116 research outputs found
Competition between surface relaxation and ballistic deposition models in scale free networks
In this paper we study the scaling behavior of the fluctuations in the steady
state with the system size for a surface growth process given by the
competition between the surface relaxation (SRM) and the Ballistic Deposition
(BD) models on degree uncorrelated Scale Free networks (SF), characterized by a
degree distribution , where is the degree of a node.
It is known that the fluctuations of the SRM model above the critical dimension
() scales logarithmically with on euclidean lattices. However,
Pastore y Piontti {\it et. al.} [A. L. Pastore y Piontti {\it et. al.}, Phys.
Rev. E {\bf 76}, 046117 (2007)] found that the fluctuations of the SRM model in
SF networks scale logarithmically with for and as a constant
for . In this letter we found that for a pure ballistic
deposition model on SF networks scales as a power law with an exponent
that depends on . On the other hand when both processes are in
competition, we find that there is a continuous crossover between a SRM
behavior and a power law behavior due to the BD model that depends on the
occurrence probability of each process and the system size. Interestingly, we
find that a relaxation process contaminated by any small contribution of
ballistic deposition will behave, for increasing system sizes, as a pure
ballistic one. Our findings could be relevant when surface relaxation
mechanisms are used to synchronize processes that evolve on top of complex
networks.Comment: 8 pages, 6 figure
Fluctuations of a surface relaxation model in interacting scale free networks
Isolated complex networks have been studied deeply in the last decades due to
the fact that many real systems can be modeled using these types of structures.
However, it is well known that the behavior of a system not only depends on
itself, but usually also depends on the dynamics of other structures. For this
reason, interacting complex networks and the processes developed on them have
been the focus of study of many researches in the last years. One of the most
studied subjects in this type of structures is the Synchronization problem,
which is important in a wide variety of processes in real systems. In this
manuscript we study the synchronization of two interacting scale-free networks,
in which each node has dependency links with different nodes in the other
network. We map the synchronization problem with an interface growth, by
studying the fluctuations in the steady state of a scalar field defined in both
networks.
We find that as slightly increases from , there is a really
significant decreasing in the fluctuations of the system. However, this
considerable improvement takes place mainly for small values of , when the
interaction between networks becomes stronger there is only a slight change in
the fluctuations. We characterize how the dispersion of the scalar field
depends on the internal degree, and we show that a combination between the
decreasing of this dispersion and the integer nature of our growth model are
the responsible for the behavior of the fluctuations with .Comment: 11 pages, 4 figures and 1 tabl
Epidemic model with isolation in multilayer networks
The Susceptible-Infected-Recovered (SIR) model has successfully mimicked the propagation of such airborne diseases as influenza A (H1N1). Although the SIR model has recently been studied in a multilayer networks configuration, in almost all the research the isolation of infected individuals is disregarded. Hence we focus our study in an epidemic model in a two-layer network and we use an isolation parameter w to measure the effect of quarantining infected individuals from both layers during an isolation period tw. We call this process the Susceptible-Infected-Isolated-Recovered (SIIR) model. Using the framework of link percolation we find that isolation increases the critical epidemic threshold of the disease because the time in which infection can spread is reduced. In this scenario we find that this threshold increases with w and tw. When the isolation period is maximum there is a critical threshold for w above which the disease never becomes an epidemic. We simulate the process and find an excellent agreement with the theoretical results.We thank the NSF (grants CMMI 1125290 and CHE-1213217) and the Keck Foundation for financial support. LGAZ and LAB wish to thank to UNMdP and FONCyT (Pict 0429/2013) for financial support. (CMMI 1125290 - NSF; CHE-1213217 - NSF; Keck Foundation; UNMdP; Pict 0429/2013 - FONCyT)Published versio
Promoting information spreading by using contact memory
Promoting information spreading is a booming research topic in network
science community. However, the exiting studies about promoting information
spreading seldom took into account the human memory, which plays an important
role in the spreading dynamics. In this paper we propose a non-Markovian
information spreading model on complex networks, in which every informed node
contacts a neighbor by using the memory of neighbor's accumulated contact
numbers in the past. We systematically study the information spreading dynamics
on uncorrelated configuration networks and a group of real-world networks,
and find an effective contact strategy of promoting information spreading,
i.e., the informed nodes preferentially contact neighbors with small number of
accumulated contacts. According to the effective contact strategy, the high
degree nodes are more likely to be chosen as the contacted neighbors in the
early stage of the spreading, while in the late stage of the dynamics, the
nodes with small degrees are preferentially contacted. We also propose a
mean-field theory to describe our model, which qualitatively agrees well with
the stochastic simulations on both artificial and real-world networks.Comment: 6 pages, 6 figure
- …