quantifying temporal correlations a test retest evaluation of functional connectivity in resting state fmri there have been many interpretations of functional connectivity and proposed measures of temporal correlations between bold signals across different brain areas these interpretations yield from many studies on functional connectivity using resting state fmri data that have emerged in recent years however not all of these studies used the same metrics for quantifying the temporal correlations between brain regions in this paper we use a public domain test retest resting state fmri data set to perform a systematic investigation of the stability of the metrics that are often used in resting state functional connectivity fc studies the fmri data set was collected across three different sessions the second session took place approximately eleven months after the first session and the third session was an hour after the second session the fc metrics composed of cross correlation partial cross correlation cross coherence and parameters based on an autoregressive model we discussed the strengths and weaknesses of each metric we performed roi level and full brain seed based voxelwise test retest analyses using each fc metric to assess its stability for both roi level and voxel level analyses we found that cross correlation yielded more stable measurements than the other metrics we discussed the consequences of this result on the utility of the fc metrics we observed that for negatively correlated rois their partial cross correlation is shrunk towards zero thus affecting the stability of their fc for the present data set we found greater stability in fc between the second and third sessions one hour between sessions compared to the first and second sessions approximately 11 months between sessions finally we report that some of the metrics showed a positive association between strength and stability in summary the results presented in this paper suggest important implications when choosing metrics for quantifying and assessing various types of functional connectivity for resting state fmri studies

short and long run causality measures theory and inference abstract the concept of causality introduced by wiener wiener n 1956 the theory of prediction in e f beckenback ed the theory of prediction mcgraw hill new york chapter 8 and granger granger c w j 1969 investigating causal relations by econometric models and cross spectral methods econometrica 37 424 459 is defined in terms of predictability one period ahead this concept can be generalized by considering causality at any given horizon h as well as tests for the corresponding non causality dufour j m renault e 1998 short run and long run causality in time series theory econometrica 66 1099 1125 dufour j m pelletier d renault e 2006 short run and long run causality in time series inference journal of econometrics 132 2 337 362 instead of tests for non causality at a given horizon we study the problem of measuring causality between two vector processes existing causality measures have been defined only for the horizon 1 and they fail to capture indirect causality we propose generalizations to any horizon h of the measures introduced by geweke geweke j 1982 measurement of linear dependence and feedback between multiple time series journal of the american statistical association 77 304 313 nonparametric and parametric measures of unidirectional causality and instantaneous effects are considered on noting that the causality measures typically involve complex functions of model parameters in var and varma models we propose a simple simulation based method to evaluate these measures for any varma model we also describe asymptotically valid nonparametric confidence intervals based on a bootstrap technique finally the proposed measures are applied to study causality relations at different horizons between macroeconomic monetary and financial variables in the us

a study of problems encountered in granger causality analysis from a neuroscience perspective granger causality methods were developed to analyze the flow of information between time series these methods have become more widely applied in neuroscience frequency domain causality measures such as those of geweke as well as multivariate methods have particular appeal in neuroscience due to the prevalence of oscillatory phenomena and highly multivariate experimental recordings despite its widespread application in many fields there are ongoing concerns regarding the applicability of granger causality methods in neuroscience when are these methods appropriate how reliably do they recover the system structure underlying the observed data what do frequency domain causality measures tell us about the functional properties of oscillatory neural systems in this paper we analyze fundamental properties of granger geweke gg causality both computational and conceptual specifically we show that i gg causality estimates can be either severely biased or of high variance both leading to spurious results ii even if estimated correctly gg causality estimates alone are not interpretable without examining the component behaviors of the system model and iii gg causality ignores critical components of a system s dynamics based on this analysis we find that the notion of causality quantified is incompatible with the objectives of many neuroscience investigations leading to highly counterintuitive and potentially misleading results through the analysis of these problems we provide important conceptual clarification of gg causality with implications for other related causality approaches and for the role of causality analyses in neuroscience as a whole

granger geweke causality estimation and interpretation abstract in a recent pnas article1 stokes and purdon performed numerical simulations to argue that granger geweke causality ggc estimation is severely biased or of high variance and ggc application to neuroscience is problematic because the ggc measure is independent of receiver dynamics here we use the same simulation examples to show that ggc measures when properly estimated either via the spectral factorization enabled nonparametric approach or the var model based parametric approach do not have the claimed bias and high variance problems further the receiver independence property of ggc does not present a problem for neuroscience applications when the nature and context of experimental measurements are taken into consideration ggc along with other spectral quantities yield neurophysiologically interpretable results

multipeakons and the classical moment problem abstract classical results of stieltjes are used to obtain explicit formulas for the peakon antipeakon solutions of the camassa holm equation the closed form solution is expressed in terms of the orthogonal polynomials of the related classical moment problem it is shown that collisions occur only in peakon antipeakon pairs and the details of the collisions are analyzed using results from the moment problem a sharp result on the steepening of the slope at the time of collision is given asymptotic formulas are given and the scattering shifts are calculated explicitly

