Complexity, Tunneling and Geometrical Symmetry

It is demonstrated in the context of the simple one-dimensional example of a barrier in an infinite well, that highly complex behavior of the time evolution of a wave function is associated with the almost degeneracy of levels in the process of tunneling. Degenerate conditions are obtained by shifting the position of the barrier. The complexity strength depends on the number of almost degenerate levels which depend on geometrical symmetry. The presence of complex behavior is studied to establish correlation with spectral degeneracy.Comment: 9 revtex pages, 6 Postscript figures (uuencoded

The Necessity for a Time Local Dimension in Systems with Time Varying Attractors

We show that a simple non-linear system of ordinary differential equations may possess a time varying attractor dimension. This indicates that it is infeasible to characterize EEG and MEG time series with a single time global dimension. We suggest another measure for the description of non-stationary attractors.Comment: 13 Postscript pages, 12 Postscript figures (figures 3b and 4 by request from Y. Ashkenazy: [email protected]

Discrimination of the Healthy and Sick Cardiac Autonomic Nervous System by a New Wavelet Analysis of Heartbeat Intervals

We demonstrate that it is possible to distinguish with a complete certainty between healthy subjects and patients with various dysfunctions of the cardiac nervous system by way of multiresolutional wavelet transform of RR intervals. We repeated the study of Thurner et al on different ensemble of subjects. We show that reconstructed series using a filter which discards wavelet coefficients related with higher scales enables one to classify individuals for which the method otherwise is inconclusive. We suggest a delimiting diagnostic value of the standard deviation of the filtered, reconstructed RR interval time series in the range of $\sim 0.035$ (for the above mentioned filter), below which individuals are at risk.Comment: 5 latex pages (including 6 figures). Accepted in Fractal

Multifractal Properties of Price Fluctuations of Stocks and Commodities

We analyze daily prices of 29 commodities and 2449 stocks, each over a period of $\approx 15$ years. We find that the price fluctuations for commodities have a significantly broader multifractal spectrum than for stocks. We also propose that multifractal properties of both stocks and commodities can be attributed mainly to the broad probability distribution of price fluctuations and secondarily to their temporal organization. Furthermore, we propose that, for commodities, stronger higher order correlations in price fluctuations result in broader multifractal spectra.Comment: Published in Euro Physics Letters (14 pages, 5 figures

Volatility of Linear and Nonlinear Time Series

Previous studies indicate that nonlinear properties of Gaussian time series with long-range correlations, $u_i$, can be detected and quantified by studying the correlations in the magnitude series $|u_i|$, i.e., the ``volatility''. However, the origin for this empirical observation still remains unclear, and the exact relation between the correlations in $u_i$ and the correlations in $|u_i|$ is still unknown. Here we find analytical relations between the scaling exponent of linear series $u_i$ and its magnitude series $|u_i|$. Moreover, we find that nonlinear time series exhibit stronger (or the same) correlations in the magnitude time series compared to linear time series with the same two-point correlations. Based on these results we propose a simple model that generates multifractal time series by explicitly inserting long range correlations in the magnitude series; the nonlinear multifractal time series is generated by multiplying a long-range correlated time series (that represents the magnitude series) with uncorrelated time series [that represents the sign series $sgn(u_i)$]. Our results of magnitude series correlations may help to identify linear and nonlinear processes in experimental records.Comment: 7 pages, 5 figure

Regeneration of Stochastic Processes: An Inverse Method

We propose a novel inverse method that utilizes a set of data to construct a simple equation that governs the stochastic process for which the data have been measured, hence enabling us to reconstruct the stochastic process. As an example, we analyze the stochasticity in the beat-to-beat fluctuations in the heart rates of healthy subjects as well as those with congestive heart failure. The inverse method provides a novel technique for distinguishing the two classes of subjects in terms of a drift and a diffusion coefficients which behave completely differently for the two classes of subjects, hence potentially providing a novel diagnostic tool for distinguishing healthy subjects from those with congestive heart failure, even at the early stages of the disease development.Comment: 5 pages, two columns, 7 figs. to appear, The European Physical Journal B (2006

Effect of extreme data loss on long-range correlated and anti-correlated signals quantified by detrended fluctuation analysis

We investigate how extreme loss of data affects the scaling behavior of long-range power-law correlated and anti-correlated signals applying the DFA method. We introduce a segmentation approach to generate surrogate signals by randomly removing data segments from stationary signals with different types of correlations. These surrogate signals are characterized by: (i) the DFA scaling exponent $\alpha$ of the original correlated signal, (ii) the percentage $p$ of the data removed, (iii) the average length $\mu$ of the removed (or remaining) data segments, and (iv) the functional form of the distribution of the length of the removed (or remaining) data segments. We find that the {\it global} scaling exponent of positively correlated signals remains practically unchanged even for extreme data loss of up to 90%. In contrast, the global scaling of anti-correlated signals changes to uncorrelated behavior even when a very small fraction of the data is lost. These observations are confirmed on the examples of human gait and commodity price fluctuations. We systematically study the {\it local} scaling behavior of signals with missing data to reveal deviations across scales. We find that for anti-correlated signals even 10% of data loss leads to deviations in the local scaling at large scales from the original anti-correlated towards uncorrelated behavior. In contrast, positively correlated signals show no observable changes in the local scaling for up to 65% of data loss, while for larger percentage, the local scaling shows overestimated regions (with higher local exponent) at small scales, followed by underestimated regions (with lower local exponent) at large scales. Finally, we investigate how the scaling is affected by the statistics of the remaining data segments in comparison to the removed segments