755 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
Robustness of interdependent networks under targeted attack
When an initial failure of nodes occurs in interdependent networks, a cascade
of failure between the networks occurs. Earlier studies focused on random
initial failures. Here we study the robustness of interdependent networks under
targeted attack on high or low degree nodes. We introduce a general technique
and show that the {\it targeted-attack} problem in interdependent networks can
be mapped to the {\it random-attack} problem in a transformed pair of
interdependent networks. We find that when the highly connected nodes are
protected and have lower probability to fail, in contrast to single scale free
(SF) networks where the percolation threshold , coupled SF networks are
significantly more vulnerable with significantly larger than zero. The
result implies that interdependent networks are difficult to defend by
strategies such as protecting the high degree nodes that have been found useful
to significantly improve robustness of single networks.Comment: 11 pages, 2 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
The robustness of interdependent clustered networks
It was recently found that cascading failures can cause the abrupt breakdown
of a system of interdependent networks. Using the percolation method developed
for single clustered networks by Newman [Phys. Rev. Lett. {\bf 103}, 058701
(2009)], we develop an analytical method for studying how clustering within the
networks of a system of interdependent networks affects the system's
robustness. We find that clustering significantly increases the vulnerability
of the system, which is represented by the increased value of the percolation
threshold in interdependent networks.Comment: 6 pages, 6 figure
Financial factor influence on scaling and memory of trading volume in stock market
We study the daily trading volume volatility of 17,197 stocks in the U.S.
stock markets during the period 1989--2008 and analyze the time return
intervals between volume volatilities above a given threshold q. For
different thresholds q, the probability density function P_q(\tau) scales with
mean interval as P_q(\tau)=^{-1}f(\tau/) and the tails of
the scaling function can be well approximated by a power-law f(x)~x^{-\gamma}.
We also study the relation between the form of the distribution function
P_q(\tau) and several financial factors: stock lifetime, market capitalization,
volume, and trading value. We find a systematic tendency of P_q(\tau)
associated with these factors, suggesting a multi-scaling feature in the volume
return intervals. We analyze the conditional probability P_q(\tau|\tau_0) for
following a certain interval \tau_0, and find that P_q(\tau|\tau_0)
depends on \tau_0 such that immediately following a short/long return interval
a second short/long return interval tends to occur. We also find indications
that there is a long-term correlation in the daily volume volatility. We
compare our results to those found earlier for price volatility.Comment: 17 pages, 6 figure
Diffusion and spectral dimension on Eden tree
We calculate the eigenspectrum of random walks on the Eden tree in two and
three dimensions. From this, we calculate the spectral dimension and the
walk dimension and test the scaling relation (
for an Eden tree). Finite-size induced crossovers are observed, whereby the
system crosses over from a short-time regime where this relation is violated
(particularly in two dimensions) to a long-time regime where the behavior
appears to be complicated and dependent on dimension even qualitatively.Comment: 11 pages, Plain TeX with J-Phys.sty style, HLRZ 93/9
Absence of kinetic effects in reaction-diffusion processes in scale-free networks
We show that the chemical reactions of the model systems of A+A->0 and A+B->0
when performed on scale-free networks exhibit drastically different behavior as
compared to the same reactions in normal spaces. The exponents characterizing
the density evolution as a function of time are considerably higher than 1,
implying that both reactions occur at a much faster rate. This is due to the
fact that the discerning effects of the generation of a depletion zone (A+A)
and the segregation of the reactants (A+B) do not occur at all as in normal
spaces. Instead we observe the formation of clusters of A (A+A reaction) and of
mixed A and B (A+B reaction) around the hubs of the network. Only at the limit
of very sparse networks is the usual behavior recovered.Comment: 4 pages, 4 figures, to be published in Physical Review Letter
Diffusion and Trapping on a one-dimensional lattice
The properties of a particle diffusing on a one-dimensional lattice where at
each site a random barrier and a random trap act simultaneously on the particle
are investigated by numerical and analytical techniques. The combined effect of
disorder and traps yields a decreasing survival probability with broad
distribution (log-normal). Exact enumerations, effective-medium approximation
and spectral analysis are employed. This one-dimensional model shows rather
rich behaviours which were previously believed to exist only in higher
dimensionality. The possibility of a trapping-dominated super universal class
is suggested.Comment: 20 pages, Revtex 3.0, 13 figures in compressed format using uufiles
command, to appear in Phys. Rev. E, for an hard copy or problems e-mail to:
[email protected]
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