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

existence and multiplicity of solutions for quasilinear nonhomogeneous problems an orlicz sobolev space setting abstract we study the boundary value problem div log 1 u q u p 2 u f u in u 0 on where is a bounded domain in r n with smooth boundary we distinguish the cases where either f u u p 2 u u r 2 u or f u u p 2 u u r 2 u with p q 1 p q min n r and r n p n p n p in the first case we show the existence of infinitely many weak solutions for any 0 in the second case we prove the existence of a nontrivial weak solution if is sufficiently large our approach relies on adequate variational methods in orlicz sobolev spaces

a multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids the goal of this correction is to correct a mistake that appears in the proof of both lemma 3 9 and 3 10 in the article mih ilescu r dulescu 2006 1 the mistake in the proof of lemma 3 9 and 3 10 is mainly owing to the fact that we wrongly computed the expression of function g x t

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

multiple solutions for a nonhomogeneous dirichlet problem in orlicz sobolev spaces abstract in this paper moving within the framework of orlicz sobolev spaces we guarantee through variational arguments the existence of three weak solutions to the nonhomogeneous boundary value problem div a u x u x f x u g x u in u 0 on with bounded domain in r n with smooth boundary real parameters f g r r caratheodory functions and the function t a t t odd increasing homeomorphism from r onto r applications and comparisons are also presented in particular we improve a result for an eigenvalue problem established by mih ilescu and repovs in 15

the decomposition and measurement of the interdependency between second order stationary processes for a given pair of multivariate stationary processes the process of one way effect is extracted from each of the processes each process is decomposed into two orthogonal processes namely into the process generated by the one way effect of the other process and the process orthogonal to it based on the decomposition three measures characterizing the interdependency of the pair of processes are introduced they are the measure of association the measure of one way effect and the measure of reciprocity each of the measures is defined as overall as well as frequencywise measure the paper shows that the measure of association is equal to the sum of the others it discusses the relationships of those measures to the ones proposed by gel fand yaglom and by geweke

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

variable exponent linear growth functionals in image restoration we study a functional with variable exponent 1 leq p x leq 2 which provides a model for image denoising enhancement and restoration the diffusion resulting from the proposed model is a combination of total variation tv based regularization and gaussian smoothing the existence uniqueness and long time behavior of the proposed model are established experimental results illustrate the effectiveness of the model in image restoration

perturbed kirchhoff type neumann problems in orlicz sobolev spaces the aim of this paper is to establish the existence of infinitely many solutions for perturbed kirchhoff type non homogeneous neumann problems involving two parameters to be precise we prove that an appropriate oscillating behaviour of the nonlinear term even under small perturbations ensures the existence of infinitely many solutions our approach is based on recent variational methods for smooth functionals defined on orlicz sobolev spaces

a further three critical points theorem abstract if x is a real banach space we denote by w x the class of all functionals x r possessing the following property if u n is a sequence in x converging weakly to u x and lim inf n u n u then u n has a subsequence converging strongly to u in this paper we prove the following result let x be a separable and reflexive real banach space i r an interval x r a sequentially weakly lower semicontinuous c 1 functional belonging to w x bounded on each bounded subset of x and whose derivative admits a continuous inverse on x j x r a c 1 functional with compact derivative assume that for each i the functional j is coercive and has a strict local not global minimum say x then for each compact interval a b i for which sup a b x j x there exists r 0 with the following property for every a b and every c 1 functional x r with compact derivative there exists 0 such that for each 0 the equation x j x x has at least three solutions whose norms are less than r

analysis of economic growth fluctuations based on eemd and causal decomposition abstract in this paper we first apply ensemble empirical mode decomposition eemd to analyze the change rate of gdp time series for ten major countries each signal is decomposed into four modes with different scales and a residual trend the variance contribution and averaged period cycle for each mode is then calculated results show that economic growth fluctuations for most of the countries mainly fluctuate at a short period between 3 5 years then the causal decomposition proposed by yang et al is utilized to detect the mutual causation among different countries the novelty of this method is that the causal interaction is identified in instantaneous phase coherence at a specific time scale the strengths and directions of causal relationship for each mode among countries differ from each other which mirrors the fact that the world economic activities are fluctuated and changeable over varying periods however no visible causation for the fourth mode long term cycle among countries is characterized meaning that the development of economy over a long period for most countries depends on its own conditions

