detection of couplings in ensembles of stochastic oscillators the problem of detection and quantitative characterization of directional couplings in an ensemble of noisy oscillators from a time series is addressed we suggest estimators for the strengths of couplings which are based on modeling the observed oscillations with a set of stochastic phase oscillators and easily interpreted from a physical viewpoint moreover we present an analytic formula for a statistical significance level allowing to reveal an architecture of couplings reliably from a relatively short time series the technique applies to weakly coupled nonsynchronized oscillators it is introduced for oscillators with close basic frequencies but can be readily generalized to the case of arbitrary frequencies efficiency of the technique is demonstrated in numerical experiments

a robust method for detecting interdependences application to intracranially recorded eeg we present a measure for characterizing statistical relationships between two time sequences in contrast to commonly used measures like cross correlations coherence and mutual information the proposed measure is non symmetric and provides information about the direction of interdependence it is closely related to recent attempts to detect generalized synchronization however we do not assume a strict functional relationship between the two time sequences and try to define the measure so as to be robust against noise and to detect also weak interdependences we apply our measure to intracranially recorded electroencephalograms of patients suffering from severe epilepsies

detecting dynamical interdependence and generalized synchrony through mutual prediction in a neural ensemble a method to characterize dynamical interdependence among nonlinear systems is derived based on mutual nonlinear prediction systems with nonlinear correlation will show mutual nonlinear prediction when standard analysis with linear cross correlation might fail mutual nonlinear prediction also provides information on the directionality of the coupling between systems furthermore the existence of bidirectional mutual nonlinear prediction in unidirectionally coupled systems implies generalized synchrony numerical examples studied include three classes of unidirectionally coupled systems systems with identical parameters nonidentical parameters and stochastic driving of a nonlinear system this technique is then applied to the activity of motoneurons within a spinal cord motoneuron pool the interrelationships examined include single neuron unit firing the total number of neurons discharging at one time as measured by the integrated monosynaptic reflex and intracellular measurements of integrated excitatory postsynaptic potentials epsp s dynamical interdependence perhaps generalized synchrony was identified in this neuronal network between simultaneous single unit firings between units and the population and between units and intracellular epsp s

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

comparison of nonlinear granger causality extensions for low dimensional systems the identification of hidden interdependences among the parts of a complex system is a fundamental issue typically the objective is given only a sequence of scalar measurements to infer as much as possible about the internal dynamics of the system and about the interactions between its subsystems in general such interactions are not only nonlinear but also asymmetric constraints on the estimation of hidden relationships are further posed by noise and by the length of signals sampled from real world systems the focus of this paper is causal dependences between bivariate time series we especially focus on the nonlinear extension of granger causality with polynomial terms of the conventional embedding vector in this paper we study the performance of this measure in comparison with three alternative methods proposed recently in low dimensional and low order nonlinearity systems those methods are tested with three different artificial chaotic maps with several noise contamination setups as a result we find that the polynomial embedding technique successfully detects asymmetric causal dependences between bivariate time series in many low dimensional cases

local predictability and information flow in complex dynamical systems abstract predictability is by observation a local notion in complex dynamical systems its spatiotemporal structure implies a flow or transfer in discrete cases of information that redistributes the local predictability within the state space of concern information flow is a fundamental concept in general physics which has applications in a wide variety of disciplines such as neuroscience material science atmosphere ocean science and turbulence research to name but a few in this study it is rigorously formulated with respect to relative entropy within the framework of a system with many components each signifying a location or a structure given a component the mechanism governing the evolution of its predictability can be classified into two groups one due to the component itself another due to a transfer of information from its peers a measure of the transfer is rigorously derived and an explicit expression obtained this measure possesses a form reminiscent of that we have obtained before with respect to absolute entropy in x s liang and r kleeman a rigorous formalism of information transfer between dynamical system components physica d 227 2007 173 182 in particular when the system is of dimensionality 2 there is no difference between the formalisms with respect to absolute entropy and relative entropy except for a minus sign properties have been explored and discussed particularly discussed is the property of asymmetry or causality which states that information transfer from one component to another carries no hint about the transfer in the other direction in contrast to the transfer of other quantities such as energy this formalism has been applied to the study of the scale scale interaction and information transfer between the first two modes of the truncated burgers equation it is found that all 12 transfers are essentially zero or negligible save for a strong transfer between the sine components from the low frequency mode to the high frequency mode that is to say the predictability of the high frequency mode is controlled by the knowledge of the low frequency mode this result though from a highly idealized system has interesting implications about the dynamical closure problem in turbulence research and atmosphere ocean science i e the subgrid processes may to some extent be parameterized by the large scale dynamics this study can be adopted to investigate the propagation of uncertainties in fluid flows which has important applications in problems such as atmospheric observing platform design and may be utilized to identify the route of information flowing within a complex network

