Towards the timely detection of toxicants

We address the problem of enhancing the sensitivity of biosensors to the influence of toxicants, with an entropy method of analysis, denoted as CASSANDRA, recently invented for the specific purpose of studying non-stationary time series. We study the specific case where the toxicant is tetrodotoxin. This is a very poisonous substance that yields an abrupt drop of the rate of spike production at t approximatively 170 minutes when the concentration of toxicant is 4 nanomoles. The CASSANDRA algorithm reveals the influence of toxicants thirty minutes prior to the drop in rate at a concentration of toxicant equal to 2 nanomoles. We argue that the success of this method of analysis rests on the adoption of a new perspective of complexity, interpreted as a condition intermediate between the dynamic and the thermodynamic state.Comment: 6 pages and 3 figures. Accepted for publication in the special issue of Chaos Solitons and Fractal dedicated to the conference "Non-stationary Time Series: A Theoretical, Computational and Practical Challenge", Center for Nonlinear Science at University of North Texas, from October 13 to October 19, 2002, Denton, TX (USA

The 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)= 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.Comment: LaTeX, 4 pages, 3 figure

Probability flux as a method for detecting scaling

We introduce a new method for detecting scaling in time series. The method uses the properties of the probability flux for stochastic self-affine processes and is called the probability flux analysis (PFA). The advantages of this method are: 1) it is independent of the finiteness of the moments of the self-affine process; 2) it does not require a binning procedure for numerical evaluation of the the probability density function. These properties make the method particularly efficient for heavy tailed distributions in which the variance is not finite, for example, in Levy alpha-stable processes. This utility is established using a comparison with the diffusion entropy (DE) method

The Dynamics of EEG Entropy

EEG time series are analyzed using the diffusion entropy method. The resulting EEG entropy manifests short-time scaling, asymptotic saturation and an attenuated alpha-rhythm modulation. These properties are faithfully modeled by a phenomenological Langevin equation interpreted within a neural network context

Skewness as measure of the invariance of instantaneous renormalized drop diameter distributions – Part 2: Orographic precipitation

Abstract. Here we use the skewness parameter, and the procedure developed in the companion paper (Ignaccolo and De Michele, 2012), to investigate the variability of instantaneous renormalized spectra of rain drop diameter in presence of orographic precipitation. Disdrometer data, available at Bodega Bay and Cazadero, California, are analyzed either as a whole, or as divided (using the bright band echo) in precipitation intervals weakly and strongly influenced by orography, and compared to results obtained at Darwin, Australia. We find that also at Bodega Bay and Cazadero exists a most common distribution of the skewness values of instantaneous spectra of drop diameter, but peaked at values greater than 0.64, found at Darwin. No appreciable differences are found in the skewness distributions of precipitation weakly and strongly influenced by orography. However the renormalized drop diameter spectra of precipitation with strong orographic component have fatter right tail than precipitation with a weaker orographic component. The differences between orographic and non-orographic precipitation are investigated within the parametric space represented by number of drops, mean value and standard deviation of drop diameter. A filter is developed which is able to identify 1 min time intervals during which precipitation is mostly of orographic origin

Skewness as measure of the invariance of instantaneous renormalized drop diameter distributions – Part 1: Convective vs. stratiform precipitation

Abstract. We investigate the variability of the shape of the renormalized drop diameter instantaneous distribution using of the third order central moment: the skewness. Disdrometer data, collected at Darwin Australia, are considered either as whole or as divided in convective and stratiform precipitation intervals. We show that in all cases the distribution of the skewness is strongly peaked around 0.64. This allows to identify a most common distribution of renormalized drop diameters and two main variations, one with larger and one with smaller skewness. The distributions shapes are independent from the stratiform vs. convective classification