233 research outputs found
Evaluating Maximum Likelihood Estimation Methods to Determine the Hurst Coefficient
A maximum likelihood estimation method implemented in S-PLUS (S-MLE) to estimate the Hurst coefficient (H) is evaluated. The Hurst coefficient, with 0.5\u3cHS-MLE was developed to estimate H for fractionally differenced (fd) processes. However, in practice it is difficult to distinguish between fd processes and fractional Gaussian noise (fGn) processes. Thus, the method is evaluated for estimating H for both fd and fGn processes. S-MLE gave biased results of H for fGn processes of any length and for fd processes of lengths less than 210. A modified method is proposed to correct for this bias. It gives reliable estimates of H for both fd and fGn processes of length greater than or equal to 211
Minimizing the effect of sinusoidal trends in detrended fluctuation analysis
The detrended fluctuation analysis (DFA) [Peng et al., 1994] and its
extensions (MF-DFA) [Kantelhardt et al., 2002] have been used extensively to
determine possible long-range correlations in self-affine signals. While the
DFA has been claimed to be a superior technique, recent reports have indicated
its susceptibility to trends in the data. In this report, a smoothing filter is
proposed to minimize the effect of sinusoidal trends and distortion in the
log-log plots obtained by DFA and MF-DFA techniques
Ion-channel-like behavior in lipid bilayer membranes at the melting transition
It is well known that at the gel-liquid phase transition temperature a lipid
bilayer membrane exhibits an increased ion permeability. We analyze the
quantized currents in which the increased permeability presents itself. The
open time histogram shows a "-3/2" power law which implies an open-closed
transition rate that decreases like as time evolves. We
propose a "pore freezing" model to explain the observations. We discuss how
this model also leads to the noise that is commonly observed in
currents across biological and artificial membranes.Comment: 5 pages, 4 figure
Correlation function and generalized master equation of arbitrary age
We study a two-state statistical process with a non-Poisson distribution of
sojourn times. In accordance with earlier work, we find that this process is
characterized by aging and we study three different ways to define the
correlation function of arbitrary age of the corresponding dichotomous
fluctuation based respectively on the Generalized Master Equation formalism, on
a Liouville-like approach and on a trajectory perspective.Comment: 11 pages, 1figur
Distinguishing cancerous from non-cancerous cells through analysis of electrical noise
Since 1984, electric cell-substrate impedance sensing (ECIS) has been used to
monitor cell behavior in tissue culture and has proven sensitive to cell
morphological changes and cell motility. We have taken ECIS measurements on
several cultures of non-cancerous (HOSE) and cancerous (SKOV) human ovarian
surface epithelial cells. By analyzing the noise in real and imaginary
electrical impedance, we demonstrate that it is possible to distinguish the two
cell types purely from signatures of their electrical noise. Our measures
include power-spectral exponents, Hurst and detrended fluctuation analysis, and
estimates of correlation time; principal-component analysis combines all the
measures. The noise from both cancerous and non-cancerous cultures shows
correlations on many time scales, but these correlations are stronger for the
non-cancerous cells.Comment: 8 pages, 4 figures; submitted to PR
Avalanches in the lung: A statistical mechanical model
We study a statistical mechanical model for the dynamics of lung inflation
which incorporates recent experimental observations on the opening of
individual airways by a cascade or avalanche mechanism. Using an exact mapping
of the avalanche problem onto percolation on a Cayley tree, we analytically
derive the exponents describing the size distribution of the first avalanches
and test the analytical solution by numerical simulations. We find that the
tree-like structure of the airways together with the simplest assumptions
concerning opening threshold pressures of each airway, is sufficient to explain
the existence of power-law distributions observed experimentally.Comment: 4 pages, Figures avaliable by mail from [email protected], REVTE
Levy stable noise induced transitions: stochastic resonance, resonant activation and dynamic hysteresis
A standard approach to analysis of noise-induced effects in stochastic
dynamics assumes a Gaussian character of the noise term describing interaction
of the analyzed system with its complex surroundings. An additional assumption
about the existence of timescale separation between the dynamics of the
measured observable and the typical timescale of the noise allows external
fluctuations to be modeled as temporally uncorrelated and therefore white.
However, in many natural phenomena the assumptions concerning the
abovementioned properties of "Gaussianity" and "whiteness" of the noise can be
violated. In this context, in contrast to the spatiotemporal coupling
characterizing general forms of non-Markovian or semi-Markovian L\'evy walks,
so called L\'evy flights correspond to the class of Markov processes which
still can be interpreted as white, but distributed according to a more general,
infinitely divisible, stable and non-Gaussian law. L\'evy noise-driven
non-equilibrium systems are known to manifest interesting physical properties
and have been addressed in various scenarios of physical transport exhibiting a
superdiffusive behavior. Here we present a brief overview of our recent
investigations aimed to understand features of stochastic dynamics under the
influence of L\'evy white noise perturbations. We find that the archetypal
phenomena of noise-induced ordering are robust and can be detected also in
systems driven by non-Gaussian, heavy-tailed fluctuations with infinite
variance.Comment: 7 pages, 8 figure
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
Scaling-violation phenomena and fractality in the human posture control systems
By analyzing the movements of quiet standing persons by means of wavelet
statistics, we observe multiple scaling regions in the underlying body
dynamics. The use of the wavelet-variance function opens the possibility to
relate scaling violations to different modes of posture control. We show that
scaling behavior becomes close to perfect, when correctional movements are
dominated by the vestibular system.Comment: 12 pages, 4 figures, to appear in Phys. Rev.
Scale Invariance in the Nonstationarity of Physiological Signals
We introduce a segmentation algorithm to probe temporal organization of
heterogeneities in human heartbeat interval time series. We find that the
lengths of segments with different local values of heart rates follow a
power-law distribution. This scale-invariant structure is not a simple
consequence of the long-range correlations present in the data. We also find
that the differences in mean heart rates between consecutive segments display a
common functional form, but with different parameters for healthy individuals
and for patients with heart failure. This finding may provide information into
the way heart rate variability is reduced in cardiac disease.Comment: 13 pages, 5 figures, corrected typo
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