389 research outputs found
Effect of network topology on the ordering dynamics of voter models
We introduce and study the reverse voter model, a dynamics for spin variables
similar to the well-known voter dynamics. The difference is in the way
neighbors influence each other: once a node is selected and one among its
neighbors chosen, the neighbor is made equal to the selected node, while in the
usual voter dynamics the update goes in the opposite direction. The reverse
voter dynamics is studied analytically, showing that on networks with degree
distribution decaying as k^{-nu}, the time to reach consensus is linear in the
system size N for all nu>2. The consensus time for link-update voter dynamics
is computed as well. We verify the results numerically on a class of
uncorrelated scale-free graphs.Comment: 7 pages, 4 figures; to appear in the Proceedings of the 8th Granada
Seminar - Computational and Statistical Physic
Fast growth at low temperature in vacancy-mediated phase-separation
We study the phase-separation dynamics of a two-dimensional Ising model where
A and B particles can only exchange position with a vacancy. In a wide range of
temperatures the kinetics is dominated, during a long preasymptotic regime, by
diffusion processes of particles along domain interfaces. The dynamical
exponent z associated to this mechanism differs from the one usually expected
for Kawasaki dynamics and is shown to assume different values depending on
temperature and relative AB concentration. At low temperatures, in particular,
domains grow as t^{1/2}, for equal AB volume fractions.Comment: LaTeX, 5 pages, 4 figures, to appear on Phys. Rev.
Uncertainty Reduction for Stochastic Processes on Complex Networks
Many real-world systems are characterized by stochastic dynamical rules where
a complex network of interactions among individual elements probabilistically
determines their state. Even with full knowledge of the network structure and
of the stochastic rules, the ability to predict system configurations is
generally characterized by a large uncertainty. Selecting a fraction of the
nodes and observing their state may help to reduce the uncertainty about the
unobserved nodes. However, choosing these points of observation in an optimal
way is a highly nontrivial task, depending on the nature of the stochastic
process and on the structure of the underlying interaction pattern. In this
paper, we introduce a computationally efficient algorithm to determine
quasioptimal solutions to the problem. The method leverages network sparsity to
reduce computational complexity from exponential to almost quadratic, thus
allowing the straightforward application of the method to mid-to-large-size
systems. Although the method is exact only for equilibrium stochastic processes
defined on trees, it turns out to be effective also for out-of-equilibrium
processes on sparse loopy networks.Comment: 5 pages, 2 figures + Supplemental Material. A python implementation
of the algorithm is available at
https://github.com/filrad/Maximum-Entropy-Samplin
Rapid decay in the relative efficiency of quarantine to halt epidemics in networks
Several recent studies have tackled the issue of optimal network immunization
by providing efficient criteria to identify key nodes to be removed in order to
break apart a network, thus preventing the occurrence of extensive epidemic
outbreaks. Yet, although the efficiency of those criteria has been demonstrated
also in empirical networks, preventive immunization is rarely applied to
real-world scenarios, where the usual approach is the a posteriori attempt to
contain epidemic outbreaks using quarantine measures. Here we compare the
efficiency of prevention with that of quarantine in terms of the tradeoff
between the number of removed and saved nodes on both synthetic and empirical
topologies. We show how, consistent with common sense, but contrary to common
practice, in many cases preventing is better than curing: depending on network
structure, rescuing an infected network by quarantine could become inefficient
soon after the first infection.Comment: 10 pages, 7 figure
- …