a new method to detect nonlinearity in a time series synthesizing surrogate data using a kolmogorov smirnoff tested hidden markov model abstract a way of statistically testing for nonlinearity in a time series is to employ the method of surrogate data this method often makes use of the fourier transform ft in order to generate the surrogate as various authors have shown this can lead to artefacts in the surrogates and spurious detection of nonlinearity can result this paper documents a new method to synthesize surrogate data using a 1st order hidden markov model hmm combined with a kolmogorov smirnoff test ks test to determine the required resolution of the hmm significance test results for a sinewave henon map and gaussian noise time series are presented it is demonstrated that ks tested hmm surrogates can be successfully used to distinguish between a deterministic and stochastic time series then by applying a simple test for linearity using linear and nonlinear predictors it is possible to determine the nature of the deterministic class and hence conclude whether the system is linear deterministic or nonlinear deterministic furthermore it is demonstrated that the method works for periodic functions too where ft surrogates break down

multifractal detrended cross correlation analysis of carbon and crude oil markets abstract the complex dynamics between carbon and crude oil markets have been an increasingly interesting area of research in this paper we try to take a fresh look at the cross correlations between carbon and crude oil markets as well as their dynamic behavior employing multifractal detrended cross correlation analysis first we find that the return series of carbon and crude oil markets are significantly cross correlated second we confirm the existence of multifractality for the return series of carbon and crude oil markets by the multifractal detrended fluctuation analysis third based on the multifractal detrended cross correlation analysis we find the existence of power law cross correlations between carbon and crude oil markets the cross correlated behavior of small fluctuations is found to be more persistent than that of large fluctuations at last some relevant discussions and implications of the empirical results are presented

effective normalization of complexity measurements for epoch length and sampling frequency the algorithmic complexity of a symbol sequence is sensitive to the length of the message additionally in those cases where the sequence is constructed by the symbolic reduction of an experimentally observed wave form the corresponding value of algorithmic complexity is also sensitive to the sampling frequency in this contribution we present definitions of algorithmic redundancy that are sequence sensitive generalizations of shannon s original definition of information redundancy in contrast with algorithmic complexity we demonstrate that algorithmic redundancy is not sensitive to message length or to observation scale sampling frequency when stationary systems are examined

directionality of coupling from bivariate time series how to avoid false causalities and missed connections we discuss some problems encountered in inference of directionality of coupling or in the case of two interacting systems in inference of causality from bivariate time series we identify factors and influences that can lead to either decreased test sensitivity or false detections and propose ways to cope with them in order to perform tests with high sensitivity and a low rate of false positive results

assessment of the relative ratio of correlated and uncorrelated waiting times in the southern california earthquakes catalogue abstract in the present study we investigated the interevent time interval distribution of earthquakes in southern california we analyzed and compared datasets of waiting times between consecutive earthquakes and time structure distorted datasets the aim of this study was to determine the proportion of waiting time values in the original catalogue that can be regarded as statistically distinguishable or indistinguishable from the baseline time intervals datasets where the original structure of the temporal distribution of earthquakes was disrupted we compiled two types of time structure distorted baseline sequences which comprised mean values of a shuffled original interevent data and b interevent times data from time randomized catalogues to compare the dynamical characteristics of the original and time structure distorted baseline sequences we used several data analysis methods such as power spectrum regression detrended fluctuation and multifractal detrended fluctuation analysis we also tested the nonlinear structure of the original and baseline sequences using the magnitude and sign scaling analysis method we calculated the z s c o r e in order to assess whether the interevent time values in the original dataset shared statistical similarity or dissimilarity with the time structure distorted baseline interevent data sequence we compared the interevent time values in the original dataset with the mean baseline interevent times computed for two types of time structure distorted sequences the results showed that about 30 of the original interevent times were statistically indistinguishable from the mean of the shuffled dataset and 10 from the mean of the time structure distorted baseline interevent dataset we performed similar analyses for other catalogues obtained from different parts of the world according to the results of this analysis the proportion of events in the original catalogues that were indistinguishable from sequences with disturbed time structure did not contradict the results obtained for the southern california catalogue

a segregated finite element solution for non isothermal flow abstract a segregated finite element algorithm for the solution of the supg formulation of the incompressible steady state navier stokes equations for non isothermal flow is presented in this paper the method features equal order interpolation for all the flow variables the simpler and simplest algorithms are employed and the sets of non symmetric linear equations are solved by means of the preconditioned conjugate gradient squared solver whilst the preconditioned conjugate gradient solver is used to solve the sets of symmetric linear equations three cases are used as a basis for the study i e the flow in a square cavity the flow between parallel plates and natural convection in a square cavity the effect that the choice of the values of the relaxation parameters has on the number of iterations which is needed to obtain a converged solution is investigated in each case there is an optimum combination which is amongst others a function of the grid and the flow parameters a non optimum choice may lead either to an unnecessary number of iterations or the solution becoming unstable from the results it is concluded that the method performs well when the optimum combination of the values for the relaxation parameters is used however much can still be done to improve the robustness of the method

measurement of the lyapunov spectrum from a chaotic time series the exponential divergence or convergence of nearby trajectories lyapunov exponents is conceptually the most basic indicator of deterministic chaos we propose a new method to determine the spectrum of several lyapunov exponents including positive zero and even negative ones from the observed time series of a single variable we have applied the method to various known model systems and also to the rayleigh b enard experiment and have elucidated the dependence of the lyapunov exponents on the rayleigh number

minimal faithful upper triangular matrix representations for solvable lie algebras the existence of matrix representations for any given finite dimensional complex lie algebra is a classic result on lie theory in particular such representations can be obtained by means of an isomorphic matrix lie algebra consisting of upper triangular square matrices unfortunately there is no general information about the minimal order for the matrices involved in such representations in this way our main goal is to revisit debug and implement an algorithm which provides the minimal order for matrix representations of any finite dimensional solvable lie algebra when inserting its law as well as returning a matrix representative of such an algebra by using the minimal order previously computed in order to show the applicability of this procedure we have computed minimal representatives not only for each solvable lie algebra with dimension less than 6 but also for some solvable lie algebras of arbitrary dimension