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

entropy and predictability of stock market returns abstract we examine the predictability of stock market returns by employing a new metric entropy measure of dependence with several desirable properties we compare our results with a number of traditional measures the metric entropy is capable of detecting nonlinear dependence within the returns series and is also capable of detecting nonlinear affinity between the returns and their predictions obtained from various models thereby serving as a measure of out of sample goodness of fit or model adequacy several models are investigated including the linear and neural network models as well as nonparametric and recursive unconditional mean models we find significant evidence of small nonlinear unconditional serial dependence within the returns series but fragile evidence of superior conditional predictability profit opportunity when using market switching versus buy and hold strategies

order selection for vector autoregressive models order selection criteria for vector autoregressive ar modeling are discussed the performance of an order selection criterion is optimal if the model of the selected order is the most accurate model in the considered set of estimated models here vector ar models suboptimal performance can be a result of underfit or overfit the akaike 1969 information criterion aic is an asymptotically unbiased estimator of the kullback leibler discrepancy kld that can be used as an order selection criterion aic is known to suffer from overfit the selected model order can be greater than the optimal model order two causes of overfit are finite sample effects and asymptotic effects as a consequence of finite sample effects aic underestimates the kld for higher model orders leading to overfit asymptotically overfit is the result of statistical variations in the order selection criterion to derive an accurate order selection criterion both causes of overfit have to be addressed moreover the cost of underfit has to be taken into account the combined information criterion cic for vector signals is robust to finite sample effects and has the optimal asymptotic penalty factor this penalty factor is the result of a tradeoff of underfit and overfit the optimal penalty factor depends on the number of estimated parameters per model order the cic is compared to other criteria such as the aic the corrected akaike information criterion aicc and the consistent minimum description length mdl

on a nonlinear and non homogeneous problem without a r type condition in orlicz sobolev spaces using variational methods we prove some existence and multiplicity results for a class of nonlinear and non homogeneous problems without a r type condition in orlicz sobolev spaces

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

existence and multiplicity of solutions for a class of ź 1 ź 2 laplacian elliptic system in r n via genus theory in this paper we investigate the following nonlinear and non homogeneous elliptic system involving 1 2 laplacian div 1 u u v 1 x 1 u u f u x u v in r n div 2 v v v 2 x 2 v v f v x u v in r n u v w 1 1 r n w 1 2 r n with n 2 where the functions v i x i 1 2 are bounded and positive in r n the functions i t t i 1 2 are increasing homeomorphisms from r onto r and the function f is of class c 1 r n 2 r and has a sub linear orlicz sobolev growth by using the least action principle we obtain that system has at least one nontrivial solution when f satisfies an additional symmetric condition by using the genus theory we obtain that system has infinitely many solutions

measurement of linear dependence and feedback between multiple time series abstract measures of linear dependence and feedback for multiple time series are defined the measure of linear dependence is the sum of the measure of linear feedback from the first series to the second linear feedback from the second to the first and instantaneous linear feedback the measures are nonnegative and zero only when feedback causality of the relevant type is absent the measures of linear feedback from one series to another can be additively decomposed by frequency a readily usable theory of inference for all of these measures and their decompositions is described the computations involved are modest

temporal aggregation of multivariate garch processes this paper derives results for the temporal aggregation of multivariate garch 1 1 processes in the general vector specification it is shown that the class of weak multivariate garch 1 1 processes is closed under temporal aggregation fourth moment characteristics turn out to be crucial for the low frequency dynamics for both stock and flow variables in some aspects the aggregation characteristics of multivariate garch processes are shown to be different from those of vector autoregressive moving average processes a numerical example illustrates some of the results

