608 research outputs found
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 (for the above mentioned filter), below
which individuals are at risk.Comment: 5 latex pages (including 6 figures). Accepted in Fractal
Box modeling of the Eastern Mediterranean sea
In âŒ1990 a new source of deep water formation in the Eastern Mediterranean was found in the southern part of the Aegean sea. Till then, the only source of deep water formation in the Eastern Mediterranean was in the Adriatic sea; the rate of the deep water formation of the new Aegean source is 1 Sv, three times larger than the Adriatic source. We develop a simple three-box model to study the stability of the thermohaline circulation of the Eastern Mediterranean sea. The three boxes represent the Adriatic sea, Aegean sea, and the Ionian seas. The boxes exchange heat and salinity and may be described by a set of nonlinear differential equations. We analyze these equations and find that the system may have one, two, or four stable flux states. We conjecture that the change in the deep water formation in the Eastern Mediterranean sea is attributed to a switch between the different states on the thermohaline circulation; this switch may result from decreased temperature and/or increased salinity over the Aegean sea
Fractal Analysis of River Flow Fluctuations (with Erratum)
We use some fractal analysis methods to study river flow fluctuations.
The result of the Multifractal Detrended Fluctuation Analysis (MF-DFA) shows
that there are two crossover timescales at and
months in the fluctuation function. We discuss how the
existence of the crossover timescales are related to a sinusoidal trend. The
first crossover is due to the seasonal trend and the value of second ones is
approximately equal to the well known cycle of sun activity. Using Fourier
detrended fluctuation analysis, the sinusoidal trend is eliminated. The value
of Hurst exponent of the runoff water of rivers without the sinusoidal trend
shows a long range correlation behavior. For the Daugava river the value of
Hurst exponent is and also we find that these fluctuations have
multifractal nature. Comparing the MF-DFA results for the remaining data set of
Daugava river to those for shuffled and surrogate series, we conclude that its
multifractal nature is almost entirely due to the broadness of probability
density function.Comment: 13 pages, 10 figures, V2: Added comments, references and one more
figure, improved numerical calculations with new version of data, accepted
for publication in Physica A: Statistical Mechanics and its Applications. The
version with Erratum contains some notes concerning Ref. [58
Effect of significant data loss on identifying electric signals that precede rupture by detrended fluctuation analysis in natural time
Electric field variations that appear before rupture have been recently
studied by employing the detrended fluctuation analysis (DFA) as a scaling
method to quantify long-range temporal correlations. These studies revealed
that seismic electric signals (SES) activities exhibit a scale invariant
feature with an exponent over all scales investigated
(around five orders of magnitude). Here, we study what happens upon significant
data loss, which is a question of primary practical importance, and show that
the DFA applied to the natural time representation of the remaining data still
reveals for SES activities an exponent close to 1.0, which markedly exceeds the
exponent found in artificial (man-made) noises. This, in combination with
natural time analysis, enables the identification of a SES activity with
probability 75% even after a significant (70%) data loss. The probability
increases to 90% or larger for 50% data loss.Comment: 12 Pages, 11 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 of the original correlated signal, (ii) the percentage of
the data removed, (iii) the average length 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
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