surrogate analysis of volatility series from long range correlated noise detrended fluctuation analysis dfa c k peng s v buldyrev a l goldberger s havlin f sciortino m simons h e stanley nature 356 1992 168 of volatility series has been proposed to identify possible nonlinear multifractal signatures in the given empirical sample y ashkenazy p ch ivanov s havlin c k peng a l goldberger h e stanley phys rev lett 86 2001 1900 y ashkenazy s havlin p ch ivanov c k peng v schulte frohlinde h e stanley physica a 323 2003 19 t kalisky y ashkenazy s havlin phys rev e 72 2005 011913 long range volatility correlation can be an outcome of static as well as dynamical nonlinearity in order to argue in favor of dynamical nonlinearity surrogate testing is used in conjunction with volatility analysis y ashkenazy p ch ivanov s havlin c k peng a l goldberger h e stanley phys rev lett 86 2001 1900 y ashkenazy s havlin p ch ivanov c k peng v schulte frohlinde h e stanley physica a 323 2003 19 t kalisky y ashkenazy s havlin phys rev e 72 2005 011913 in this brief communication surrogate testing of volatility series from long range correlated monofractal noise and their static invertible nonlinear transforms is investigated long range correlated noise is generated from fractional auto regressive integrated moving average farima 0 d 0 with gaussian and non gaussian innovations we show significant deviation in the scaling behavior between the empirical sample and the surrogate counterpart at large time scales in the case of farima 0 d 0 with non gaussian innovations whereas no such discrepancy was observed in the case of gaussian innovations the results encourage cautious interpretation of surrogate analysis of volatility series in the presence of non gaussian innovations

forecasting volatility in shanghai and shenzhen markets based on multifractal analysis abstract this paper analyzes the multifractality in shanghai and shenzhen stock markets using multifractal spectrum analysis and multifractal detrended fluctuation analysis we find that the main source of multifractality is long range correlations of large and small fluctuations then we introduce a multifractal volatility measure mv and find that by taking mv as daily conditional volatility the simulated series displayed similar stylized facts to the original daily return series by capturing the dynamics of mv using the arfima model we find that the out of sample forecasting performance of the arfima mv model is better than some garch class models and the arfima rv model under some criteria of loss function

nonlinearity in high frequency stock returns evidence from the athens stock exchange abstract this study investigates empirically the presence of nonlinearities in the athens composite share price index high frequency returns a preliminary analysis indicates that volatility exhibits a periodic intraday inverse j shaped pattern associated with the opening and closing of the market periodicity is then removed employing a flexible fourier form subsequently an arma figarch model over several frequencies yields that return volatility is long memory and self similar nonlinear analysis with the use of the embedding dimension suggests that the filtered return process does not exhibit deterministic or higher order stochastic nonlinearity rather it is reminiscent of a random process we conclude that the acspi data are nonlinear however nonlinearity is attributed to persistent arch effects

detecting determinism in short time series using a quantified averaged false nearest neighbors approach we propose a criterion to detect determinism in short time series this criterion is based on the estimation of the parameter e 2 defined by the averaged false neighbors method for analyzing time series cao physica d 110 43 1997 using surrogate data testing with several chaotic and stochastic simulated time series we show that the variation coefficient of e 2 over a few values of the embedding dimension d defines a suitable statistic to detect determinism in short data sequences this result holds for a time series generated by a high dimensional chaotic system such as the mackey glass one different decreasing lengths of the time series are included in the numerical experiments for both synthetic and real world data we also investigate the robustness of the criterion in the case of deterministic time series corrupted by additive noise

detrended fluctuation analysis on spot and futures markets of west texas intermediate crude oil abstract in this paper we study the auto correlations and cross correlations of west texas intermediate wti crude oil spot and futures return series employing detrended fluctuation analysis dfa and detrended cross correlation analysis dcca scaling analysis shows that for time scales smaller than a month the auto correlations and cross correlations are persistent for time scales larger than a month but smaller than a year the correlations are anti persistent while for time scales larger than a year the series are neither auto correlated nor cross correlated indicating the efficient operation of the crude oil markets moreover for small time scales the degree of short term cross correlations is higher than that of auto correlations using the multifractal extension of dfa and dcca we find that for small time scales the correlations are strongly multifractal while for large time scales the correlations are nearly monofractal analyzing the multifractality of shuffled and surrogated series we find that both long range correlations and fat tail distributions make important contributions to the multifractality our results have important implications for market efficiency and asset pricing models

a curvilinear finite element model for simulating two well tracer tests and transport in stratified aquifers the problem of solute transport in steady nonuniform flow created by a recharging and discharging well pair is investigated numerical difficulties encountered with the standard galerkin formulation in cartesian coordinates are illustrated an improved finite element solution strategy is presented to overcome the numerical problem the strategy is based on a formulation performed in three dimensional curvilinear coordinates this formulation is developed especially for the simulation of two well injection withdrawal tracer tests conducted in homogeneous or stratified aquifers the formulation can also be applied to other types of problems involving transport in homogeneous and stratified aquifers a three dimensional finite element approximation is derived by two successive applications of upstream weighted residual and subdomain collocation procedures first the weighted residual procedure is formulated in the horizontal flow plane using curvilinear coordinates along and normal to streamlines upstream weighting is included but automatically controlled and limited to one dimension along the main flow direction second the subdomain collocation procedure is formulated in the vertical dimension spatial discretization of the three dimensional flow region is performed using a curvilinear finite element mesh that is point centered in the horizontal plane and block centered in the vertical direction general algorithms are developed for mesh generation time stepping and matrix reduction the solution algorithm is designed to accommodate several thousand nodal unknowns with minimal core storage and cpu time requirement two simulation examples are presented to verify and validate the numerical model in two dimensions using an analytical solution and experimental laboratory and field data a comparative study shows that the proposed formulation is superior to the standard galerkin formulation in cartesian coordinates both in terms of accuracy and computational efficiency the field simulation example indicates the need to conduct a more elaborate three dimensional simulation study allowing for vertical variation in hydraulic conductivity such a study has been completed and is reported in the follow up paper of this series

testing for the source of multifractality in water level records abstract the multifractality in hydrologic data has been studied in many literatures but few literatures focus on its source which is helpful for understanding the underlying mechanisms that generate hydrologic data we propose a hypothesis testing procedure for the source of multifractality in water level records based on the empirical distributions of generalized hurst exponent estimated from a set of shuffled or surrogate series the proposed hypothesis testing procedure can show more details about the source of multifractality than previous methods with some statistics especially about the effects of large and small fluctuations on multifractality the generalized hurst exponents are estimated via multifractal detrended fluctuation analysis the data set contains about two million high frequency water level records of a northern china river at its 10 observation stations the testing results show that the multifractality in water levels is mainly caused by nonlinear correlations in small fluctuations and linear correlations in small and large fluctuations and is also related to the probability distribution of small fluctuations this conclusion is validated via some constructed semi surrogate series and values of statistics for source testing

