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

discrete breathers in thermal equilibrium distributions and energy gaps we study a discrete two dimensional nonlinear system that allows for discrete breather solutions we perform a spectral analysis of the lattice dynamics at thermal equilibrium and use a cooling technique to measure the amount of breathers at thermal equilibrium our results confirm the existence of an energy threshold for discrete breathers the cooling method provides a novel way of measuring and analyzing discrete breather distribution properties in thermal equilibrium

hopf bifurcation in a diffusive lotka volterra type system with nonlocal delay effect abstract the dynamics of a diffusive lotka volterra type model for two species with nonlocal delay effect and dirichlet boundary conditions is investigated in this paper the existence and multiplicity of spatially nonhomogeneous steady state solutions are obtained by means of lyapunov schmidt reduction the stability of spatially nonhomogeneous steady state solutions and the existence of hopf bifurcation with the changes of the time delay are obtained by analyzing the distribution of eigenvalues of the infinitesimal generator associated with the linearized system by the normal form theory and the center manifold reduction the stability and bifurcation direction of hopf bifurcating periodic orbits are derived finally our theoretical results are illustrated by a model with homogeneous kernels and one dimensional spatial domain

information based detection of nonlinear granger causality in multivariate processes via a nonuniform embedding technique we present an approach framed in information theory to assess nonlinear causality between the subsystems of a whole stochastic or deterministic dynamical system the approach follows a sequential procedure for nonuniform embedding of multivariate time series whereby embedding vectors are built progressively on the basis of a minimization criterion applied to the entropy of the present state of the system conditioned to its past states a corrected conditional entropy estimator compensating for the biasing effect of single points in the quantized hyperspace is used to guarantee the existence of a minimum entropy rate at which to terminate the procedure the causal coupling is detected according to the granger notion of predictability improvement and is quantified in terms of information transfer we apply the approach to simulations of deterministic and stochastic systems showing its superiority over standard uniform embedding effects of quantization data length and noise contamination are investigated as practical applications we consider the assessment of cardiovascular regulatory mechanisms from the analysis of heart period arterial pressure and respiration time series and the investigation of the information flow across brain areas from multichannel scalp electroencephalographic recordings

reconstructing the topology of sparsely connected dynamical networks given a general physical network and measurements of node dynamics methods are proposed for reconstructing the network topology we focus on networks whose connections are sparse and where data are limited under these conditions common in many biological networks constrained optimization techniques based on the l1 vector norm are found to be superior for inference of the network connections

dynamics in a diffusive predator prey system with ratio dependent predator influence abstract a diffusive predator prey system with predator functional response subject to neumann boundary conditions is considered existence nonexistence and boundedness of positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation hopf and steady state bifurcation analyses are carried out in detail these results provide theoretical evidences to the complex spatio temporal dynamics found by numerical simulation

turing patterns in the lengyel epstein system for the cima reaction the first experimental evidence of the turing pattern was observed by de kepper and her associates 1990 on the cima reaction in an open unstirred gel reactor almost 40 years after turing s prediction lengyel and epstein characterized this famous experiment using a system of reaction diffusion equations in this paper we report some fundamental analytic properties of the lengyel epstein system our result also indicates that if either of the initial concentrations of the reactants the size of the reactor or the effective diffusion rate are not large enough then the system does not admit nonconstant steady states a priori estimates are fundamental to our approach for this nonexistence result the degree theory was combined with the a priori estimates to derive existence of nonconstant steady states

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

nonlinear parametric model for granger causality of time series the notion of granger causality between two time series examines if the prediction of one series could be improved by incorporating information of the other in particular if the prediction error of the first time series is reduced by including measurements from the second time series then the second time series is said to have a causal influence on the first one we propose a radial basis function approach to nonlinear granger causality the proposed model is not constrained to be additive in variables from the two time series and can approximate any function of these variables still being suitable to evaluate causality usefulness of this measure of causality is shown in two applications in the first application a physiological one we consider time series of heart rate and blood pressure in congestive heart failure patients and patients affected by sepsis we find that sepsis patients unlike congestive heart failure patients show symmetric causal relationships between the two time series in the second application we consider the feedback loop in a model of excitatory and inhibitory neurons we find that in this system causality measures the combined influence of couplings and membrane time constants

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

simple statistical explanation for the localization of energy in nonlinear lattices with two conserved quantities the localization of energy in the discrete nonlinear schrodinger equation is explained with statistical methods the partition function and the entropy of the system are computed for low amplitude initial conditions detailed predictions for the long time solution are derived localized high amplitude excitations absorb a surplus of energy when they emerge as a by product of the production of entropy in the small fluctuations the thermodynamic interpretation of this process applies to many dynamical systems with two conserved quantities

