Scaling of noisy fluctuations in complex networks and applications to network prediction.

We study the collective dynamics of oscillator-network systems in the presence of noise. By focusing on the time-averaged fluctuation of dynamical variable of interest about the mean field, we discover a scaling law relating the average fluctuation to the node degree. The scaling law is quite robust as it holds for a variety of network topologies and node dynamics.

Detection of seizure rhythmicity by recurrences.

Epileptic seizures show a certain degree of rhythmicity, a feature of heuristic and practical interest. In this paper, we introduce a simple model of this type of behavior, and suggest a measure for detecting and quantifying it. To evaluate our method, we develop a set of test segments that incorporate rhythmicity features, and present results from the application of this measure to test segments.

Correlation dimension and integral do not predict epileptic seizures.

Reports in the literature have indicated potential value of the correlation integral and dimension for prediction of epileptic seizures up to several minutes before electrographic onset. We apply these measures to over 2000 total hours of continuous electrocortiogram, taken from 20 patients with epilepsy, examine their sensitivity to quantifiable properties such as the signal amplitude and autocorrelation, and investigate the influence of embedding and filtering strategies on their performance. The results are compared against those obtained from surrogate time series.

Accumulated energy revisited.

Objective: To examine the seizure prediction and detection abilities of the accumulated energy on multi-center data submitted to the First International Collaborative Workshop on Seizure Prediction.

Methods: The accumulated energy (AE), windowed average power, and FHS seizure detection algorithm were applied to a single channel of ECoG data taken from the data sets contributed to the workshop. The FHS seizure detection algorithm was used to perform automated scoring of the data in order to locate subclinical events not picked up by the centers where the data was collected.

Controlled test for predictive power of Lyapunov exponents: their inability to predict epileptic seizures.

Lyapunov exponents are a set of fundamental dynamical invariants characterizing a system's sensitive dependence on initial conditions. For more than a decade, it has been claimed that the exponents computed from electroencephalogram (EEG) or electrocorticogram (ECoG) signals can be used for prediction of epileptic seizures minutes or even tens of minutes in advance. The purpose of this paper is to examine the predictive power of Lyapunov exponents.

Inability of Lyapunov exponents to predict epileptic seizures.

It has been claimed that Lyapunov exponents computed from electroencephalogram or electrocorticogram (ECoG) time series are useful for early prediction of epileptic seizures. We show, by utilizing a paradigmatic chaotic system, that there are two major obstacles that can fundamentally hinder the predictive power of Lyapunov exponents computed from time series: finite-time statistical fluctuations and noise. A case study with an ECoG signal recorded from a patient with epilepsy is presented.

Correlation-dimension and autocorrelation fluctuations in epileptic seizure dynamics.

We focus on an anomalous scaling region in correlation integral [C(epsilon)] analysis of electrocorticogram in epilepsy patients. We find that epileptic seizures typically are accompanied by wide fluctuations in the slope of this scaling region. An explanation, based on analyzing the interplay between the autocorrelation and C(epsilon), is provided for these fluctuations.