quantum theory the church turing principle and the universal quantum computer it is argued that underlying the church turing hypothesis there is an implicit physical assertion here this assertion is presented explicitly as a physical principle every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means classical physics and the universal turing machine because the former is continuous and the latter discrete do not obey the principle at least in the strong form above a class of model computing machines that is the quantum generalization of the class of turing machines is described and it is shown that quantum theory and the universal quantum computer are compatible with the principle computing machines resembling the universal quantum computer could in principle be built and would have many remarkable properties not reproducible by any turing machine these do not include the computation of non recursive functions but they do include quantum parallelism a method by which certain probabilistic tasks can be performed faster by a universal quantum computer than by any classical restriction of it the intuitive explanation of these properties places an intolerable strain on all interpretations of quantum theory other than everett s some of the numerous connections between the quantum theory of computation and the rest of physics are explored quantum complexity theory allows a physically more reasonable definition of the complexity or knowledge in a physical system than does classical complexity theory

statistical tests for deterministic effects in broad band time series we derive a normalized version of the indicators of savit and green and prove that these normalized statistics have asymptotically a normal distribution with a mean of zero and standard deviation of one if the time series is random in the sense of being lid independent and identically distributed we verify this result numerically and study the magnitude of the finite size effects we also show that these statistics are very sensitive to the existence of deterministic effects in the series even if the underlying deterministic structure is complex such as those generated by a chaotic system we show that with moderate amounts of data the statistics can easily indicate the presence of an underlying attractor even in the presence of iid noise which is as large as or greater than the signal finally we discuss the generalization of our approach to include 1 other null hypotheses besides lid which express assumptions of specific dependencies and 2 the study of deterministic effects between more than one time series

determining anomalous dynamic patterns in price indexes of the london metal exchange by data synchronization abstract data synchronization based on the kuramoto model for collective synchronization and hypothesis testing based on the rank test combined with the random shuffling surrogate method are applied to finding major feature patterns of weekly nonferrous metal returns from the time series of daily spot and futures price indexes in the london metal exchange since 1989 our results suggest the existence of day of the week anomalies in the metal returns we conjecture that such anomalies are large scale manifestations of synchronously accumulated risk aversive actions of individual market players

a new method to estimate the kolmogorov entropy from recurrence plots its application to neuronal signals recurrence plots are a useful graphic tool for studying dynamical systems a new variable is proposed to quantify their deterministic structure it allows an easy computation of the k2 entropy since the distance between points needs to be calculated only once instead of every time for each new embedding dimension and it bypasses some of the limitations inherent to the classical grassberger and procaccia method it is valuable for biological data as illustrated here by tests with various dynamical models and its application to experimental signals recorded from neurons

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100

the analysis of chaotic time series data this paper presents a brief survey of time series analysis methods that are applicable to processes whose behavior can be described as low dimensional chaos the goal of these methods is to allow experimentalists to obtain local estimates of the dynamics directly from a set of data these estimates are often sufficiently accurate to attempt noise reduction prediction and control

synchronization likelihood an unbiased measure of generalized synchronization in multivariate data sets the study of complex systems consisting of many interacting subsystems requires the use of analytical tools which can detect statistical dependencies between time series recorded from these subsystems typical examples are the electroencephalogram eeg and magnetoencephalogram meg which may involve the simultaneous recording of 150 or more time series coherency which is often used to study such data is only sensitive to linear and symmetric interdependencies and cannot deal with non stationarity recently several algorithms based upon the concept of generalized synchronization have been introduced to overcome some of the limitations of coherency estimates e g physica d 134 1999 419 brain res 792 1998 24 however these methods are biased by the degrees of freedom of the interacting subsystems physica d 134 1999 419 physica d 148 2001 147 we propose a novel measure for generalized synchronization in multivariate data sets which avoids this bias and can deal with non stationary dynamics

a tukey nonadditivity type test for time series nonlinearity the past few years have seen a revived interest in the study of nonlinear stationary time series the most general form of a nonlinear stationary process is that referred to as a volterra expansion this is to a linear process what a higher order polynomial is to a linear function the so called bilinear model is a special case which is quite broad and is defined by a small number of parameters volterra expansions involve more than secondorder theory and require higher order cumulant spectra various tests for linearity have been proposed although none is totally satisfactory because of the similarity of volterra expansions to polynomials an analogue of tukey s 1949 one degree of freedom for nonadditivity test seems quite reasonable as a diagnostic for linearity versus a second order volterra expansion such a test would be time domain based and computationally less complex than the frequency domain based alternatives directly generalizable to higher order than second and possibly suggestive of a power transformation toward linearity

multifractal analysis of stock exchange crashes abstract we analyze the complexity of rare events of the djia index we reveal that the returns of the time series exhibit strong multifractal properties meaning that temporal correlations play a substantial role the effect of major stock market crashes can be best illustrated by the comparison of the multifractal spectra of the time series before and after the crash aftershock periods compared to foreshock periods exhibit richer and more complex dynamics compared to an average crash calculated by taking into account the larger 5 crashes of the djia index the 1929 event exhibits significantly more increase in multifractality than the 1987 crisis

a positivity preserving variational method for multi dimensional convectiondiffusionreaction equation a new positivity preserving variational ppv procedure is proposed to solve the convectiondiffusionreaction cdr equation through the generalization of stabilized finite element methods the present variational procedure offers minimal phase and amplitude errors for different regimes associated with convection diffusion and reaction effects by means of fourier analysis we first review the shortcomings of the galerkin least squares gls and the subgrid scale sgs methods during the change in sign of the reaction coefficient that motivates us for the present linear stabilization as a combined gls sgs methodology discrete upwind operator with a solution dependent nonlinear term is then introduced in high gradient regions which enables the positivity preserving property in the variational formulation direct extension to multi dimensions is carried out by considering the principle streamline and crosswind directions the efficacy of the method is demonstrated by the systematic accuracy and stability analyses in one and two dimensions results show the reduction of oscillations in the solution in one and two dimensional cases and a remarkable reduction in the phase error is observed for the cases with negative reaction coefficient the proposed formulation provides a superior solution in the reaction dominated as well as the convection dominated regimes due to the minimization of spurious oscillations and accurate capturing of the high gradient regions

