Attempt to distinguish electric signals of a dichotomous nature

Effect of nonlinear filters on detrended fluctuation analysis

When investigating the dynamical properties of complex multiple-component physical and physiological systems, it is often the case that the measurable system's output does not directly represent the quantity we want to probe in order to understand the underlying mechanisms. Instead, the output signal is often a linear or nonlinear function of the quantity of interest. Here, we investigate how various linear and nonlinear transformations affect the correlation and scaling properties of a signal, using the detrended fluctuation analysis (DFA) which has been shown to accurately quantify power-law correlations in nonstationary signals. Specifically, we study the effect of three types of transforms: (i) linear ( y(i) =a x(i) +b) , (ii) nonlinear polynomial ( y(i) =a x(k)(i) ) , and (iii) nonlinear logarithmic [ y(i) =log ( x(i) +Delta) ] filters. We compare the correlation and scaling properties of signals before and after the transform. We find that linear filters do not change the correlation properties, while the effect of nonlinear polynomial and logarithmic filters strongly depends on (a) the strength of correlations in the original signal, (b) the power k of the polynomial filter, and (c) the offset Delta in the logarithmic filter. We further apply the DFA method to investigate the "apparent" scaling of three analytic functions: (i) exponential [exp (+/-x+a) ] , (ii) logarithmic [log (x+a) ] , and (iii) power law [ (x+a)(lambda) ] , which are often encountered as trends in physical and biological processes. While these three functions have different characteristics, we find that there is a broad range of values for parameter a common for all three functions, where the slope of the DFA curves is identical. We further note that the DFA results obtained for a class of other analytic functions can be reduced to these three typical cases. We systematically test the performance of the DFA method when estimating long-range power-law correlations in the output signals for different parameter values in the three types of filters and the three analytic functions we consider.

Natural entropy fluctuations discriminate similar-looking electric signals emitted from systems of different dynamics

Complexity measures are introduced that quantify the change of the natural entropy fluctuations at different length scales in time series emitted from systems operating far from equilibrium. They identify impending sudden cardiac death (SD) by analyzing 15 min electrocardiograms, and comparing to those of truly healthy humans (H). These measures seem to be complementary to the ones suggested recently [Phys. Rev. E 70, 011106 (2004)]] and altogether enable the classification of individuals into three categories: H, heart disease patients, and SD. All the SD individuals, who exhibit critical dynamics, result in a common behavior.

Aging in coherent noise models and natural time

Event correlation between aftershocks in the coherent noise model is studied by making use of natural time, which has recently been introduced in complex time-series analysis. It is found that the aging phenomenon and the associated scaling property discovered in the observed seismic data are well reproduced by the model. It is also found that the scaling function is given by the q-exponential function appearing in nonextensive statistical mechanics, showing power-law decay of event correlation in natural time.

Entropy in the natural time domain

A surrogate data analysis is presented, which is based on the fluctuations of the "entropy" S defined in the natural time domain [Phys. Rev. E 68, 031106 (2003)]]. This entropy is not a static one such as, for example, the Shannon entropy. The analysis is applied to three types of time series, i.e., seismic electric signals, "artificial" noises, and electrocardiograms, and it "recognizes" the non-Markovianity in all these signals. Furthermore, it differentiates the electrocardiograms of healthy humans from those of the sudden cardiac death ones. If deltaS and deltaSshuf denote the standard deviation when calculating the entropy by means of a time window sweeping through the original data and the "shuffled" (randomized) data, respectively, it seems that the ratio deltaSshuf /deltaS plays a key role. The physical meaning of deltaSshuf is investigated.

Electric fields that "arrive" before the time derivative of the magnetic field prior to major earthquakes

The low frequency electric signals (emitted from the focal area when the stress reaches a critical value) that precede major earthquakes, are recorded at distances approximately 100 km being accompanied by magnetic field variations. The electric field "arrives" 1 to 2 s before the time derivative of the horizontal magnetic field. An explanation, which is still awaiting, should consider, beyond criticality, the large spatial scale as well as that the transmission of the electromagnetic fields (through an inhomogeneous weakly conductive medium like the Earth) obeys diffusion type equations.