causality analysis of neural connectivity critical examination of existing methods and advances of new methods granger causality gc is one of the most popular measures to reveal causality influence of time series and has been widely applied in economics and neuroscience especially its counterpart in frequency domain spectral gc as well as other granger like causality measures have recently been applied to study causal interactions between brain areas in different frequency ranges during cognitive and perceptual tasks in this paper we show that 1 gc in time domain cannot correctly determine how strongly one time series influences the other when there is directional causality between two time series and 2 spectral gc and other granger like causality measures have inherent shortcomings and or limitations because of the use of the transfer function or its inverse matrix and partial information of the linear regression model on the other hand we propose two novel causality measures in time and frequency domains for the linear regression model called new causality and new spectral causality respectively which are more reasonable and understandable than gc or granger like measures especially from one simple example we point out that in time domain both new causality and gc adopt the concept of proportion but they are defined on two different equations where one equation for gc is only part of the other for new causality thus the new causality is a natural extension of gc and has a sound conceptual theoretical basis and gc is not the desired causal influence at all by several examples we confirm that new causality measures have distinct advantages over gc or granger like measures finally we conduct event related potential causality analysis for a subject with intracranial depth electrodes undergoing evaluation for epilepsy surgery and show that in the frequency domain all measures reveal significant directional event related causality but the result from new spectral causality is consistent with event related time frequency power spectrum activity the spectral gc as well as other granger like measures are shown to generate misleading results the proposed new causality measures may have wide potential applications in economics and neuroscience

a comparative study of synchrony measures for the early diagnosis of alzheimer s disease based on eeg it is well known that eeg signals of alzheimer s disease ad patients are generally less synchronous than in age matched control subjects however this effect is not always easily detectable this is especially the case for patients in the pre symptomatic phase commonly referred to as mild cognitive impairment mci during which neuronal degeneration is occurring prior to the clinical symptoms appearance in this paper various synchrony measures are studied in the context of ad diagnosis including the correlation coefficient mean square and phase coherence granger causality phase synchrony indices information theoretic divergence measures state space based measures and the recently proposed stochastic event synchrony measures experiments with eeg data show that many of those measures are strongly correlated or anti correlated with the correlation coefficient and hence provide little complementary information about eeg synchrony measures that are only weakly correlated with the correlation coefficient include the phase synchrony indices granger causality measures and stochastic event synchrony measures in addition those three families of synchrony measures are mutually uncorrelated and therefore they each seem to capture a specific kind of interdependence for the data set at hand only two synchrony measures are able to convincingly distinguish mci patients from age matched control patients i e granger causality in particular full frequency directed transfer function and stochastic event synchrony those two measures are used as features to distinguish mci patients from age matched control subjects yielding a leave one out classification rate of 83 the classification performance may be further improved by adding complementary features from eeg this approach may eventually lead to a reliable eeg based diagnostic tool for mci and ad

exploration of synergistic and redundant information sharing in static and dynamical gaussian systems to fully characterize the information that two source variables carry about a third target variable one must decompose the total information into redundant unique and synergistic components i e obtain a partial information decomposition pid however shannon s theory of information does not provide formulas to fully determine these quantities several recent studies have begun addressing this some possible definitions for pid quantities have been proposed and some analyses have been carried out on systems composed of discrete variables here we present an in depth analysis of pids on gaussian systems both static and dynamical we show that for a broad class of gaussian systems previously proposed pid formulas imply that i redundancy reduces to the minimum information provided by either source variable and hence is independent of correlation between sources and ii synergy is the extra information contributed by the weaker source when the stronger source is known and can either increase or decrease with correlation between sources we find that gaussian systems frequently exhibit net synergy i e the information carried jointly by both sources is greater than the sum of information carried by each source individually drawing from several explicit examples we discuss the implications of these findings for measures of information transfer and information based measures of complexity both generally and within a neuroscience setting importantly by providing independent formulas for synergy and redundancy applicable to continuous time series data we provide an approach to characterizing and quantifying information sharing amongst complex system variables

kernel canonical correlation granger causality for multiple time series canonical correlation analysis as a multivariate statistical technique has been applied to multivariate granger causality analysis to infer information flow in complex systems it shows unique appeal and great superiority over the traditional vector autoregressive method due to the simplified procedure that detects causal interaction between multiple time series and the avoidance of potential model estimation problems however it is limited to the linear case here we extend the framework of canonical correlation to include the estimation of multivariate nonlinear granger causality for drawing inference about directed interaction its feasibility and effectiveness are verified on simulated data

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

synchronization in dynamical networks evolution along commutative graphs starting from an initial wiring of connections we show that the synchronizability of a network can be significantly improved by evolving the graph along a time dependent connectivity matrix we consider the case of connectivity matrices that commute at all times and compare several approaches to engineer the corresponding commutative graphs in particular we show that synchronization in a dynamical network can be achieved even in the case in which each individual commutative graphs does not give rise to synchronized behavior

measuring synchronization in coupled model systems a comparison of different approaches the investigation of synchronization phenomena on measured experimental data such as biological time series has recently become an increasing focus of interest different approaches for measuring synchronization have been proposed that rely on certain characteristic features of the dynamical system under investigation for experimental data the underlying dynamics are usually not completely known therefore it is difficult to decide a priori which synchronization measure is most suitable for an analysis in this study we use three different coupled model systems to create a controlled setting for a comparison of six different measures of synchronization all measures are compared to each other with respect to their ability to distinguish between different levels of coupling and their robustness against noise results show that the measure to be applied to a certain task can not be chosen according to a fixed criterion but rather pragmatically as the measure which most reliably yields plausible information in test applications although certain dynamical features of a system under investigation e g power spectra dimension may render certain measures more suitable than others c 2006 elsevier b v all rights reserved