nonlinear strength quantifier based on phase correlation abstract distinguishing linear series from nonlinear ones is of great importance for not only understanding the processes generating these series but also their modeling and prediction there are many methods and their nonlinear quantifiers to reach this goal but no one is powerful enough to deal with any given series in this study the artificially generating series with given tailored phase correlation strength is applied to test the performance of some widely used methods and their nonlinear quantifiers given in the previous studies both advantages and shortcomings are shown for these methods and their nonlinear metrics especially spurious results from these methods and their nonlinear metrics can be found for some cases much weak or strong phase correlations in order to avoid these spurious results modified phase correlation quantifiers are proposed at the same time multiple stripes found in the phase map can be explained from the view point of enhanced nonlinear strength

fractal rock slope dynamics anticipating a collapse time series of dilatometric measurements of relative displacements on rock cracks on stable and unstable sandstone slopes were analyzed the inherent dynamics of rock slopes lack any significant nonlinearity however the residuals obtained by removing meteorological influences are fat tailed non gaussian fluctuations with short range correlations in the case of stable slopes the fluctuations of unstable slopes exhibit self affine dynamics of fractional brownian motions with power law long range correlations and are characterized by asymptotic power law probability distributions with decay coefficients outside the range of stable l evy distributions

subspace based identification algorithm for characterizing causal networks in resting brain the resting brain has been extensively investigated for low frequency synchrony between brain regions namely functional connectivity fc however the other main stream of brain connectivity analysis that seeks causal interactions between brain regions effective connectivity ec has been little explored inherent complexity of brain activities in resting state as observed in bold blood oxygenation level dependant fluctuations calls for exploratory methods for characterizing these causal networks on the other hand the inevitable effects that hemodynamic system imposes on causal inferences in fmri data lead us toward the methods in which causal inferences can take place in latent neuronal level rather than observed bold time series to simultaneously satisfy these two concerns in this paper we introduce a novel state space system identification approach for studying causal interactions among brain regions in the absence of explicit cognitive task this algorithm is a geometrically inspired method for identification of stochastic systems purely based on output observations using extensive simulations three aspects of our proposed method are investigated ability in discriminating existent interactions from non existent ones the effect of observation noise and downsampling on algorithm performance our simulations demonstrate that subspace based identification algorithm sia is sufficiently robust against above mentioned factors and can reliably uncover the underlying causal interactions of resting state fmri furthermore in contrast to previously established state space approaches in effective connectivity studies this method is able to characterize causal networks with large number of brain regions in addition we utilized the proposed algorithm for identification of causal relationships underlying anti correlation of default mode and dorsal attention networks during the rest using fmri we observed that default mode network places in a higher order in hierarchical structure of brain functional networks compared to dorsal attention networks

on spurious oscillations at layers diminishing sold methods for convection diffusion equations part i a review abstract an unwelcome feature of the popular streamline upwind petrov galerkin supg stabilization of convection dominated convection diffusion equations is the presence of spurious oscillations at layers since the mid of the 1980s a number of methods have been proposed to remove or at least to diminish these oscillations without leading to excessive smearing of the layers the paper gives a review and state of the art of these methods discusses their derivation proposes some alternative choices of parameters in the methods and categorizes them some numerical studies which supplement this review provide a first insight into the advantages and drawbacks of the methods

efficiency and multifractality analysis of csi 300 based on multifractal detrending moving average algorithm abstract we apply the multifractal detrending moving average mfdma to investigate and compare the efficiency and multifractality of 5 min high frequency china securities index 300 csi 300 the results show that the csi 300 market becomes closer to weak form efficiency after the introduction of csi 300 future we find that the csi 300 is featured by multifractality and there are less complexity and risk after the csi 300 index future was introduced with the shuffling surrogating and removing extreme values procedures we unveil that extreme events and fat distribution are the main origin of multifractality besides we discuss the knotting phenomena in multifractality and find that the scaling range and the irregular fluctuations for large scales in the f q s vs s plot can cause a knot

finite element solution of the navier stokes equations for incompressible flow using a segregated algorithm abstract a segregated finite element algorithm for the solution of the supg formulation of the incompressible steady state navier stokes equations is investigated in this paper the method features equal order interpolation for all the flow variables the simplest algorithm is employed which results in symmetric coefficient matrices for the momentum equations the same iterative linear equation solver can therefore be employed for the solution of the momentum and pressure equations the effect of applying the supg weighting functions only to the convective terms is compared with the effect of applying the functions to all the terms in the momentum equations the effect of using an iterative linear equation solver as opposed to a direct linear equation solver is also discussed

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

multifractal moving average analysis and test of multifractal model with tuned correlations we address two common major problems in the study of time series characterizing fluctuations in complex systems multifractal analysis and multifractal modeling specifically we introduce a multi fractal centered moving average mf cma analysis which is computationally easier but equivalently performing compared with the well established multi fractal detrended fluctuation analysis mf dfa with linear detrending in addition we study in detail a generalized binomial multi fractal model gb mfm to conveniently and reliably generate multifractal surrogate data with arbitrary singularity strengths and arbitrary long term persistence we use the data generated by this model as well as realistic by construction monofractal data series with crossovers and trends to test and compare the multifractal analysis methods and discuss finite size effects as well as limitations due to spurious multifractality

price volume multifractal analysis of the moroccan stock market abstract in this paper we analyzed price volume multifractal cross correlations of moroccan stock exchange we chose the period from january 1st 2000 to january 20th 2017 to investigate the multifractal behavior of price change and volume change series then we used multifractal detrended cross correlations analysis method mf dcca and multifractal detrended fluctuation analysis mf dfa to analyze the series we computed bivariate generalized hurst exponent renyi exponent and spectrum of singularity for each pair of indices to measure quantitatively cross correlations furthermore we used detrended cross correlations coefficient dcca and cross correlation test q m to analyze cross correlation quantitatively and qualitatively by analyzing results we found existence of price volume multifractal cross correlations the spectrum width has a strong multifractal cross correlation we remarked that volume change series is anti persistent when we analyzed the generalized hurst exponent for all moments q the cross correlation test showed the presence of a significant cross correlation however dcca coefficient had a small positive value which means that the level of correlation is not very significant finally we analyzed sources of multifractality and their degree of contribution in the series

