Dynamics of electroencephalogram entropy and pitfalls of scaling detection.

In recent studies a number of research groups have determined that human electroencephalograms (EEG) have scaling properties. In particular, a crossover between two regions with different scaling exponents has been reported. Herein we study the time evolution of diffusion entropy to elucidate the scaling of EEG time series. For a cohort of 20 awake healthy volunteers with closed eyes, we find that the diffusion entropy of EEG increments (obtained from EEG waveforms by differencing) exhibits three features: short-time growth, an alpha wave related oscillation whose amplitude gradually decays in time, and asymptotic saturation which is achieved after approximately 1 s. This analysis suggests a linear, stochastic Ornstein-Uhlenbeck Langevin equation with a quasiperiodic forcing (whose frequency and/or amplitude may vary in time) as the model for the underlying dynamics. This model captures the salient properties of EEG dynamics. In particular, both the experimental and simulated EEG time series exhibit short-time scaling which is broken by a strong periodic component, such as alpha waves. The saturation of EEG diffusion entropy precludes the existence of asymptotic scaling. We find that the crossover between two scaling regions seen in detrended fluctuation analysis (DFA) of EEG increments does not originate from the underlying dynamics but is merely an artifact of the algorithm. This artifact is rooted in the failure of the "trend plus signal" paradigm of DFA.

Impairment of cardiovascular autonomic pattern in obese adolescents with Type 2 diabetes mellitus.

UNLABELLED: The aim of this study was to assess the behaviour of insulin sensitivity and insulin resistance (IR) indexes in a group of obese adolescents with Type 2 diabetes mellitus (T2DM) in comparison to obese adolescents without diabetes and normal controls, moreover to compare these parameters with the cardiac autonomic pattern. Seven T2DM obese (12.7 ± 0.5 yr), 18 obese without T2DM, and 10 nonobese control adolescents age matched were studied. In all subjects we performed oral glucose tolerance test (OGTT) with insulin and glucose determination, 24-h electrocardiogram Holter, blood pressure monitoring, ecohocardiogram. RESULTS: serum lipids were significantly higher in obese and T2DM. Insulin sensitivity was significantly reduced in T2DM and obese vs controls; T2DM showed a more pronounced oral glucose insulin sensitivity (OGIS) reduction vs obese. Both obese and T2DM presented an higher IR. T2DM showed an impaired ß-cell function, with insulin areas under the curve and disposition index significantly reduced in comparison to controls and obese who showed similar values. A progressive reduction of vagal indexes and an increase of sympathetic indexes were found in obese adolescents and were more pronounced in T2DM. These parameters were correlated with OGIS and ß-cell function parameters in both obese and T2DM adolescents. T2DM showed a significant relative wall thickness increase suggesting a trend toward concentric remodeling. In conclusion, T2DM adolescents are characterized by a more marked IR reduced ß-cell function in comparison to non-diabetic obese. These modifications may lead to an early impairment of the autonomic pattern.

Random growth of interfaces as a subordinated process.

We study the random growth of surfaces from within the perspective of a single column, namely, the fluctuation of the column height around the mean value, y (t) identical with h (t)-, which is depicted as being subordinated to a standard fluctuation-dissipation process with friction gamma. We argue that the main properties of Kardar-Parisi-Zhang theory, in one dimension, are derived by identifying the distribution of return times to y (0) =0, which is a truncated inverse power law, with the distribution of subordination times. The agreement of the theoretical prediction with the numerical treatment of the (1+1) -dimensional model of ballistic deposition is remarkably good, in spite of the finite-size effects affecting this model.

Scaling breakdown: a signature of aging.

We prove that the Lévy walk is characterized by bilinear scaling. This effect mirrors the existence of a form of aging that does not require the adoption of nonstationary conditions.

Sporadic randomness: the transition from the stationary to the nonstationary condition.

We address the study of sporadic randomness by means of the Manneville map. We point out that the Manneville map is the generator of fluctuations yielding the Lévy processes, and that these processes are currently regarded by some authors as statistical manifestations of a nonextensive form of thermodynamics. For this reason we study the sensitivity to initial conditions with the help of a nonextensive form of the Lyapunov coefficient. The purpose of this research is twofold. The former is to assess whether a finite diffusion coefficient might emerge from the nonextensive approach. This property, at first sight, seems to be plausible in the nonstationary case, where conventional Kolmogorov-Sinai analysis predicts a vanishing Lyapunov coefficient. The latter purpose is to confirm or reject conjectures about the nonextensive nature of Lévy processes. We find that the adoption of a nonextensive approach does not serve any predictive purpose: It does not even signal a transition from a stationary to a nonstationary regime. These conclusions are reached by means of both numerical and analytical calculations that shed light on why the Lévy processes do not imply any need to depart from the adoption of traditional complexity measures.