3,058,476 research outputs found
General behaviour of Bianchi VI_0 solutions with an exponential-potential scalar field
The solutions to the Einstein-Klein-Gordon equations without a cosmological
constant are investigated for an exponential potential in a Bianchi VI_0
metric. There exists a two-parameter family of solutions which have a power-law
inflationary behaviour when the exponent of the potential, k, satisfies k^2<2.
In addition, there exists a two-parameter family of singular solutions for all
k^2 values. A simple anisotropic exact solution is found to be stable when
2<k^2.Comment: 10 pages, no figures. To be published in General Relativity and
Gravitatio
Flexible construction of hierarchical scale-free networks with general exponent
Extensive studies have been done to understand the principles behind
architectures of real networks. Recently, evidences for hierarchical
organization in many real networks have also been reported. Here, we present a
new hierarchical model which reproduces the main experimental properties
observed in real networks: scale-free of degree distribution (frequency
of the nodes that are connected to other nodes decays as a power-law
) and power-law scaling of the clustering coefficient
. The major novelties of our model can be summarized as
follows: {\it (a)} The model generates networks with scale-free distribution
for the degree of nodes with general exponent , and arbitrarily
close to any specified value, being able to reproduce most of the observed
hierarchical scale-free topologies. In contrast, previous models can not obtain
values of . {\it (b)} Our model has structural flexibility
because {\it (i)} it can incorporate various types of basic building blocks
(e.g., triangles, tetrahedrons and, in general, fully connected clusters of
nodes) and {\it (ii)} it allows a large variety of configurations (i.e., the
model can use more than copies of basic blocks of nodes). The
structural features of our proposed model might lead to a better understanding
of architectures of biological and non-biological networks.Comment: RevTeX, 5 pages, 4 figure
Random sampling vs. exact enumeration of attractors in random Boolean networks
We clarify the effect different sampling methods and weighting schemes have
on the statistics of attractors in ensembles of random Boolean networks (RBNs).
We directly measure cycle lengths of attractors and sizes of basins of
attraction in RBNs using exact enumeration of the state space. In general, the
distribution of attractor lengths differs markedly from that obtained by
randomly choosing an initial state and following the dynamics to reach an
attractor. Our results indicate that the former distribution decays as a
power-law with exponent 1 for all connectivities in the infinite system
size limit. In contrast, the latter distribution decays as a power law only for
K=2. This is because the mean basin size grows linearly with the attractor
cycle length for , and is statistically independent of the cycle length
for K=2. We also find that the histograms of basin sizes are strongly peaked at
integer multiples of powers of two for
What determines the spreading of a wave packet?
The multifractal dimensions D2^mu and D2^psi of the energy spectrum and
eigenfunctions, resp., are shown to determine the asymptotic scaling of the
width of a spreading wave packet. For systems where the shape of the wave
packet is preserved the k-th moment increases as t^(k*beta) with
beta=D2^mu/D2^psi, while in general t^(k*beta) is an optimal lower bound.
Furthermore, we show that in d dimensions asymptotically in time the center of
any wave packet decreases spatially as a power law with exponent D_2^psi - d
and present numerical support for these results.Comment: Physical Review Letters to appear, 4 pages postscript with figure
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