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

surrogate testing of linear feedback processes with non gaussian innovations abstract surrogate testing is used widely to determine the nature of the process generating the given empirical sample in the present study the usefulness of phase randomized surrogates amplitude adjusted fourier transform and iterated amplitude adjusted fourier transform surrogates on statistical inference of linearly correlated noise with non gaussian innovations and their static invertible nonlinear transforms from their empirical samples are discussed existing surrogate testing procedures which retain the auto correlation function in the surrogates may not be appropriate in the presence of non gaussian innovations

aging regularity and variability in maximum isometric moments this study examined the variability and regularity of maximum isometric moment production of the plantar flexors in young and old subjects it was hypothesized that in the development of maximum isometric moments there would be greater regularity in the moment profiles for older subjects compared with young subjects due to the reduced number of motor units present in elderly muscle two groups of subjects produced three maximal isometric plantar flexions young n 11 mean age 23 8 2 8 years mean mass 81 2 10 4 kg mean height 1 78 0 05 m elderly n 13 mean age 74 0 3 3 years mean mass 78 5 3 4 kg mean height 1 73 0 05 m the plateau of the moment time curve was analyzed for each trial a repeat measures analysis of variance showed the young subjects produced statistically greater peak plantar flexion moments than the elderly subjects but similar coefficients of variation signal regularity was determined by computing the signal s approximate entropy which demonstrated that the older group had greater regularity in their generation of moment profiles the hypothesis was accepted with a potential explanation for this increased regularity in old age being the reduced number of motor units to coordinate

probing the linearity and nonlinearity in dna sequences abstract in this paper we apply the principles of information theory that relate to the definition of nonlinear predictability which is a measure that describes both the linear and nonlinear components of a system by comparing this measure to a measure of linear predictability one can assess whether a given system has a strong linear or a strong nonlinear component this provides insights as to whether the system should be modeled by a nonlinear or a linear model we apply these ideas to dna sequences our results which extend previous results on this issue indicate that all dna sequences coding and noncoding exhibit strong nonlinear structure at the same time the results provide insights to understand dna structure and possible clues about evolutionary mechanisms

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

nonlinearity tests for time series summary this paper considers two nonlinearity tests for stationary time series the idea of tukey s one degree of freedom for nonadditivity test is generalized to the time series setting the case of concurrent nonlinearity is discussed in detail simulation results show that the proposed tests are more powerful than that of keenan 1985

responses of a hodgkin huxley neuron to various types of spike train inputs numerical investigations have been made of responses of a hodgkin huxley hh neuron to spike train inputs whose interspike interval isi is modulated by deterministic semi deterministic chaotic and stochastic signals as deterministic one we adopt inputs with the time independent isi and with time dependent isi modulated by sinusoidal signal the rossler and lorentz models are adopted for chaotic modulations of isi stochastic isi inputs with the gamma distribution are employed it is shown that distribution of output isi data depends not only on the mean of isis of spike train inputs but also on their fluctuations the distinction of responses to the three kinds of inputs can be made by return maps of input and output isis but not by their histograms the relation between the variations of input and output isis is shown to be different from that of the integrate and fire if model because of the refractory period in the hh neuron

an assessment of flow oriented schemes for reducing false diffusion un facteur limitatif important dans la modelisation precise des problemes d ecoulement est la representation numerique des termes de convection dans les equations de navier stokes revue des differentes methodes d approximation des termes de convection pour reduire les erreurs de fausse diffusion dans le contexte des methodes de differences finies et de volumes finis

a wavelet based method for surrogate data generation hypothesis testing based on surrogate data has emerged as a popular way to test the null hypothesis that a signal is a realisation of a linear gaussian stochastic process if these surrogates are constrained to the values and power spectrum of the original data there is no need to formulate a pivotal test statistic in this paper a method is presented for generating constrained surrogates using a wavelet transform introducing a threshold above which wavelet detail coefficients are pinned to their original values such surrogates avoid problems of nonstationarity for pseudo periodic data and appear to be more robust than conventional approaches for situations where period modulation is corrupting a gaussian stochastic process when used for generating ensemble realisations of a process the approach used here avoids some of the difficulties of methods based on simple randomisation of wavelet coefficients

a search for chaotic behavior in large and mesoscale motions in the pacific ocean the lagrangian trajectories of three satellite tracked bouys deployed in the pacific ocean for a one year period are studied from the standpoint of dynamical systems theory time series of the bouy positions are analyzed to estimate the correlation dimension and kolmogorov entropy we find a small finite value of correlation dimension near 1 4 and a finite kolmogorov entropy of about 0 2 day 1 these results at first suggest that the bouy motions may be dominated by a low dimensional chaotic attractor using standard ideas from the mathematics of fractals and a new method which we call multivariate scaling analysis we are able to demonstrate however that the bouy trajectories are instead fractal curves in the physical plane x y these results may be viewed from the standpoint of multivariate nongaussian convergence of the scales which occur when the fourier spectrum is described by a power law such systems can have a small finite value for the correlation dimension and are therefore fractal even when no underlying attractor is present systems of this type are more easily related to turbulent behavior stochastic many degrees of freedom rather than to strange attractor deterministic few degrees of freedom

evaluation of dynamical models dissipative synchronization and other techniques some recent developments for the validation of nonlinear models built from data are reviewed besides giving an overall view of the field a procedure is proposed and investigated based on the concept of dissipative synchronization between the data and the model which is very useful in validating models that should reproduce dominant dynamical features like bifurcations of the original system in order to assess the discriminating power of the procedure four well known benchmarks have been used namely duffing ueda duffingholmes and van der pol oscillators plus the henon map the procedure developed for discrete time systems is focused on the dynamical properties of the model rather than on statistical issues for all the systems investigated it is shown that the discriminating power of the procedure is similar to that of bifurcation diagrams which in turn is much greater than say that of correlation dimension but at a much lower computational cost

nonlinear analysis of data sampled nonuniformly in time abstract we demonstrate how some of thee common methods in nonlinear data analysis can be modified to account for nonuniform time sampling by using fuzzy delay coordinate reconstructions the effects of measurement noise and time sampling errors are compared we have also developed a learning algorithm to find optimal fuzzy delay coordinate reconstructions of the data to suit one s goals this can be employed to find representations optimized for measuring topological invariants forecasting control or other goals

algorithms for generating surrogate data for sparsely quantized time series abstract the method of surrogate data is frequently used for a statistical examination of nonlinear properties underlying original data if surrogate data sets are generated by a null hypothesis that the data are derived by a linear process a rejection of the hypothesis means that the original data have more complex properties however we found that if an algorithm for generating surrogate data for example amplitude adjusted fourier transformed is applied to sparsely quantized data there are large discrepancies between their power spectrum and that of the original data in lower frequency regions we performed some simulations to confirm that these errors often lead to false rejections in this paper in order to prevent such drawbacks we advance an extended hypothesis and propose two improved algorithms for generating surrogate data that reduce the discrepancies of the power spectra we also confirm the validity of the two improved algorithms with numerical simulations by showing that the extended null hypothesis can be rejected if the time series is produced from chaotic dynamical systems finally we applied these algorithms for analyzing financial tick data as a real example then we showed that the extended null hypothesis cannot be rejected because the nonlinear statistics or nonlinear prediction errors exhibited are the same as those of the original financial tick time series

