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.Comment: 29 pages, 5 figures, paper accepted for publication in Physica

Nonlinear denoising of transient signals with application to event related potentials

We present a new wavelet based method for the denoising of {\it event related potentials} ERPs), employing techniques recently developed for the paradigm of deterministic chaotic systems. The denoising scheme has been constructed to be appropriate for short and transient time sequences using circular state space embedding. Its effectiveness was successfully tested on simulated signals as well as on ERPs recorded from within a human brain. The method enables the study of individual ERPs against strong ongoing brain electrical activity.Comment: 16 pages, Postscript, 6 figures, Physica D in pres

Fluctuation Analysis of Human Electroencephalogram

The scaling behaviors of the human electroencephalogram (EEG) time series are studied using detrended fluctuation analysis. Two scaling regions are found in nearly every channel for all subjects examined. The scatter plot of the scaling exponents for all channels (up to 129) reveals the complicated structure of a subject's brain activity. Moment analyses are performed to extract the gross features of all the scaling exponents, and another universal scaling behavior is identified. A one-parameter description is found to characterize the fluctuation properties of the nonlinear behaviors of the brain dynamics.Comment: 4 pages in RevTeX + 6 figures in ep

Kullback-Leibler and Renormalized Entropy: Applications to EEGs of Epilepsy Patients

Recently, renormalized entropy was proposed as a novel measure of relative entropy (P. Saparin et al., Chaos, Solitons & Fractals 4, 1907 (1994)) and applied to several physiological time sequences, including EEGs of patients with epilepsy. We show here that this measure is just a modified Kullback-Leibler (K-L) relative entropy, and it gives similar numerical results to the standard K-L entropy. The latter better distinguishes frequency contents of e.g. seizure and background EEGs than renormalized entropy. We thus propose that renormalized entropy might not be as useful as claimed by its proponents. In passing we also make some critical remarks about the implementation of these methods.Comment: 15 pages, 4 Postscript figures. Submitted to Phys. Rev. E, 199

Conedy: a scientific tool to investigate Complex Network Dynamics

We present Conedy, a performant scientific tool to numerically investigate dynamics on complex networks. Conedy allows to create networks and provides automatic code generation and compilation to ensure performant treatment of arbitrary node dynamics. Conedy can be interfaced via an internal script interpreter or via a Python module

What Models and Tools can Contribute to a Better Understanding of Brain Activity?

This is the final version. Available on open access from Frontiers Media via the DOI in this recordData Availability Statement: The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.Despite impressive scientific advances in understanding the structure and function of the human brain, big challenges remain. A deep understanding of healthy and aberrant brain activity at a wide range of temporal and spatial scales is needed. Here we discuss, from an interdisciplinary network perspective, the advancements in physical and mathematical modeling as well as in data analysis techniques that, in our opinion, have potential to further advance our understanding of brain structure and function.Spanish Ministry of Science and InnovationState Research AgencySpanish Ministerio de Ciencia, Innovacion y UniversidadesCREA ACADEMIA program, Generalitat de Cataluny

Separating neural oscillations from aperiodic 1/f activity: Challenges and recommendations

Electrophysiological power spectra typically consist of two components: An aperiodic part usually following an 1/f power law [Formula: see text] and periodic components appearing as spectral peaks. While the investigation of the periodic parts, commonly referred to as neural oscillations, has received considerable attention, the study of the aperiodic part has only recently gained more interest. The periodic part is usually quantified by center frequencies, powers, and bandwidths, while the aperiodic part is parameterized by the y-intercept and the 1/f exponent [Formula: see text]. For investigation of either part, however, it is essential to separate the two components. In this article, we scrutinize two frequently used methods, FOOOF (Fitting Oscillations & One-Over-F) and IRASA (Irregular Resampling Auto-Spectral Analysis), that are commonly used to separate the periodic from the aperiodic component. We evaluate these methods using diverse spectra obtained with electroencephalography (EEG), magnetoencephalography (MEG), and local field potential (LFP) recordings relating to three independent research datasets. Each method and each dataset poses distinct challenges for the extraction of both spectral parts. The specific spectral features hindering the periodic and aperiodic separation are highlighted by simulations of power spectra emphasizing these features. Through comparison with the simulation parameters defined a priori, the parameterization error of each method is quantified. Based on the real and simulated power spectra, we evaluate the advantages of both methods, discuss common challenges, note which spectral features impede the separation, assess the computational costs, and propose recommendations on how to use them

Identifying phase synchronization clusters in spatially extended dynamical systems

We investigate two recently proposed multivariate time series analysis techniques that aim at detecting phase synchronization clusters in spatially extended, nonstationary systems with regard to field applications. The starting point of both techniques is a matrix whose entries are the mean phase coherence values measured between pairs of time series. The first method is a mean field approach which allows to define the strength of participation of a subsystem in a single synchronization cluster. The second method is based on an eigenvalue decomposition from which a participation index is derived that characterizes the degree of involvement of a subsystem within multiple synchronization clusters. Simulating multiple clusters within a lattice of coupled Lorenz oscillators we explore the limitations and pitfalls of both methods and demonstrate (a) that the mean field approach is relatively robust even in configurations where the single cluster assumption is not entirely fulfilled, and (b) that the eigenvalue decomposition approach correctly identifies the simulated clusters even for low coupling strengths. Using the eigenvalue decomposition approach we studied spatiotemporal synchronization clusters in long-lasting multichannel EEG recordings from epilepsy patients and obtained results that fully confirm findings from well established neurophysiological examination techniques. Multivariate time series analysis methods such as synchronization cluster analysis that account for nonlinearities in the data are expected to provide complementary information which allows to gain deeper insights into the collective dynamics of spatially extended complex systems