phase shifts of synchronized oscillators and the systolic diastolic blood pressure relation we study the phase synchronization properties of systolic and diastolic arterial pressure in healthy subjects we find that delays in the oscillatory components of the time series depend on the frequency bands that are considered in particular we find a change of sign in the phase shift going from the very low frequency band to the high frequency band this behavior should reflect a collective behavior of a system of nonlinear interacting elementary oscillators we prove that some models describing such systems e g the winfree and the kuramoto models offer a clue to this phenomenon for these theoretical models there is a linear relationship between phase shifts and the difference of natural frequencies of oscillators and a change of sign in the phase shift naturally emerges

visibility graph similarity a new measure of generalized synchronization in coupled dynamic systems abstract synchronization is defined as interdependencies among coupled dynamic systems in most coupled systems the intrinsic and internal variants and the interdependencies among their subsystems are not accessible therefore in order to quantify the interdependencies among the coupled systems attempts have been made through measuring the synchronization between their outputs represented mostly as time series in this paper a new method called visibility graph similarity vgs is presented as a method of measuring generalized synchronization first each time series is reconstructed as a trajectory in a state space next a distance time series dts is created from a sequence of relative distances of the states to a reference state subsequently a visibility graph vg is constructed using dts then a sequence of degrees of the vg called degree sequence ds is obtained correlation of the dss of two coupled systems is called vgs and is presented as a measurement of similarity of dynamics of the coupled systems the synchronization measurement performance of the vgs is compared with synchronization likelihood sl and the classical cross correlation method using two identical and non identical models of two coupled henon map over the entire time domain also it is compared with sl for tracing temporal synchronization using both models it is shown that vgs provides a more accurate measure of the overall synchronization compared with sl it is more reliable for measuring weak couplings compared with the cross correlation method moreover vgs uses fewer parameters and detects the temporal synchronization sooner than the sl

a rigorous formalism of information transfer between dynamical system components i discrete mapping we put the concept of information transfer on a rigorous footing and establish for it a formalism within the framework of discrete maps the resulting transfer measure possesses a property of directionality or transfer asymmetry as emphasized by schreiber t schreiber measuring information transfer phys rev lett 85 2 2000 461 it also verifies the transfer measure for two dimensional systems which was obtained by liang and kleeman x s liang r kleeman information transfer between dynamical system components phys rev lett 95 24 2005 244101 through a different avenue connections to classical formalisms are explored and applications presented we find that in the context of the baker transformation there is always information flowing from the stretching direction to the folding direction while no transfer occurs in the opposite direction we also find that within the henon map system the transfer from the quadratic component to the linear component is of a simple form as expected on physical grounds this latter result is unique to our formalism

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

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

assessing causality from multivariate time series in this work we propose a general nonparametric test of causality for weakly dependent time series more precisely we study the problem of attribution i e the proper comparison of the relative influence that two or more external dynamics trigger on a given system of interest we illustrate the possible applications of the proposed methodology in very different fields like physiology and climate science

conditional correlation as a measure of mediated interactivity in fmri and meg eeg many measures have been proposed so far to extract brain functional interactivity from functional magnetic resonance imaging fmri and magnetoencephalography electroencephalography meg eeg data sets unfortunately none has been able to provide a relevant self contained and common definition of brain interaction in this paper we propose a first step in this direction we first introduce a common terminology together with a cross modal definition of interaction in this setting we investigate the commonalities shared by some measures of interaction proposed in the literature we show that temporal correlation nonlinear correlation mutual information generalized synchronization phase synchronization coherence and phase locking value plv actually measure the same quantity namely correlation when one is investigating linear interactions between independently and identically distributed gaussian variables we also demonstrate that these data driven measures can only partly account for the interaction patterns that can be expressed by the effective connectivity of structural equation modeling sem to bridge this gap we suggest the use of conditional correlation which is shown to be related to mediated interaction