finite correlation dimension for stochastic systems with power law spectra abstract we discuss a counter example to the traditional view that stochastic processes lead to a non convergence of the correlation dimension in computed or measured time series specifically we show that a simple class of colored random noises characterized by a power law power spectrum have a finite and predictable value for the correlation dimension these results have implications on the experimental study of deterministic chaos as they indicate that the soie observation of a finite fractal dimension from the analysis of a time series is not sufficient to infer the presence of a strange attractor in the system dynamics we demonstrate that the types of random noises considered herein may be given an interpretation in terms of their fractal properties the consequent exploitation of the non gaussian behavior of these random noises leads us to the introduction of a new time series analysis method which we call multivariate scaling analysis we apply this approach to characterize several global properties of random noise

fractal fluctuations in spatiotemporal variables when walking on a self paced treadmill abstract this study investigated the fractal dynamic properties of stride time st stride length sl and stride speed ss during walking on a self paced treadmill stm in which the belt speed is automatically controlled by the walking speed twelve healthy young subjects participated in the study the subjects walked at their preferred walking speed under four conditions stm stm with a metronome stm met fixed speed conventional treadmill ftm and ftm with a metronome ftm met to compare the fractal dynamics between conditions the mean variability and fractal dynamics of st sl and ss were compared moreover the relationship among the variables was examined under each walking condition using three types of surrogates the mean values of all variables did not differ between the two treadmills and the variability of all variables was generally larger for stm than for ftm the use of a metronome resulted in a decrease in variability in st and ss for all conditions the fractal dynamic characteristics of ss were maintained with stm in contrast to ftm and only the fractal dynamic characteristics of st disappeared when using a metronome in addition the fractal dynamic patterns of the cross correlated surrogate results were identical to those of all variables for the two treadmills in terms of the fractal dynamic properties stm walking was generally closer to overground walking than ftm walking although further research is needed the present results will be useful in research on gait fractal dynamics and rehabilitation

development of a high resolution scheme for a multi dimensional advection diffusion equation in this article we present a composite scheme to solve the scalar transport equation in a two dimensional space the aim of this study is to accurately resolve sharp profiles in the flow the theory of the m matrix serves as the theoretical foundation for achieving this goal attempts to extend the approach to resolve discontinuities in all cases motivate the development of the composite scheme for this study a conditionally monotonic legendre polynomial finite element model is used together with an unconditionally monotonic scheme computational evidence reveals that the composite model improves stability while it maintains accuracy the application scope is thus greatly extended

asymmetric multifractal detrending moving average analysis in time series of pm2 5 concentration abstract in this paper we propose the asymmetric multifractal detrending moving average analysis a mfdma method to explore the asymmetric correlation in non stationary time series the proposed method is applied to explore the asymmetric correlation of pm2 5 daily average concentration with uptrends or downtrends in china in addition shuffling and phase randomization procedures are applied to detect the sources of multifractality the results show that existences of asymmetric correlations and the asymmetric correlations are multifractal further the multifractal scaling behavior in the chinese pm2 5 is caused not only by long range correlation but also by fat tailed distribution but the major source of multifractality is fat tailed distribution

the spectrum of the locked state for the kuramoto model of coupled oscillators we analyze the linear stability of the phase locked state in the kuramoto model of coupled oscillators the main result is the first rigorous characterization of the spectrum and its associated eigenvectors for any finite number of oscillators all but two of the eigenvalues are negative and merge into a continuous spectrum as the number of oscillators tends to infinity one eigenvalue is always zero by rotational invariance the final eigenvalue corresponding to a collective mode determines the stability of the locked state

estimating the dimension of high dimensional attractors a comparison between two algorithms abstract we compare two algorithms for the numerical estimation of the correlation dimension from a finite set of vectors the classical algorithm of grassberger and procaccia gpa and the recently proposed algorithm of judd ja data set size requirements and their relations to systematic and statistical errors of the estimates are investigated it is demonstrated that correlation dimensions of the order of 6 can correctly be resolved on the basis of the about 100000 data points in the case of a continuous trajectory on a strange attractor the minimum data set size is however noticeably dependent on the geometrical structure of the system from which the vectors were sampled

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

deterministic and random synthesis of discrete chaos in this paper two anticontrol algorithms for synthesis of discrete chaos are introduced in these algorithms the control parameter of a discrete dynamical system is switched either randomly or in a deterministic way between two or more values corresponding to periodic motions the result being chaotic behavior these algorithms require no knowledge of specific mathematical properties of the underlying map modeling the system the existence of chaos is demonstrated using various tools including graphical iteration histogram lyapunov exponent and surrogate tests in this paper these very simple and implementable chaotifiers are applied to the logistic map

a rotated monotone difference scheme for the two dimensional anisotropic drift diffusion equation a rotated upwind discretization scheme is presented for the discretization of the steady state two dimensional anisotropic drift diffusion equation taking into account the local characteristic nature of the solution the notable features of the algorithm lie in the projection of the governing partial differential equation onto two orthogonal axes to yield a vanishing mixed derivative term and in the utilization of the upwind flow of information as a result the limiting behaviour of the elliptic equation is preserved in the discretization the scheme produces an m matrix which guarantees an oscillation free solution and which enables the discrete system to be solved using standard iterative solvers the method is illustrated by numerical examples for which the analytical solutions are known

partial entrainment in the finite kuramoto sakaguchi model abstract although modifications of the kuramoto model have been the subject of extensive research the model itself is not yet fully understood we offer several results and observations some analytic others through simulations we derive a sufficient condition for the existence of a solution exhibiting partial entrainment with respect to a given subset of oscillators the result also implies persistence of the entrainment behavior under perturbations the critical values of the coupling strength defining the transitions between different forms of partial entrainment are predicted by an analytical approximation based on the fact that oscillators with large differences in their natural frequencies have little influence on each other s entrainment behavior the predictions agree with the actual values obtained by simulations we indicate by simulations that entrainment can disappear with increasing coupling strength and that in arrays of josephson junctions a similar phenomenon can be observed where it is also possible that a junction leaving one entrained subset joins another entrained subset