multivariate granger causality and generalized variance granger causality analysis is a popular method for inference on directed interactions in complex systems of many variables a shortcoming of the standard framework for granger causality is that it only allows for examination of interactions between single univariate variables within a system perhaps conditioned on other variables however interactions do not necessarily take place between single variables but may occur among groups or ensembles of variables in this study we establish a principled framework for granger causality in the context of causal interactions among two or more multivariate sets of variables building on geweke s seminal 1982 work we offer additional justifications for one particular form of multivariate granger causality based on the generalized variances of residual errors taken together our results support a comprehensive and theoretically consistent extension of granger causality to the multivariate case treated individually they highlight several specific advantages of the generalized variance measure which we illustrate using applications in neuroscience as an example we further show how the measure can be used to define partial granger causality in the multivariate context and we also motivate reformulations of causal density and granger autonomy our results are directly applicable to experimental data and promise to reveal new types of functional relations in complex systems neural and otherwise

redundant variables and granger causality we discuss the use of multivariate granger causality in presence of redundant variables the application of the standard analysis in this case leads to under estimation of causalities using the un normalized version of the causality index we quantitatively develop the notions of redundancy and synergy in the frame of causality and propose two approaches to group redundant variables i for a given target the remaining variables are grouped so as to maximize the total causality and ii the whole set of variables is partitioned to maximize the sum of the causalities between subsets we show the application to a real neurological experiment aiming to a deeper understanding of the physiological basis of abnormal neuronal oscillations in the migraine brain the outcome by our approach reveals the change in the informational pattern due to repetitive transcranial magnetic stimulations

framework to study dynamic dependencies in networks of interacting processes the analysis of dynamic dependencies in complex systems such as the brain helps to understand how emerging properties arise from interactions here we propose an information theoretic framework to analyze the dynamic dependencies in multivariate time evolving systems this framework constitutes a fully multivariate extension and unification of previous approaches based on bivariate or conditional mutual information and granger causality or transfer entropy we define multi information measures that allow us to study the global statistical structure of the system as a whole the total dependence between subsystems and the temporal statistical structure of each subsystem we develop a stationary and a nonstationary formulation of the framework we then examine different decompositions of these multi information measures the transfer entropy naturally appears as a term in some of these decompositions this allows us to examine its properties not as an isolated measure of interdependence but in the context of the complete framework more generally we use causal graphs to study the specificity and sensitivity of all the measures appearing in these decompositions to different sources of statistical dependence arising from the causal connections between the subsystems we illustrate that there is no straightforward relation between the strength of specific connections and specific terms in the decompositions furthermore causal and noncausal statistical dependencies are not separable in particular the transfer entropy can be nonmonotonic in dependence on the connectivity strength between subsystems and is also sensitive to internal changes of the subsystems so it should not be interpreted as a measure of connectivity strength altogether in comparison to an analysis based on single isolated measures of interdependence this framework is more powerful to analyze emergent properties in multivariate systems and to characterize functionally relevant changes in the dynamics

steady state bifurcation and hopf bifurcation for a diffusive leslie gower predator prey model we consider a diffusive leslie gower predator prey model subject to the homogeneous neumann boundary condition treating the diffusion coefficient d as a parameter the hopf bifurcation and steady state bifurcation from the positive constant solution branch are investigated moreover the global structure of the steady state bifurcations from simple eigenvalues is established by bifurcation theory in particular the local structure of the steady state bifurcations from double eigenvalues is also obtained by the techniques of space decomposition and implicit function theorem

disclosing large scale directed functional connections in meg with the multivariate phase slope index abstract the phase slope index psi is a method to disclose the direction of frequency specific neural interactions from magnetoencephalographic meg time series a fundamental property of psi is that of vanishing for linear mixing of independent neural sources this property allows psi to cope with the artificial instantaneous connectivity among meg sensors or brain sources induced by the field spread nevertheless psi is limited by being a bivariate estimator of directionality as opposite to the multidimensional nature of brain activity as revealed by meg the purpose of this work is to provide a multivariate generalization of psi we termed this measure as the multivariate phase slope index mpsi in order to test the ability of mpsi in estimating the directionality and to compare the mpsi results to those obtained by bivariate psi approaches based on maximizing imaginary part of coherency and on canonical correlation analysis we used extensive simulations we proved that mpsi achieves the highest performance and that in a large number of simulated cases the bivariate methods as opposed to mpsi do not detect a statistically significant directionality finally we applied mpsi to assess seed based directed functional connectivity in the alpha band from resting state meg data of 61 subjects from the human connectome project the obtained results highlight a directed functional coupling in the alpha band between the primary visual cortex and several key regions of well known resting state networks e g dorsal attention network and fronto parietal network

direction of coupling from phases of interacting oscillators an information theoretic approach a directionality index based on conditional mutual information is proposed for application to the instantaneous phases of weakly coupled oscillators its abilities to distinguish unidirectional from bidirectional coupling as well as to reveal and quantify asymmetry in bidirectional coupling are demonstrated using numerical examples of quasiperiodic chaotic and noisy oscillators as well as real human cardiorespiratory data

