected in contrast with the structured varimax which demands a stronger more consolidated ps regime this is due to the fact that the different rotations do not have the same efficiency in achieving a simple structure of the m ssa eigenvectors nevertheless for well established ps regimes the same robustness of the original m ssa approach against high levels of additive gaussian noise was found for the structured quartimax and biquartimax rotations however for all approaches we found an overshoot of the qualitative range for the ps onset due to noise

distinguishing between low dimensional dynamics and randomness in measured time series the success of current attempts to distinguish between low dimensional chaos and random behavior in a time series of observations is considered first we discuss stationary stochastic processes which produce finite numerical estimates of the correlation dimension and k2 entropy under naive application of correlation integral methods we then consider several straightforward tests to evaluate whether correlation integral methods reflect the global geometry or the local fractal structure of the trajectory this determines whether the methods are applicable to a given series if they are we evaluate the significance of a particular result for example by considering the results of the analysis of stochastic signals with statistical properties similar to those of observed series from the examples considered it is clear that the correlation integral should not be used in isolation but as one of a collection of tools to distinguish chaos from stochasticity

using renyi parameter to improve the predictive power of singular value decomposition entropy on stock market abstract this paper generalizes the method of traditional singular value decomposition entropy by incorporating orders q of renyi entropy we analyze the predictive power of the entropy based on trajectory matrix using shanghai composite index and dow jones index data in both static test and dynamic test in the static test on sci results of global granger causality tests all turn out to be significant regardless of orders selected but this entropy fails to show much predictability in american stock market in the dynamic test we find that the predictive power can be significantly improved in sci by our generalized method but not in dji this suggests that noises and errors affect sci more frequently than dji in the end results obtained using different length of sliding window also corroborate this finding

reconstruction expansion as a geometry based framework for choosing proper delay times abstract the quality of attractor reconstruction using the method of delays is known to be sensitive to the delay parameter here we develop a new computationally efficient approach to choosing that quantifies reconstruction expansion from the identity line of the embedding space we show that reconstruction expansion is related to the concept of reconstruction signal strength and that increased expansion corresponds to diminished effects of measurement error thus reconstruction expansion represents a simple geometrical framework for choosing furthermore we describe the role of dynamical error in attractor expansion and argue that algorithms for determining should be considered as attempts at estimating an upper bound to the optimal delay

flow transitions resembling bifurcations of the logistic map in simulations of the baroclinic rotating annulus we present evidence for a sequence of bifurcations in simulations of the differentially heated baroclinic rotating annulus similar to bifurcations of the logistic map the met office oxford rotating annulus laboratory simulation morals code is used to construct a detailed numerical regime diagram for the annulus and the distribution of regimes in parameter space is discussed the bifurcations are observed in a sequence of runs at high temperature forcing identified by poincare sections of the dominant temperature mode amplitude time series higher order return maps and predictions using quadratic fits to the data are used to verify this result and lyapunov exponents are calculated to identify and quantify the chaotic parts of the sequence

approximating stable and unstable manifolds in experiments we introduce a procedure to reveal invariant stable and unstable manifolds given only experimental data we assume a model is not available and show how coordinate delay embedding coupled with invariant phase space regions can be used to construct stable and unstable manifolds of an embedded saddle we show that the method is able to capture the fine structure of the manifold is independent of dimension and is efficient relative to previous techniques

correlation of local stretchings as a way of characterising chaotic dynamics amid noise abstract a positive lyapunov exponent can result from either chaotic dynamics or noise as a possible means of assessing the degree to which the exponent is noise affected and as a possible index in its own right the localised divergence of two neighbouring trajectories from a fiducial trajectory is compared in the expectation of finding strong correlation when the source of stretching is deterministic chaos and little or no correlation when the source is coloured or uncoloured noise the method is applied to various equation systems and to a periodic time series from the self excited oscillation of flexible tube collapsed by external pressure and conveying a flow

observation of a strange attractor abstract phase space portraits have been constructed and analyzed for noisy nonperiodic data obtained in an experiment on a nonequilibrium homogeneous chemical reaction the phase space trajectories define a limit set that is an attractor following a perturbation the trajectory quickly returns to the attracting set this attracting set is shown to be strange nearby trajectories separate exponentially on the average moreover the poincare sections exhibit the stretching and folding that is characteristic of strange attractors

reconstructing attractors from filtered time series abstract in this paper we investigate the criteria necessary to reconstruct an attractor from a time series that has been passed through an iir filter to guarantee that the whole of the attractor is reconstructed requires uniform bounds on the contraction rate of the dynamics however we show that if we use a condition that is only based on the average contraction rates the lyapunov exponents then a set of high probability can still be reconstructed we argue that in practice this is all that is necessary

on periodic block tridiagonal matrices abstract periodic block tridiagonal matrices are defined and conditions are given for factorizing their characteristic polynomial by means of the zeros of chebyshev polynomials of the second kind these conditions are expressed by the block centrosymmetry of certain submatrices along the main diagonal the main theorems can be considered as generalizations of an earlier result published by elsner and redheffer and by rozsa

the metrically trimmed mean as a robust estimator of location the metrically trimmed mean is defined as the average of observations remaining after a fixed number of outlying observations have been removed a metric the distance from the median is used to determine which points are outlying the influence curve and the asymptotic normality of the metrically trimmed mean are derived using von mises expansions the relative merits of the median the trimmed mean and the metrically trimmed mean are discussed in neighborhoods of nonparametric models with natural parameters it is observed that the metrically trimmed mean works well for the center of symmetry of a symmetric distribution function with asymmetric contamination a multivariate extension of the metrically trimmed mean is discussed