Inferring direct directed-information flow from multivariate nonlinear time series.

Estimating the functional topology of a network from multivariate observations is an important task in nonlinear dynamics. We introduce the nonparametric partial directed coherence that allows disentanglement of direct and indirect connections and their directions. We illustrate the performance of the nonparametric partial directed coherence by means of a simulation with data from synchronized nonlinear oscillators and apply it to real-world data from a patient suffering from essential tremor.

[1]  Mingzhou Ding,et al.  Estimating Granger causality from fourier and wavelet transforms of time series data. , 2007, Physical review letters.

[2]  Jens Timmer,et al.  Revealing direction of coupling between neuronal oscillators from time series: phase dynamics modeling versus partial directed coherence. , 2007, Chaos.

[3]  C. Granger Investigating Causal Relations by Econometric Models and Cross-Spectral Methods , 1969 .

[4]  Rainer Dahlhaus,et al.  Partial phase synchronization for multivariate synchronizing systems. , 2006, Physical review letters.

[5]  F Babiloni,et al.  Signal Informatics as an Advanced Integrative Concept in the Framework of Medical Informatics , 2009, Methods of Information in Medicine.

[6]  Yijun Liu,et al.  Analyzing brain networks with PCA and conditional Granger causality , 2009, Human brain mapping.

[7]  Michael Eichler,et al.  Abstract Journal of Neuroscience Methods xxx (2005) xxx–xxx Testing for directed influences among neural signals using partial directed coherence , 2005 .

[8]  Ali H. Sayed,et al.  A survey of spectral factorization methods , 2001, Numer. Linear Algebra Appl..

[9]  F. Mormann,et al.  Mean phase coherence as a measure for phase synchronization and its application to the EEG of epilepsy patients , 2000 .

[10]  Karin Schwab,et al.  Comparison of linear signal processing techniques to infer directed interactions in multivariate neural systems , 2005, Signal Process..

[11]  J. Kurths,et al.  From Phase to Lag Synchronization in Coupled Chaotic Oscillators , 1997 .

[12]  B. Efron Bootstrap Methods: Another Look at the Jackknife , 1979 .

[13]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[14]  Luiz A. Baccalá,et al.  Partial directed coherence: a new concept in neural structure determination , 2001, Biological Cybernetics.

[15]  J. Timmer,et al.  Tremor-correlated cortical activity in essential tremor , 2001, The Lancet.

[16]  Jürgen Kurths,et al.  Estimation of the direction of the coupling by conditional probabilities of recurrence. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  G. Wilson The Factorization of Matricial Spectral Densities , 1972 .

[18]  B Hellwig,et al.  On Studentising and Blocklength Selection for the Bootstrap on Time Series , 2005, Biometrical journal. Biometrische Zeitschrift.

[19]  Katarzyna J. Blinowska,et al.  A new method of the description of the information flow in the brain structures , 1991, Biological Cybernetics.

[20]  Jens Timmer,et al.  Detecting Coupling Directions in Multivariate Oscillatory Systems , 2007, Int. J. Bifurc. Chaos.

[21]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

[22]  M. Rosenblum,et al.  Detecting direction of coupling in interacting oscillators. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Mingzhou Ding,et al.  Analyzing information flow in brain networks with nonparametric Granger causality , 2008, NeuroImage.

[24]  Jürgen Kurths,et al.  Recurrence plots for the analysis of complex systems , 2009 .

[25]  M. Winterhalder,et al.  Mixing properties of the Rössler system and consequences for coherence and synchronization analysis. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.