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

on the problem of reconstructing an unknown topology via locality properties of the wiener filter determining interrelatedness structure of various entities from multiple time series data is of significant interest to many areas knowledge of such a structure can aid in identifying cause and effect relationships clustering of similar entities identification of representative elements and model reduction the majority of existing results are based on correlation based indices which effectively assume a static relationship between the time series data and are not suitable for detecting interrelatedness when the time series are dynamically related or when the time series involve loops in this paper a methodology for identifying the interrelatedness structure of dynamically related time series data is presented that also allows for the presence of loops in the connectivity structure a linear dynamic graph model is presented where it is assumed that each time series data is the sum of an independent stochastic noise source and a dynamically weighted sum of other time series data a link is assumed to be present between two time series if the weight of a time series which is a linear time invariant filter is nonzero in the formation of the other reconstruction of the link connectivity structure under various scenarios is considered it is shown that when the linear dynamic graph is allowed to admit non causal weights then the links structure can be recovered with the possibility of identifying spurious connections however it is shown that the spurious links remain local where a spurious link is restricted to be within one hop of a true link furthermore strategies for exact reconstruction of the link structure when the weights are restricted to be causal are developed the main tools for determining the network topology are based on variations of wiener filtering a significant insight provided by the article is that in the class of network models considered in the paper the wiener filter estimating a stochastic process based on other processes remains local in the sense that the wiener filter utilizes only measurements local to the node being estimated

coarsening dynamics in a simplified dnls model we investigate the coarsening evolution occurring in a simplified stochastic model of the discrete nonlinear schrodinger dnls equation in the so called negative temperature region we provide an explanation of the coarsening exponent n 1 3 by invoking an analogy with a suitable exclusion process in spite of the equivalence with the exponent observed in other known universality classes this model is certainly different in that it refers to a dynamics with two conservation laws

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 granger non causality using nonparametric measure of conditional independence in recent years granger causality has become a popular method in a variety of research areas including engineering neuroscience and economics however despite its simplicity and wide applicability the linear granger causality is an insufficient tool for analyzing exotic stochastic processes such as processes involving non linear dynamics or processes involving causality in higher order statistics in order to analyze such processes more reliably a different approach toward granger causality has become increasingly popular this new approach employs conditional independence as a tool to discover granger non causality without any assumption on the underlying stochastic process this paper discusses the concept of discovering granger non causality using measures of conditional independence and proposes a novel measure of conditional independence in brief the proposed approach estimates the conditional distribution function through a kernel based least square regression approach this paper also explores the strengths and weaknesses of the proposed method compared to other available methods and provides a detailed comparison of these methods using a variety of synthetic data sets

synchronization between main rhythmic processes in the human cardiovascular system for the cases of spontaneous respiration and paced respiration with a fixed frequency and linearly increasing frequency we investigate synchronization between three main rhythmic processes governing the cardiovascular dynamics in humans namely the main heart rhythm respiration and the process whose fundamental frequency is close to 0 1 hz the analysis of the experimental records reveals synchronous regimes of different orders n m between all the three main rhythms the influence of the regime of breathing and the magnitude of heart rate variability on the degree of synchronization is considered

mitigating the effects of measurement noise on granger causality computing granger causal relations among bivariate experimentally observed time series has received increasing attention over the past few years such causal relations if correctly estimated can yield significant insights into the dynamical organization of the system being investigated since experimental measurements are inevitably contaminated by noise it is thus important to understand the effects of such noise on granger causality estimation the first goal of this paper is to provide an analytical and numerical analysis of this problem specifically we show that due to noise contamination 1 spurious causality between two measured variables can arise and 2 true causality can be suppressed the second goal of the paper is to provide a denoising strategy to mitigate this problem specifically we propose a denoising algorithm based on the combined use of the kalman filter theory and the expectation maximization algorithm numerical examples are used to demonstrate the effectiveness of the denoising approach

granger causality maps of diffusion processes granger causality is a statistical concept devised to reconstruct and quantify predictive information flow between stochastic processes although the general concept can be formulated model free it is often considered in the framework of linear stochastic processes here we show how local linear model descriptions can be employed to extend granger causality into the realm of nonlinear systems this novel treatment results in maps that resolve granger causality in regions of state space through examples we provide a proof of concept and illustrate the utility of these maps moreover by integration we convert the local granger causality into a global measure that yields a consistent picture for a global ornstein uhlenbeck process finally we recover invariance transformations known from the theory of autoregressive processes