two non trivial solutions for a non homogeneous neumann problem an orlicz sobolev space setting in this paper we study a non homogeneous neumann type problem which involves a nonlinearity satisfying a non standard growth condition by using a recent variational principle of ricceri we establish the existence of at least two non trivial solutions in an appropriate orlicz sobolev space

nonparametric estimation and inference for conditional density based granger causality measures we propose a nonparametric estimation and inference for conditional density based granger causality measures that quantify linear and nonlinear granger causalities we first show how to write the causality measures in terms of copula densities thereafter we suggest consistent estimators for these measures based on a consistent nonparametric estimator of copula densities furthermore we establish the asymptotic normality of these nonparametric estimators and discuss the validity of a local smoothed bootstrap that we use in finite sample settings to compute a bootstrap bias corrected estimator and to perform statistical tests a monte carlo simulation study reveals that the bootstrap bias corrected estimator behaves well and the corresponding test has quite good finite sample size and power properties for a variety of typical data generating processes and different sample sizes finally two empirical applications are considered to illustrate the practical relevance of nonparametric causality measures

granger causality analysis with nonuniform sampling and its application to pulse coupled nonlinear dynamics the granger causality gc analysis is an effective approach to infer causal relations for time series however for data obtained by uniform sampling i e with an equal sampling time interval it is known that gc can yield unreliable causal inference due to aliasing if the sampling rate is not sufficiently high to solve this unreliability issue we consider the nonuniform sampling scheme as it can mitigate against aliasing by developing an unbiased estimation of power spectral density of nonuniformly sampled time series we establish a framework of spectrum based nonparametric gc analysis applying this framework to a general class of pulse coupled nonlinear networks and utilizing some particular spectral structure possessed by these nonlinear network data we demonstrate that for such nonlinear networks with nonuniformly sampled data reliable gc inference can be achieved at a low nonuniform mean sampling rate at which the traditional uniform sampling gc may lead to spurious causal inference

the effect of filtering on granger causality based multivariate causality measures in the past causality measures based on granger causality have been suggested for assessing directionality in neural signals in frequency domain analyses power or coherence of neural data it is common to preprocess the time series by filtering or decimating however in other fields it has been shown theoretically that filtering in combination with granger causality may lead to spurious or missed causalities we investigated whether this result translates to multivariate causality methods derived from granger causality with a a simulation study and b an application to magnetoencephalographic data to this end we performed extensive simulations of the effect of applying different filtering techniques and evaluated the performance of five different multivariate causality measures in combination with two numerical significance measures random permutation and leave one out method the analysis included three of the most widely used filters high pass low pass notch filter four different filter types butterworth chebyshev i and ii elliptic filter variation of filter order decimating and interpolation the simulation results suggest that preprocessing without a strong prior about the artifact to be removed disturbs the information content and time ordering of the data and leads to spurious and missed causalities only if apparent artifacts like a current or movement artifact are present filtering out the respective disturbance seems advisable while oversampling poses no problem decimation by a factor greater than the minimum time shift between the time series may lead to wrong inferences in general the multivariate causality measures are very sensitive to data preprocessing

source coding with feed forward rate distortion theorems and error exponents for a general source in this work we consider a source coding model with feed forward we analyze a system with a noiseless feed forward link where the decoder has knowledge of all previous source samples while reconstructing the present sample the rate distortion function for an arbitrary source with feed forward is derived in terms of directed information a variant of mutual information we further investigate the nature of the rate distortion function with feed forward for two common types of sources discrete memory less sources and gaussian sources we then characterize the error exponent for a general source with feed forward the results are then extended to feed forward with an arbitrary delay larger than the block length

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

inference on one way effect and evidence in japanese macroeconomic data this paper provides an approach to testing a variety of causal characteristics expressed in terms of the measures of one way effect for cointegrated vector time series for this purpose we propose wald tests and their computational algorithm by means of the measures of one way effect incorporating johansen s algorithm for the maximum likelihood estimates and the likelihood ratio tests using the wald test statistics the paper also provides a method of confidence set construction for the causal measures the approach proposed in the paper includes testing granger s non causality as an instance of its multiple applications as an illustration the paper presents a characterization of the causal structure of the recent japanese macroeconomy on the basis of the proposed method and the derived evidence