from granger causality to long term causality application to climatic data quantitative characterization of interaction between processes from time series is often required in different fields of natural science including geophysics and biophysics typically one estimates short term influences e g the widely used granger causality is defined via one step ahead predictions such an approach does not reveal how strongly the long term behavior of one process under study is affected by the others to overcome this problem we introduce the concept of long term causality which extends the concept of granger causality the long term causality is estimated from data via empirical modeling and analysis of model dynamics under different conditions apart from mathematical examples we apply both approaches to find out how strongly the global surface temperature gst is affected by variations in carbon dioxide atmospheric content solar activity and volcanic activity during the last 150 years influences of all the three factors on gst are detected with the granger causality however the long term causality shows that the rise in gst during the last decades can be explained only if the anthropogenic factor co 2 is taken into account in a model

generalized synchronization of chaos in directionally coupled chaotic systems synchronization of chaotic systems is frequently taken to mean actual equality of the variables of the coupled systems as they evolve in time we explore a generalization of this condition which equates dynamical variables from one subsystem with a function of the variables of another subsystem this means that synchronization implies a collapse of the overall evolution onto a subspace of the system attractor in full space we explore this idea in systems where a response system bold y ital t is driven with the output of a driving system bold x ital t but there is no feedback to the driver we lose generality but gain tractability with this restriction to investigate the existence of the synchronization condition bold y ital t phi bold x ital t we introduce the idea of mutual false nearest neighbors to determine when closeness in response space implies closeness in driving space the synchronization condition also implies that the response dynamics is determined by the drive alone and we provide tests for this as well examples are drawn from computer simulations on various known cases of synchronization and on data from nonlinear electrical circuits determining the presence of generalized synchronization will be quite important when one has only scalarmore observations from the drive and from the response systems since the use of time delay or other embedding methods will produce imperfect coordinates in which strict equality of the synchronized variables is unlikely to transpire less

fedosov quantization on symplectic ringed spaces we expose the basics of the fedosov quantization procedure placed in the general framework of symplectic ringed spaces this framework also includes some poisson manifolds with nonregular poisson structures presymplectic manifolds complex analytic symplectic manifolds etc

confidence bands for the median survival time as a function of the covariates in the cox model abstract let p x be the pth quantile of the distribution of the life length of an individual with covariate vector x in the cox model we introduce an estimator p x of p x and develop several families of confidence bands for x as a function of x to construct one type of band we proceed as follows we show that as n where n is the number of individuals in the study converges weakly to a gaussian process w x with a complicated covariance structure we then estimate this covariance structure from the data and simulate many gaussian processes with this estimated covariance structure the critical constants required for the construction of the confidence bands are obtained from the simulated processes another type of bands is obtained by bootstrapping we obtain an asymptotic theory for both types of bands simulation studies are used to compare the two types of bands the methods are illustrated on the stanford heart transplant data

detecting phase synchronization in noisy data from coupled chaotic oscillators two schemes are proposed to detect phase synchronization from chaotic data contaminated by noise the first is a neighborhood based method which links time delay embedding with instantaneous phase estimation the second adopts the local projection method as a preprocessing filter to noisy data both schemes utilize the state recurrence an important feature of chaotic data the proposed schemes are applied to data measured from two typical chaotic systems i e the coupled rossler systems and the coupled lorenz systems respectively the results show that phase synchronization which may be buried by noise is detected even when the noise level is high moreover the overestimation of the degree of phase synchronization which may be introduced by the hilbert transform combined with a traditional linear bandpass filter can be avoided when the data are contaminated by only measurement noise

detection of synchronization between chaotic signals an adaptive similarity based approach we present an adaptive similarity based approach to detect generalized synchronization gs with n m phase synchronization ps where n and m are integers and one of them is 1 this approach is based on the similarity index si and gaussian mixture model with the minimum description length criterion the clustering method which is shown to be superior to the closeness and connectivity of a continuous function is employed in this study to detect the existence of gs with n m ps we conducted a computer simulation and a finger lifting experiment to illustrate the effectiveness of the proposed method in the simulation of a rossler lorenz system our method outperformed the conventional si and gs with 2 1 ps within the coupled system was found in the experiment of self paced finger lifting movement cortico muscular gs with 1 2 and 1 3 ps was found between the surface electromyogram signals on the first dorsal interossei muscle and the magnetoencephalographic data in the motor area the gs with n m ps n or m 1 has been simultaneously resolved from both simulation and experiment the proposed approach thereby provides a promising means for advancing research into both nonlinear dynamics and brain science