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

the dynamics of complex amplitude norm preserving lattices of coupled oscillators we introduce a class of models composed by lattices of coupled complex amplitude oscillators which preserve the norm these models are particularly well adapted to investigate phenomena described by the nonlinear schr6 odinger equation the coupling between oscillators is parameterized by the mass while their local dynamics is illustrated for two area preserving maps one obtained from the exact local solution of the schr6 odinger equation the other obtained from its crank nicholson discretization in both cases we determine all periodic orbits and show how to detect artifacts introduced by the discretization c

network topology inference from infection statistics abstract we introduce a mathematical framework for identification of network topology based on data collected from infectious sis process occurring on a network an exact expression for the weight of each network link existing or not as a function of infectious statistics is obtained an algorithm for proper implementation of the analyzed concept is suggested and the validity of the obtained result is confirmed by numerical simulations performed on a number of synthetic computer generated networks

inferring the directionality of coupling with conditional mutual information uncovering the directionality of coupling is a significant step in understanding drive response relationships in complex systems in this paper we discuss a nonparametric method for detecting the directionality of coupling based on the estimation of information theoretic functionals we consider several different methods for estimating conditional mutual information the behavior of each estimator with respect to its free parameter is shown using a linear model where an analytical estimate of conditional mutual information is available numerical experiments in detecting coupling directionality are performed using chaotic oscillators where the influence of the phase extraction method and relative frequency ratio is investigated

mean phase coherence as a measure for phase synchronization and its application to the eeg of epilepsy patients abstract we apply the concept of phase synchronization of chaotic and or noisy systems and the statistical distribution of the relative instantaneous phases to electroencephalograms eegs recorded from patients with temporal lobe epilepsy using the mean phase coherence as a statistical measure for phase synchronization we observe characteristic spatial and temporal shifts in synchronization that appear to be strongly related to pathological activity in particular we observe distinct differences in the degree of synchronization between recordings from seizure free intervals and those before an impending seizure indicating an altered state of brain dynamics prior to seizure activity

persistence and global stability in a delayed leslie gower type three species food chain abstract our investigation concerns the three dimensional delayed continuous time dynamical system which models a predator prey food chain this model is based on the holling type ii and a leslie gower modified functional response this model can be considered as a first step towards a tritrophic model of leslie gower and holling tanner type with inverse trophic relation and time delay that is when a certain species that is usually eaten can consume immature predators it is proved that the system is uniformly persistent under some appropriate conditions by constructing a proper lyapunov function we obtain a sufficient condition for global stability of the positive equilibrium

kernel granger causality mapping effective connectivity on fmri data although it is accepted that linear granger causality can reveal effective connectivity in functional magnetic resonance imaging fmri the issue of detecting nonlinear connectivity has hitherto not been considered in this paper we address kernel granger causality kgc to describe effective connectivity in simulation studies and real fmri data of a motor imagery task based on the theory of reproducing kernel hilbert spaces kgc performs linear granger causality in the feature space of suitable kernel functions assuming an arbitrary degree of nonlinearity our results demonstrate that kgc captures effective couplings not revealed by the linear case in addition effective connectivity networks between the supplementary motor area sma as the seed and other brain areas are obtained from kgc

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

steady states of a leslie gower model with diffusion and advection abstract this paper focuses on a stationary leslie gower model with diffusion and advection firstly some existence conditions of nonconstant positive solutions are obtained by means of the leray schauder degree theory as diffusion and advection of one of the species both tend to infinity we obtain a limiting system which is a semi linear elliptic equation with nonlocal constraint in the simplified 1d case the global bifurcation structure of nonconstant solutions of the limiting system is classified

probabilistic methods for discrete nonlinear schrodinger equations we show that the thermodynamics of the focusing cubic discrete nonlinear schrodinger equation are exactly solvable in dimension 3 and higher a number of explicit formulas are derived

a diffusive predator prey model in heterogeneous environment abstract in this paper we demonstrate some special behavior of steady state solutions to a predator prey model due to the introduction of spatial heterogeneity we show that positive steady state solutions with certain prescribed spatial patterns can be obtained when the spatial environment is designed suitably moreover we observe some essential differences of the behavior of our model from that of the classical lotka volterra model that seem to arise only in the heterogeneous case

expanding the transfer entropy to identify information circuits in complex systems we propose a formal expansion of the transfer entropy to put in evidence irreducible sets of variables which provide information for the future state of each assigned target multiplets characterized by a large contribution to the expansion are associated to the informational circuits present in the system with an informational character which can be associated to the sign of the contribution for the sake of computational complexity we adopt the assumption of gaussianity and use the corresponding exact formula for the conditional mutual information we report the application of the proposed methodology on two electroencephalography eeg data sets

non constant positive steady states of a diffusive predator prey system in homogeneous environment abstract in this paper we investigate the existence and non existence of non constant positive steady states of a diffusive predator prey interaction system under homogeneous neumann boundary condition in homogeneous environment we show that the predator prey model with leslie gower functional response has no non constant positive solution but the system with a general functional response may have at least one non constant positive steady state under some conditions

limiting structure of steady states to the lotka volterra competition model with large diffusion and advection abstract this paper is concerned with the neumann problem of a stationary lotka volterra competition model with diffusion and advection first we obtain some sufficient conditions of the existence of nonconstant solutions by the leray schauder degree theory next we derive a limiting system as diffusion and advection of one of the species tend to infinity the limiting system can be reduced to a semilinear elliptic equation with nonlocal constraint in the simplified 1d case the global bifurcation structure of nonconstant solutions of the limiting system can be classified depending on the coefficients for example this structure involves a global bifurcation curve which connects two different singularly perturbed states boundary layer solutions and internal layer solutions our proof employs a levelset analysis for the associate integral mapping