does sunspot numbers cause global temperatures a reconsideration using non parametric causality tests abstract in a recent paper gupta et al 2015 analyzed whether sunspot numbers cause global temperatures based on monthly data covering the period 1880 1 2013 9 the authors find that standard time domain granger causality test fails to reject the null hypothesis that sunspot numbers do not cause global temperatures for both full and sub samples namely 1880 1 1936 2 1936 3 1986 11 and 1986 12 2013 9 identified based on tests of structural breaks however frequency domain causality test detects predictability for the full sample at short 2 2 6 months cycle lengths but not the sub samples but since full sample causality cannot be relied upon due to structural breaks gupta et al 2015 conclude that the evidence of causality running from sunspot numbers to global temperatures is weak and inconclusive given the importance of the issue of global warming our current paper aims to revisit this issue of whether sunspot numbers cause global temperatures using the same data set and sub samples used by gupta et al 2015 based on an nonparametric singular spectrum analysis ssa based causality test based on this test we however show that sunspot numbers have predictive ability for global temperatures for the three sub samples over and above the full sample thus generally speaking our non parametric ssa based causality test outperformed both time domain and frequency domain causality tests and highlighted that sunspot numbers have always been important in predicting global temperatures

exact closed form solutions of a fully nonlinear asymptotic two fluid model abstract a fully nonlinear model of choi and camassa 1999 describing one dimensional incompressible dynamics of two non mixing fluids in a horizontal channel under a shallow water approximation is considered an equivalence transformation is presented leading to a special dimensionless form of the system involving a single dimensionless constant physical parameter as opposed to five parameters present in the original model a first order dimensionless ordinary differential equation describing traveling wave solutions is analyzed several multi parameter families of physically meaningful exact closed form solutions of the two fluid model are derived corresponding to periodic solitary and kink type bidirectional traveling waves specific examples are given and properties of the exact solutions are analyzed

comparing alternative tests of causality in temporal systems abstract this paper discusses eight alternative tests of the absence of casual ordering all of which are asymptotically valid under the null hypothesis in the sense that their limiting size is known their behavior under alternatives is compared analytically using the concept of approximate slope and these results are supported by the outcomes of monte carlo experiments the implications of these comparisons for applied work are unambiguous wald variants of a test attributed to granger and a lagged dependent variable version of sim s test introduced in this paper are equivalent in all relevant respects and are preferred to the other tests discussed

validity of time reversal for testing granger causality inferring causal interactions from observed data is a challenging problem especially in the presence of measurement noise to alleviate the problem of spurious causality haufe 2013 proposed to contrast measures of information flow obtained on the original data against the same measures obtained on time reversed data they show that this procedure time reversed granger causality trgc robustly rejects causal interpretations on mixtures of independent signals while promising results have been achieved in simulations it was so far unknown whether time reversal leads to valid measures of information flow in the presence of true interaction here we prove that for linear finite order autoregressive processes with unidirectional information flow between two variables the application of time reversal for testing granger causality indeed leads to correct estimates of information flow and its directionality using simulations we further show that trgc is able to infer correct directionality with similar statistical power as the net granger causality between two variables while being much more robust to the presence of measurement noise

estimation of the generalized prediction error variance of a multiple time series abstract for a multivariate stationary time series we propose a nonparametric estimator for its generalized prediction error variance using a multivariate analog of the szego kolmogorov formula replacing the integral by a sum and replacing the unknown spectral density matrix by a consistent estimator asymptotic normality of this estimator is established and its small sample behavior is assessed through simulation and application to two real data sets these examples show that the proposed method works reasonably well in comparison with parametric models in contrast to the univariate case where smoothing the periodogram is optional and generally not recommended in the multivariate case this smoothing is a necessity because the raw periodogram is a matrix of rank one to obtain a consistent estimator of a full rank spectral density matrix one must necessarily choose larger bandwidths for higher dimensional time series a bias correction factor is computed using the asymptotic properties of our propo

a stability criterion for two fluid interfaces and applications we derive a new stability criterion for two fluid interfaces that ensures the existence of stable local solutions that do not break down too fast due to kelvin helmholtz instabilities it can be seen both as a two fluid generalization of the rayleigh taylor criterion and as a nonlinear version of the kelvin stability condition we show that gravity can control the inertial effects of the shear up to frequencies that are high enough for the surface tension to play a relevant role this explains why surface tension is a necessary condition for well posedness while the low frequency main dynamics of interfacial waves are unaffected by it in order to derive a practical version of this criterion we work with a nondimensionalized version of the equations and allow for the possibility of various asymptotic regimes such as the shallow water limit this limit being singular we have to derive a new symbolic analysis of the dirichlet neumann operator that includes an infinitely smoothing tail accounting for the contribution of the bottom we then validate our criterion by comparison with experimental data in two important settings air water interfaces and internal waves the good agreement we observe allows us to discuss the scenario of wave breaking and the behavior of water brine interfaces and to propose a formula for the maximal amplitude of interfacial waves we also show how to rigorously justify two fluid asymptotic models used for applications and how to relate some of their properties to kelvin helmholtz instabilities