modeling and synchronizing chaotic systems from time series data the problem of obtaining ordinary differential equations ode s from chaotic time series data is addressed the vector fields for the ode s are polynomials constructed from a basis set that is orthonormal on the data the method for constructing the model is similar to the integration of ode s using adams predictor corrector integration the method is compared to the usual euler model and is shown to be accurate for much larger sampling intervals in addition the method used to construct the model is capable of determining the optimal polynomial vector field for the given data finally we demonstrate that it is possible to synchronize in the sense of fujisaka and yamada prog theor phys 69 32 1983 as well as pecora and carroll phys rev lett 64 821 1990 phys rev a 44 2374 1991 the model to a time series synchronization is used as a nontrivial test to determine how close the model vector field is to the true vector field implications and possible applications of synchronization are discussed

nonlinear analysis of river flow time sequences within the field of chaos theory several methods for the analysis of complex dynamical systems have recently been proposed in light of these ideas we study the dynamics which control the behavior over time of river flow investigating the existence of a low dimension deterministic component the present article follows the research undertaken in the work of porporato and ridolfi 1996a in which some clues as to the existence of chaos were collected particular emphasis is given here to the problem of noise and to nonlinear prediction with regard to the latter the benefits obtainable by means of the interpolation of the available time series are reported and the remarkable predictive results attained with this nonlinear method are shown

discrete time dynamic systems synchronization information transmission and model matching some recently published results have highlighted the role of synchronization phenomena in recovering perturbation signals injected in nonlinear continuous time oscillators in the present contribution those results are extended to the realm of discrete time systems it is also shown that the synchronization of nonlinear discrete time systems provide very interesting ramifications to the problem of measuring the discrepancy between mathematical models and the corresponding original dynamical system from which the data were measured moreover the noise impact on the proposed approach is discussed

characterization of iran electricity market indices with pay as bid payment mechanism abstract market data analysis in iran s electricity market as a market with a pay as bid payment mechanism has been considered in this paper the analysis procedure includes both predictability and correlation analysis of the most important load and price indices the experimental data from iran s electricity market has been employed in its real size which is long enough to take properties such as non stationarity of the market into account for predictability the characteristics of the hourly accepted weighted average price wap as the topmost price index of this market is analyzed the analysis tools are time series analysis methods such as power spectral density analysis phase space reconstruction and test of surrogates the fractional dimension and the slope of integral sums and the recurrence plots the results indicate a deterministic un stationary and seasonal behavior in addition to unstable periodic orbits and even chaotic behavior in wap time series these observations imply just short term predictability of wap behavior the interactive behavior of wap with the hourly required load rl is also considered for this interaction analysis in addition to the common correlation methods cross and joint recurrence plot are also employed the joint behavioral analysis represents an un stationary mimic correlation between wap and rl

integrated approach to the assessment of long range correlation in time series data to assess whether a given time series can be modeled by a stochastic process possessing long range correlation one usually applies one of two types of analysis methods the spectral method and the random walk analysis the first objective of this work is to show that each one of these methods used alone can be susceptible to producing false results we thus advocate an integrated approach which requires the use of both methods in a consistent fashion we provide the theoretical foundation of this approach and illustrate the main ideas using examples the second objective relates to the observation of long range anticorrelation hurst exponent hl1 2 in real world time series data the very peculiar nature of such processes is emphasized in light of the stringent condition under which such processes can occur using examples we discuss the possible factors that could contribute to the false claim of long range anticorrelations and demonstrate the particular importance of the integrated approach in this case

detection of weak directional coupling phase dynamics approach versus state space approach we compare two conceptually different approaches to the detection of weak directional couplings between two oscillatory systems from bivariate time series the first approach is based on the analysis of the systems phase dynamics whereas the other one tests for interdependencies in the reconstructed state spaces of the systems we analyze the sensitivity of both techniques to weak couplings in numerical experiments by considering couplings between almost identical as well as between significantly different nonlinear systems we study different degrees of phase diffusion test the robustness of the two techniques against observational noise and investigate the influence of the time series length our results show that none of the two approaches is generally superior to the other and we conclude that it is probably the combination of both techniques that would allow the most comprehensive and reliable characterization of coupled systems

collective synchronization as a method of learning and generalization from sparse data we propose a method for extracting general features from multivariate data using a network of phase oscillators subject to an analogue of the kuramoto model for collective synchronization in this method the natural frequencies of the oscillators are extended to vector quantities to which multivariate data are assigned the common frequency vectors of the groups of partially synchronized oscillators are interpreted to be the template vectors representing the general features of the data set we show that the proposed method becomes equivalent to the self organizing map algorithm devised by kohonen when the governing equations are linearized about their solutions of partial synchronization as a case study to test the utility of our method we applied it to care needs certification data in the japanese public long term care insurance program and found major general patterns in the health status of the elderly needing nursing care

genuinely upwind algorithms for the multidimensional euler equations a new method for the solution of the multidimensional euler equations is presented as opposed to the classical schemes it is genuinely multidimensional in that the local characteristic directions into which information is propagated are detected based on this approach a conservative cell centered scheme has been formulated the numerical fluxes are evaluated using muscl extrapolations along the characteristic directions this leads to a family of first and second order accurate schemes with an improved resolution as compared to the classical schemes

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

scale invariance of human electroencephalogram signals in sleep in this paper we investigate the dynamical properties of electroencephalogram eeg signals of humans in sleep by using a modified random walk method we demonstrate that scale invariance is embedded in eeg signals after a detrending procedure is applied furthermore we study the dynamical evolution of the probability density function pdf of the detrended eeg signals by nonextensive statistical modeling it displays a scale independent property which is markedly different from the usual scale dependent pdf evolution and cannot be described by the fokker planck equation

long range correlation properties of stationary linear models with mixed periodicities we consider the problem of stationary and linear source systems which generate time series data with long range correlations we use the discrete fourier transform dft and build stationary linear models using artificial time series data exhibiting a 1 f spectrum where the models can include only terms that contribute significantly to the model as assessed by information criteria the result is that the optimal best model is only composed of mixed periodicities that is the model does not include all continuous periodicities and the time series data generated by the model exhibit a clear 1 f spectrum in a wide frequency range it is considered that as the 1 f spectrum is a consequence of the contributions of all periods consecutive periods are indispensable to generate such data by stationary linear models however the results indicate that there are cases where this expectation is not always met these results also imply that although we can know linear features of time series data using the dft we always cannot substantially infer the type of the source system even if the system is stationary linear

finding efficient recursions for risk aggregation by computer algebra we derive recursions for the probability distribution of random sums by computer algebra unlike the well known panjer type recursions they are of finite order and thus allow for computation in linear time this efficiency is bought by the assumption that the probability generating function of the claim size be algebraic the probability generating function of the claim number is supposed to be from the rather general class of d finite functions