invariant measures and the soliton resolution conjecture the soliton resolution conjecture for the focusing nonlinear schrodinger equation nls is the vaguely worded claim that a global solution of the nls for generic initial data will eventually resolve into a radiation component that disperses like a linear solution plus a localized component that behaves like a soliton or multisoliton solution considered to be one of the fundamental open problems in the area of nonlinear dispersive equations this conjecture has eluded a proof or even a precise formulation to date this paper proves a statistical version of this conjecture at mass subcritical nonlinearity in the following sense the uniform probability distribution on the set of all functions with a given mass and energy if such a thing existed would be a natural invariant measure for the nls flow and would reflect the long term behavior for generic initial data with that mass and energy unfortunately such a probability measure does not exist we circumvent this problem by constructing a sequence of discrete measures that in principle approximate this fictitious probability distribution as the grid size goes to 0 we then show that a continuum limit of this sequence of probability measures does exist in a certain sense and in agreement with the soliton resolution conjecture the limit measure concentrates on the unique ground state soliton combining this with results from ergodic theory we present a tentative formulation and proof of the soliton resolution conjecture in the discrete setting the above results following in the footsteps of a program of studying the long term behavior of nonlinear dispersive equations through their natural invariant measures initiated by lebowitz rose and speer and carried forward by bourgain mckean tzvetkov oh and others are proved using a combination of techniques from large deviations pdes harmonic analysis and bare hands probability theory it is valid in any dimension 2014 wiley periodicals inc

kernel granger causality and the analysis of dynamical networks we propose a method of analysis of dynamical networks based on a recent measure of granger causality between time series based on kernel methods the generalization of kernel granger causality to the multivariate case here presented shares the following features with the bivariate measures i the nonlinearity of the regression model can be controlled by choosing the kernel function and ii the problem of false causalities arising as the complexity of the model increases is addressed by a selection strategy of the eigenvectors of a reduced gram matrix whose range represents the additional features due to the second time series moreover there is no a priori assumption that the network must be a directed acyclic graph we apply the proposed approach to a network of chaotic maps and to a simulated genetic regulatory network it is shown that the underlying topology of the network can be reconstructed from time series of node s dynamics provided that a sufficient number of samples is available considering a linear dynamical network built by preferential attachment scheme we show that for limited data use of the bivariate granger causality is a better choice than methods using l1 minimization finally we consider real expression data from hela cells 94 genes and 48 time points the analysis of static correlations between genes reveals two modules corresponding to well known transcription factors granger analysis puts in evidence 19 causal relationships all involving genes related to tumor development

causal conditioning and instantaneous coupling in causality graphs this study aims at providing the definitive links between massey and kramer s directed information theory and granger causality graphs recently formalized by eichler this naturally leads to consider two concepts of causality that can occur in physical systems dynamical causality and instantaneous coupling although it is well accepted that the former is assessed by conditional transfer entropy the latter is often overlooked even if it was clearly introduced and understood in seminal studies in the bivariate case we show that directed information is decomposed into the sum of transfer entropy and instantaneous information exchange in the multivariate case encountered for conditional graph modeling such a decomposition does not hold anymore we provide a new insight into the problem of instantaneous coupling and show how it affects the estimated structure of a graphical model that should provide a sparse representation of a complex system this result is discussed and analyzed for the inference of causality graphs two synthetic examples are developed to illustrate the theoretical concepts practical issues are also briefly discussed on these examples and an extension of leonenko s k nearest neighbors based entropy estimators is used to derive a nonparametric estimator of directed information

does movement toward better environments always benefit a population abstract we study the effects of advection along environmental gradients on logistic reaction diffusion models for population growth the local population growth rate is assumed to be spatially inhomogeneous and the advection is taken to be a multiple of the gradient of the local population growth rate it is also assumed that the boundary acts as a reflecting barrier to the population we show that the effects of such advection depend crucially on the shape of the habitat of the population if the habitat is convex the movement in the direction of the gradient of the growth rate is always beneficial to the population while such advection could be harmful for certain non convex habitats

stable and metastable states and the formation and destruction of breathers in the discrete nonlinear schrodinger equation statistical mechanics explains many localization phenomena of lattices such as the discrete nonlinear schrodinger equation however numerical simulations show that the complete thermalization is rarely achieved instead one observes metastable statistical states that are robust when excited locally this paper investigates thermodynamically metastable states where the trajectory is confined to some part of the energy shell the partition function and the entropy are computed with a perturbation method this method is applicable to stable and metastable states and it allows us to give approximative analytic expressions for the entropy in the complete thermodynamic state space