on a nonlinear eigenvalue problem in orliczsobolev spaces we consider the eigenvalue problem in an arbitrary orliczsobolev space we show that the existence of an eigenvalue can be derived from a generalized version of lagrange multiplier rule our approach also applies to more general problems we emphasize that no 2 condition is imposed

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

multiple solutions for a nonlinear and non homogeneous problem in orlicz sobolev spaces abstract we study a non homogeneous boundary value problem in a smooth bounded domain in r n we prove the existence of at least two non negative and non trivial weak solutions our approach relies on orlicz sobolev spaces theory combined with adequate variational methods and a variant of mountain pass lemma

testing causality between two vectors in multivariate autoregressive moving average models abstract in the analysis of economic time series a question often raised is whether a vector of variables causes another one in the sense of granger most of the literature on this topic is concerned with bivariate relationships or uses finite order autoregressive specifications the purpose of this article is to develop a causality analysis in the sense of granger for general vector autoregressive moving average arma models we give a definition of granger noncausality between vectors which is a natural and simple extension of the notion of granger noncausality between two variables in our context this definition is shown to be equivalent to a more complex definition proposed by tjostheim for the class of linear invertible processes we derive a necessary and sufficient condition for noncausality between two vectors of variables when the latter do not necessarily include all the variables considered in the analysis this result is then specialized to the class of stationary invertible arma process

hamiltonian formulation of the extended green naghdi equations abstract a novel method is developed for extending the green naghdi gn shallow water model equation to the general system which incorporates the arbitrary higher order dispersive effects as an illustrative example we derive a model equation which is accurate to the fourth power of the shallowness parameter while preserving the full nonlinearity of the gn equation and obtain its solitary wave solutions by means of a singular perturbation analysis we show that the extended gn equations have the same hamiltonian structure as that of the gn equation we also demonstrate that zakharov s hamiltonian formulation of surface gravity waves is equivalent to that of the extended gn system by rewriting the former system in terms of the momentum density instead of the velocity potential at the free surface

granger causality for state space models granger causality has long been a prominent method for inferring causal interactions between stochastic variables for a broad range of complex physical systems however it has been recognized that a moving average ma component in the data presents a serious confound to granger causal analysis as routinely performed via autoregressive ar modeling we solve this problem by demonstrating that granger causality may be calculated simply and efficiently from the parameters of a state space ss model since ss models are equivalent to autoregressive moving average models granger causality estimated in this fashion is not degraded by the presence of a ma component this is of particular significance when the data has been filtered downsampled observed with noise or is a subprocess of a higher dimensional process since all of these operations commonplace in application domains as diverse as climate science econometrics and the neurosciences induce a ma component we show how granger causality conditional and unconditional in both time and frequency domains may be calculated directly from ss model parameters via solution of a discrete algebraic riccati equation numerical simulations demonstrate that granger causality estimators thus derived have greater statistical power and smaller bias than ar estimators we also discuss how the ss approach facilitates relaxation of the assumptions of linearity stationarity and homoscedasticity underlying current ar methods thus opening up potentially significant new areas of research in granger causal analysis

evaluating frequency wise directed connectivity of bold signals applying relative power contribution with the linear multivariate time series models in this article we propose a statistical method to evaluate directed interactions of functional magnetic resonance imaging fmri data the multivariate autoregressive mar model was combined with the relative power contribution rpc in this analysis the mar model was fitted to the data to specify the direction of connections and the rpc quantifies the strength of connections as the rpc is computed in the frequency domain we can evaluate the connectivity for each frequency component from this we can establish whether the specified connections represent low or high frequency connectivity which cannot be examined solely using the estimated mar coefficients we applied this analysis method to fmri data obtained during visual motion tasks confirming previous reports of bottom up connectivity around the frequency corresponding to the block experimental design furthermore we used the mar model with exogenous variables marx to extend our understanding of these data and to show how the input to v1 transfers to higher cortical areas