use of recurrence plot and recurrence quantification analysis in taiwan unemployment rate time series abstract the aim of the article is to answer the question if the taiwan unemployment rate dynamics is generated by a non linear deterministic dynamic process this paper applies a recurrence plot and recurrence quantification approach based on the analysis of non stationary hidden transition patterns of the unemployment rate of taiwan the case study uses the time series data of the taiwan s unemployment rate during the period from 1978 01 to 2010 06 the results show that recurrence techniques are able to identify various phases in the evolution of unemployment transition in taiwan

a discontinuity capturing crosswind dissipation for the finite element solution of the convection diffusion equation abstract to avoid the local oscillations that still remain using the streamline upwind petrov galerkin formulation for the scalar convection diffusion equation the introduction of a nonlinear crosswind dissipation is proposed it is shown that the method is less overdiffusive than other discontinuity capturing techniques and has better numerical behavior the design of the crosswind diffusion is based on the study of the discrete maximum principle for some simple cases

autocorrelation type timescale and statistical property in financial time series abstract earlier studies have documented that three types of autocorrelations exist in financial time series sign volatility and return autocorrelation in this paper we examine how each type of the above autocorrelations affects the statistical properties of financial time series and its role in maintaining such statistical properties using three different shuffling series that correspondingly destroy each type of autocorrelation upon different timescales we find that 1 the statistical properties of the shuffling series significantly vary from the original ones 2 volatility and return autocorrelations show greater impacts than sign autocorrelation 3 the effects on the statistical properties are intensified as time scale expands 4 the nonlinear component of autocorrelation is the major drive of the effect

a monotone streamline upwind finite element method for convection dominated flows a new streamline upwind approximation for treating advection dominatcd transport is presented the proposed method is quite simple to implement with existing finite element methods for this work the method is used in a two dimensional finite element computer program the new method is applied to several test cases that have been presented in previous articles to evaluate the stability and accuracy of proposed methods for treating advection dominatcd flows the results demonstrate that the new method is able to predict the test cases with a significant increase in accuracy compared to previous techniques in addition these results demonstrate conclusively that the method does not exhibit the non physical spatial oscillations that have plagued previous methods

nonlinear dynamical system identification with dynamic noise and observational noise in this paper we consider the problem of whether a nonlinear system has dynamic noise and then estimate the level of dynamic noise to add to any model we build the method we propose relies on a nonlinear model and an improved least squares method recently proposed on the assumption that observational noise is not large we do not need any a priori knowledge for systems to be considered and we can apply the method to both maps and flows we demonstrate with applications to artificial and experimental data the results indicate that applying the proposed method can detect presence or absence of dynamic noise from scalar time series and give a reliable level of dynamic noise to add to the model built in some cases

construction of multivariate surrogate sets from nonlinear data using the wavelet transform abstract the use of surrogate data has become a crucial first step in the study of nonlinearity in time series data a widely used technique to construct surrogate data is to randomize the phases of the data in the fourier domain in this paper an alternative technique based on the resampling of wavelet coefficients is discussed this approach exploits between scale correlations that exist within nonlinear data but which are either absent or weak in stochastic data it proceeds by transforming the data into the wavelet domain and permuting the wavelet coefficients experimental and numerical time series data are used to demonstrate that the performance of the wavelet resampling technique is comparable to phase randomization in terms of the preservation of linear properties removal of nonlinear structure and computational demands however the wavelet technique may have specific and distinct advantages in the application to complex data sets such as numerical analysis of turbulence and experimental brain imaging data where wavelets give a more parsimonious representation of spatio temporal patterns than fourier modes it is shown that different techniques of resampling the data in the wavelet domain may optimize the construction of surrogate data according to the properties of the experimental time series and computational constraints

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

deterministic dynamics of neural activity during absence seizures in rats the study of brain electrical activities in terms of deterministic nonlinear dynamics has recently received much attention forbidden ordinal patterns fop is a recently proposed method to investigate the determinism of a dynamical system through the analysis of intrinsic ordinal properties of a nonstationary time series the advantages of this method in comparison to others include simplicity and low complexity in computation without further model assumptions in this paper the fop of the eeg series of genetic absence epilepsy rats from strasbourg was examined to demonstrate evidence of deterministic dynamics during epileptic states experiments showed that the number of fop of the eeg series grew significantly from an interictal to an ictal state via a preictal state these findings indicated that the deterministic dynamics of neural networks increased significantly in the transition from the interictal to the ictal states and also suggested that the fop measures of the eeg series could be considered as a predictor of absence seizures

detrended fluctuation analysis of short datasets an application to fetal cardiac data abstract using detrended fluctuation analysis dfa we perform scaling analysis of short datasets of length 500 1500 data points we quantify the long range correlation exponent by computing the mean value of the local exponents l in the asymptotic regime the local exponents are obtained as the numerical derivative of the logarithm of the fluctuation function f s with respect to the logarithm of the scale factor s l d log 10 f s d log 10 s these local exponents display huge variations and complicate the correct quantification of the underlying correlations we propose the use of the phase randomized surrogate prs which preserves the long range correlations of the original data to minimize the variations in the local exponents using the numerically generated uncorrelated and long range correlated data we show that performing dfa on several realizations of prs and estimating l from the averaged fluctuation functions of all realizations can minimize the variations in l the application of this approach to the fetal cardiac data rr intervals is discussed and we show that there is a statistically significant correlation between and the gestation age

electroencephalograms in epilepsy analysis and seizure prediction within the framework of lyapunov theory abstract epileptic seizures are defined as the clinical manifestation of excessive and hypersynchronous activity of neurons in the cerebral cortex and represent one of the most frequent malfunctions of the human central nervous system therefore the search for precursors and predictors of a seizure is of utmost clinical relevance and may even guide us to a deeper understanding of the seizure generating mechanisms we extract chaos indicators such as lyapunov exponents and kolmogorov entropies from different types of electroencephalograms eegs this covers mainly intracranial eegs semi invasive and invasive recording techniques but also scalp eegs from the surface of the skin among the analytical methods we tested up to now we find that the spectral density of the local expansion exponents is best suited to predict the onset of a forthcoming seizure we also evaluate the time evolution of the dissipation in these signals it exhibits strongly significant variations that clearly relate to the time relative to a seizure onset this article is mainly devoted to an assessment of these methods with respect to their sensitivity to eeg changes e g prior to a seizure further we investigate interictal eegs i e far away from a seizure in order to characterize their more general properties such as the convergence of the reconstructed quantities with respect to the number of phase space dimensions generally we use multichannel reconstruction but we also present a comparison with the delay embedding technique