canonical granger causality between regions of interest estimating and modeling functional connectivity in the brain is a challenging problem with potential applications in the understanding of brain organization and various neurological and neuropsychological conditions an important objective in connectivity analysis is to determine the connections between regions of interest in the brain however traditional functional connectivity analyses have frequently focused on modeling interactions between time series recordings at individual sensors voxels or vertices despite the fact that a single region of interest will often include multiple such recordings in this paper we present a novel measure of interaction between regions of interest rather than individual signals the proposed measure termed canonical granger causality combines ideas from canonical correlation and granger causality analysis to yield a measure that reflects directed causality between two regions of interest in particular canonical granger causality uses optimized linear combinations of signals from each region of interest to enable accurate causality measurements from substantially less data compared to alternative multivariate methods that have previously been proposed for this scenario the optimized linear combinations are obtained using a variation of a technique developed for optimization on the stiefel manifold we demonstrate the advantages of canonical granger causality in comparison to alternative causality measures for a range of different simulated datasets we also apply the proposed measure to local field potential data recorded in a macaque brain during a visuomotor task results demonstrate that canonical granger causality can be used to identify causal relationships between striate and prestriate cortexes in cases where standard granger causality is unable to identify statistically significant interactions

granger causality and information flow in multivariate processes the multivariate versus bivariate measures of granger causality were considered granger causality in the application to multivariate physiological time series has the meaning of the information flow between channels it was shown by means of simulations and by the example of experimental electroencephalogram signals that bivariate estimates of directionality in case of mutually interdependent channels give erroneous results therefore multivariate measures such as directed transfer function should be used for determination of the information flow

breakdown of weak turbulence and nonlinear wave condensation abstract the formation of a large scale coherent structure a condensate as a result of the long time evolution of the initial value problem of a classical partial differential nonlinear wave equation is considered we consider the nonintegrable and unforced defocusing nonlinear schrodinger nls equation as a representative model in spite of the formal reversibility of the nls equation the nonlinear wave exhibits an irreversible evolution towards a thermodynamic equilibrium state the equilibrium state is characterized by a homogeneous solution condensate with small scale fluctuations superposed uncondensed particles which store the information necessary for time reversal we analyze the evolution of the cumulants of the random wave as originally formulated by d j benney and p g saffman d j benney p g saffman proc roy soc london a 289 1966 301 and a c newell a c newell rev geophys 6 1968 1 this allows us to provide a self consistent weak turbulence theory of the condensation process in which the nonequilibrium formation of the condensate is a natural consequence of the spontaneous regeneration of a non vanishing first order cumulant in the hierarchy of the cumulants equations more precisely we show that in the presence of a small condensate amplitude all relevant statistical information is contained in the off diagonal second order cumulant as described by the usual weak turbulence theory conversely in the presence of a high amplitude condensate the diagonal second order cumulants no longer vanish in the long time limit which signals a breakdown of the weak turbulence theory however we show that an asymptotic closure of the hierarchy of the cumulants equations is still possible provided one considers the bogoliubov s basis rather than the standard fourier s free particle basis the nonequilibrium dynamics turns out to be governed by the bogoliubov s off diagonal second order cumulant while the corresponding diagonal cumulants as well as the higher order cumulants are shown to vanish asymptotically the numerical discretization of the nls equation implicitly introduces an ultraviolet frequency cut off the simulations are in quantitative agreement with the weak turbulence theory without adjustable parameters despite the fact that the theory is expected to breakdown nearby the transition to condensation the fraction of condensed particles vs energy is characterized by two distinct regimes for small energies h h c the bogoliubov s regime is established whereas for h h c the small amplitude condensate regime is described by the weak turbulence theory in both regimes we derive coupled kinetic equations that describe the coupled evolution of the condensate amplitude and the incoherent field component the influence of finite size effects and of the dimensionality of the system are also considered it is shown that beyond the thermodynamic limit wave condensation is reestablished in two spatial dimensions in complete analogy with uniform and ideal 2d bose gases

evolution of dispersal in advective homogeneous environment the effect of boundary conditions abstract we consider a single species model and a two species competition model in a one dimensional advective homogeneous environment one interesting feature in these models concerns the boundary condition at the downstream end where the species can be exposed to a net loss of individuals as tuned by a parameter b which measures the magnitude of the loss we first determine necessary and sufficient conditions for the persistence of a single species for general value of b in terms of the critical habitat size and the critical advection rate then for the competition model we assume that two species are identical except their random diffusion rates we obtain complete understanding when 0 b 1 and our result indicates that larger diffusion rate is selected extending an earlier work 20 b 1 however for b 1 the dynamics can be quite different and particularly we illustrate that some intermediate diffusion rate may be selected when b 3 2

diffusion self diffusion and cross diffusion u1 x 0 u 1 0 x u2 x 0 u 2 0 x i n 0 where 2 n 1 2 x 2 is the laplace operator 0 is a bounded smooth domain of r n with n1 0 and 0 are the boundary and the closure of 0 respectively 0t 0 0 t and 0t 0 0 t for some t 0 is the outward unit normal vector on 0 di ai bi ci i 1 2 are all positive constants while ij i j 1 2 denote non negative constants the initial values u1 0 and u2 0 are non negative smooth func tions which are not identically zero the mathematical model 1 1 was proposed by shigesada et al 27 in their study of spatial segregation of interacting species where u1 and u2 represent the densities of two competing species d1 and d2 are their diffu sion rates a1 and a2 denote the intrinsic growth rates b1 and c2 account for intra specific competitions b2 and c1 are the coefficients of inter specific competitions 11 and 22 are usually referred as self diffusion pressures and 12 and 21 are cross diffusion pressures an interesting feature of 1 1 is that the movements of these two competing species are affected by the population pressures due to the mutual interference between the individuals and it was hoped that the nonlinear dispersive force due to the

