40 research outputs found
Impact of embedding on predictability of failure-recovery dynamics in networks
Failure, damage spread and recovery crucially underlie many spatially
embedded networked systems ranging from transportation structures to the human
body. Here we study the interplay between spontaneous damage, induced failure
and recovery in both embedded and non-embedded networks. In our model the
network's components follow three realistic processes that capture these
features: (i) spontaneous failure of a component independent of the
neighborhood (internal failure), (ii) failure induced by failed neighboring
nodes (external failure) and (iii) spontaneous recovery of a component.We
identify a metastable domain in the global network phase diagram spanned by the
model's control parameters where dramatic hysteresis effects and random
switching between two coexisting states are observed. The loss of
predictability due to these effects depend on the characteristic link length of
the embedded system. For the Euclidean lattice in particular, hysteresis and
switching only occur in an extremely narrow region of the parameter space
compared to random networks. We develop a unifying theory which links the
dynamics of our model to contact processes. Our unifying framework may help to
better understand predictability and controllability in spatially embedded and
random networks where spontaneous recovery of components can mitigate
spontaneous failure and damage spread in the global network.Comment: 22 pages, 20 figure
Comment on "Scaling of atmosphere and ocean temperature correlations in observations and climate models"
In a recent letter [K. Fraedrich and R. Blender, Phys. Rev. Lett. 90, 108501
(2003)], Fraedrich and Blender studied the scaling of atmosphere and ocean
temperature. They analyzed the fluctuation functions F(s) ~ s^alpha of monthly
temperature records (mostly from grid data) by using the detrended fluctuation
analysis (DFA2) and claim that the scaling exponent alpha over the inner
continents is equal to 0.5, being characteristic of uncorrelated random
sequences. Here we show that this statement is (i) not supported by their own
analysis and (ii) disagrees with the analysis of the daily observational data
from which the grid monthly data have been derived. We conclude that also for
the inner continents, the exponent is between 0.6 and 0.7, similar as for the
coastline-stations.Comment: 1 page with 2 figure
On the universality of distribution of ranked cluster masses at critical percolation
The distribution of masses of clusters smaller than the infinite cluster is
evaluated at the percolation threshold. The clusters are ranked according to
their masses and the distribution of the scaled masses M for any
rank r shows a universal behaviour for different lattice sizes L (D is the
fractal dimension). For different ranks however, there is a universal
distribution function only in the large rank limit, i.e., (y and are defined in the text), where the
universal scaling function g is found to be Gaussian in nature.Comment: 4 pages, to appear in J. Phys.
Breathing during REM and non-REM sleep: correlated versus uncorrelated behaviour
Abstract Healthy sleep can be characterized by several stages: deep sleep, light sleep, and REM sleep. Here we show that these sleep stages lead to di erent autonomic regulation of breathing. Using the detrended uctuation analysis up to the fourth order we ÿnd that breath-to-breath intervals and breath volumes separated by several breaths are long-range correlated during the REM stages and during wake states. In contrast, in the non-REM stages (deep sleep and light sleep), long-range correlations are absent. This behaviour is very similar to the correlation behaviour of the heart rate during the night and may be related to the phase synchronization between heartbeat and breathing found recently. We speculate that the di erences are caused by di erent cortically in uenced control of the autonomic nervous system
Detecting Long-range Correlations with Detrended Fluctuation Analysis
We examine the Detrended Fluctuation Analysis (DFA), which is a
well-established method for the detection of long-range correlations in time
series. We show that deviations from scaling that appear at small time scales
become stronger in higher orders of DFA, and suggest a modified DFA method to
remove them. The improvement is necessary especially for short records that are
affected by non-stationarities. Furthermore, we describe how crossovers in the
correlation behavior can be detected reliably and determined quantitatively and
show how several types of trends in the data affect the different orders of
DFA.Comment: 10 pages, including 8 figure
Multifractal detrended fluctuation analysis of nonstationary time series
We develop a method for the multifractal characterization of nonstationary
time series, which is based on a generalization of the detrended fluctuation
analysis (DFA). We relate our multifractal DFA method to the standard partition
function-based multifractal formalism, and prove that both approaches are
equivalent for stationary signals with compact support. By analyzing several
examples we show that the new method can reliably determine the multifractal
scaling behavior of time series. By comparing the multifractal DFA results for
original series to those for shuffled series we can distinguish multifractality
due to long-range correlations from multifractality due to a broad probability
density function. We also compare our results with the wavelet transform
modulus maxima (WTMM) method, and show that the results are equivalent.Comment: 14 pages (RevTex) with 10 figures (eps
Diffusion on random site percolation clusters. Theory and NMR microscopy experiments with model objects
Quasi two-dimensional random site percolation model objects were fabricate
based on computer generated templates. Samples consisting of two compartments,
a reservoir of HO gel attached to a percolation model object which was
initially filled with DO, were examined with NMR (nuclear magnetic
resonance) microscopy for rendering proton spin density maps. The propagating
proton/deuteron inter-diffusion profiles were recorded and evaluated with
respect to anomalous diffusion parameters. The deviation of the concentration
profiles from those expected for unobstructed diffusion directly reflects the
anomaly of the propagator for diffusion on a percolation cluster. The fractal
dimension of the random walk, , evaluated from the diffusion measurements
on the one hand and the fractal dimension, , deduced from the spin density
map of the percolation object on the other permits one to experimentally
compare dynamical and static exponents. Approximate calculations of the
propagator are given on the basis of the fractional diffusion equation.
Furthermore, the ordinary diffusion equation was solved numerically for the
corresponding initial and boundary conditions for comparison. The anomalous
diffusion constant was evaluated and is compared to the Brownian case. Some ad
hoc correction of the propagator is shown to pay tribute to the finiteness of
the system. In this way, anomalous solutions of the fractional diffusion
equation could experimentally be verified for the first time.Comment: REVTeX, 12 figures in GIF forma
Characterization of Sleep Stages by Correlations of Heartbeat Increments
We study correlation properties of the magnitude and the sign of the
increments in the time intervals between successive heartbeats during light
sleep, deep sleep, and REM sleep using the detrended fluctuation analysis
method. We find short-range anticorrelations in the sign time series, which are
strong during deep sleep, weaker during light sleep and even weaker during REM
sleep. In contrast, we find long-range positive correlations in the magnitude
time series, which are strong during REM sleep and weaker during light sleep.
We observe uncorrelated behavior for the magnitude during deep sleep. Since the
magnitude series relates to the nonlinear properties of the original time
series, while the signs series relates to the linear properties, our findings
suggest that the nonlinear properties of the heartbeat dynamics are more
pronounced during REM sleep. Thus, the sign and the magnitude series provide
information which is useful in distinguishing between the sleep stages.Comment: 7 pages, 4 figures, revte