information flow within stochastic dynamical systems information flow or information transfer is an important concept in general physics and dynamical systems which has applications in a wide variety of scientific disciplines in this study we show that a rigorous formalism can be established in the context of a generic stochastic dynamical system an explicit formula has been obtained for the resulting transfer measure which possesses a property of transfer asymmetry and if the stochastic perturbation to the receiving component does not rely on the giving component has a form the same as that for the corresponding deterministic system this formula is further illustrated and validated with a two dimensional langevin equation a remarkable observation is that for two highly correlated time series there could be no information transfer from one certain series say x 2 to the other x 1 that is to say the evolution of x 1 may have nothing to do with x 2 even though x 1 and x 2 are highly correlated information flow analysis thus extends the traditional notion of correlation analysis and or mutual information analysis by providing a quantitative measure of causality between dynamical events

fractal dimension of spatially extended systems properties of the invariant measure are numerically investigated in 1d chains of diffusively coupled maps the coarse grained fractal dimension is carefully computed in various embedding spaces observing an extremely slow convergence towards the asymptotic value this is in contrast with previous simulations where the analysis of an insufficient number of points led the authors to underestimate the increase of fractal dimension with increasing the dimension of the embedding space orthogonal decomposition is also performed confirming that the slow convergence is intrinsically related to local nonlinear properties of the invariant measure finally the kaplan yorke conjecture is tested for short chains showing that despite the noninvertibility of the dynamical system a good agreement is found between lyapunov dimension and information dimension

comparison of six methods for the detection of causality in a bivariate time series in this comparative study six causality detection methods were compared namely the granger vector autoregressive test the extended granger test the kernel version of the granger test the conditional mutual information transfer entropy the evaluation of cross mappings between state spaces and an assessment of predictability improvement due to the use of mixed predictions seven test data sets were analyzed linear coupling of autoregressive models a unidirectional connection of two h enon systems a unidirectional connection of chaotic systems of r ossler and lorenz type and of two different r ossler systems an example of bidirectionally connected two species systems a fishery model as an example of two correlated observables without a causal relationship and an example of mediated causality we tested not only 20 phantom rule 0 16em 0ex 000 points long clean time series but also noisy and short variants of the data the standard and the extended granger tests worked only for the autoregressive models the remaining methods were more successful with the more complex test examples although they differed considerably in their capability to reveal the presence and the direction of coupling and to distinguish causality from mere correlation

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

detecting generalized synchronization between chaotic signals a kernel based approach a unified framework for analysing generalized synchronization in coupled chaotic systems from data is proposed the key of the proposed approach is the use of the kernel methods recently developed in the field of machine learning several successful applications are presented which show the capability of the kernel based approach for detecting generalized synchronization and dynamical change of the coupling strength between two chaotic systems can be captured by the proposed approach it is also discussed how the kernel parameter is suitably chosen from data

compatible symplectic connections on a cotangent bundle and the fedosov quantization a global construction of a family of symplectic connections on a cotangent bundle compatible with some linear symmetric connection on the base space is proposed examples of the compatible symplectic connections are given a detailed analysis of an abelian connection and of flat sections for this kind of symplectic connection in the fedosov algorithm are presented some properties of the product determined by the compatible symplectic connection are shown

granger causality and cross recurrence plots in rheochaos our stress relaxation measurements on wormlike micelles using a rheo sals rheology small angle light scattering apparatus allow simultaneous measurements of the stress and the scattered depolarized intensity the latter is sensitive to orientational ordering of the micelles to determine the presence of causal influences between the stress and the depolarized intensity time series we have used the technique of linear and nonlinear granger causality we find there exists a feedback mechanism between the two time series and that the orientational order has a stronger causal effect on the stress than vice versa we have also studied the phase space dynamics of the stress and the depolarized intensity time series using the recently developed technique of cross recurrence plots crps the presence of diagonal line structures in the crps unambiguously proves that the two time series share similar phase space dynamics