granger causality and the inverse ising problem abstract the inference of the couplings of an ising model with given means and correlations is called the inverse ising problem this approach has received a lot of attention as a tool to analyze neural data we show that autoregressive methods may be used to learn the couplings of an ising model also in the case of asymmetric connections and for multispin interactions we find that for each link the linear granger causality is two times the corresponding transfer entropy i e the information flow on that link in the weak coupling limit for sparse connections and a low number of samples the l 1 regularized least squares method is used to detect the interacting pairs of spins nonlinear granger causality is related to multispin interactions

detection of synchronization from univariate data using wavelet transform a method is proposed for detecting from univariate data the presence of synchronization of a self sustained oscillator by external driving with varying frequency the method is based on the analysis of difference between the oscillator instantaneous phases calculated using continuous wavelet transform at time moments shifted by a certain constant value relative to each other we apply our method to a driven asymmetric van der pol oscillator experimental data from a driven electronic oscillator with delayed feedback and human heartbeat time series in the latest case the analysis of the heart rate variability data reveals synchronous regimes between the respiration and slow oscillations in blood pressure

spreading speed and sharp asymptotic profiles of solutions in free boundary problems for nonlinear advection diffusion equations abstract in this study we consider free boundary problems for nonlinear advection diffusion equations of the form u t u x x u x f u for t 0 g t x h t where x g t and x h t are free boundaries this problem may be used to describe the spreading of a biological or chemical species where the free boundaries represent the expanding fronts when f is a logistic nonlinearity it has been shown that the asymptotic spreading speeds of the two fronts h t and g t are different due to the advection term in this study for monostable bistable and combustion types nonlinearities we give much sharper estimates of the different spreading speeds of the fronts and we also prove that the solution converges to a semi wave in c 2 norm as t when spreading occurs we develop new approaches and extend a previous result to the problem with the advection term

radial basis function approach to nonlinear granger causality of time series we consider an extension of granger causality to nonlinear bivariate time series in this frame if the prediction error of the first time series is reduced by including measurements from the second time series then the second time series is said to have a causal influence on the first one not all the nonlinear prediction schemes are suitable to evaluate causality indeed not all of them allow one to quantify how much knowledge of the other time series counts to improve prediction error we present an approach with bivariate time series modeled by a generalization of radial basis functions and show its application to a pair of unidirectionally coupled chaotic maps and to physiological examples

estimation of the direction of the coupling by conditional probabilities of recurrence we introduce a method to detect and quantify the asymmetry of the coupling between two interacting systems based on their recurrence properties this method can detect the direction of the coupling in weakly as well as strongly coupled systems it even allows detecting the asymmetry of the coupling in the more challenging case of structurally different systems and it is very robust against noise we also address the problem of detecting the asymmetry of the coupling in passive experiments i e when the strength of the coupling cannot be systematically changed which is of great relevance for the analysis of experimental time series

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

asynchronous states in networks of pulse coupled oscillators we use a mean field approach to analyze the stability of the asynchronous state in a population of all to all pulse coupled nonlinear oscillators we determine the conditions that must be satisfied by the time constants and phase dependence characterizing the coupling between the oscillators in order for the asynchronous state to be stable we also consider the effects of noise this work complements results on synchronous states in similar models and allows us to study the validity of firing rate models commonly used for neural networks

stability and bifurcation in a diffusive lotka volterra system with delay in this paper we investigate the dynamics of a class of diffusive lotka volterra equation with time delay subject to the homogeneous dirichlet boundary condition in a bounded domain the existence of spatially nonhomogeneous steady state solution is investigated by applying lyapunov schmidt reduction the stability and nonexistence of hopf bifurcation at the spatially nonhomogeneous steady state solution with the changes of a specific parameter are obtained by analyzing the distribution of the eigenvalues moreover we illustrate our general results by applications to models with a single delay and one dimensional spatial domain

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

detecting changes in coupling with granger causality method from time series with fast transient processes abstract the ability of the granger causality method to detect directed coupling between subsystems of a complex system in a moving time window is investigated on etalon oscillators in particular the time series consisting of alternate stationary regimes characterised by the different amplitude and shape of oscillations with fast transient processes between these regimes are considered with similar transitions being possible due to changes either in the coupling or in the individual properties of subsystems two popular approaches to surrogate times series generation are used to check the significance of the method results two model structures the standard linear and the special non linear adapted to data are implemented the granger causality method using the model structure adapted to data is shown to be significantly advantageous in detecting coupling directionality and the instant time of the regime change than the standard linear method while in some cases the sensitivity and the specificity of the adapted approach are insufficient

periodic traveling waves in a reaction diffusion model with chemotaxis and nonlocal delay effect abstract in this paper we study the existence of periodic traveling wave solutions with large wave speed for a reaction diffusion model with chemotaxis and nonlocal delay effect by applying the perturbation method the proof relies on an abstract formulation of the wave profile as a solution of an operator equation in a certain banach space coupled with the lyapunov schmidt reduction and the implicit function theorem