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