Wen-Jie Bai

Epidemic spreading on heterogeneous networks with identical infectivity

In this Letter, we propose a modified susceptible-infected-recovered (SIR) model, in which each node is assigned with an identical capability of active contacts, A, at each time step. In contrast to the previous studies, we find that on scale-free networks, the density of the recovered individuals in the present model shows a threshold behavior. We obtain the analytical results using the mean-field theory and find that the threshold value equals 1/A, indicating that the threshold value is independent of the topology of the underlying network. The simulations agree well with the analytic results. Furthermore, we study the time behavior of the epidemic propagation and find a hierarchical dynamics with three plateaus. Once the highly connected hubs are reached, the infection pervades almost the whole network in a progressive cascade across smaller degree classes. Then, after the previously infected hubs are recovered, the disease can only propagate to the class of smallest degree till the infected individuals are all recovered. The present results could be of practical importance in the setup of dynamic control strategies.

Relations between average distance, heterogeneity and network synchronizability

By using the random interchanging algorithm, we investigate the relations between average distance, standard deviation of degree distribution and synchronizability of complex networks. We find that both increasing the average distance and magnifying the degree deviation will make the network synchronize harder. Only the combination of short average distance and small standard deviation of degree distribution ensures strong synchronizability. Some previous studies assert that the maximal betweenness is the right quantity to estimate network synchronizability: the larger the maximal betweenness, the poorer the network synchronizability. Here we address an interesting case, which strongly suggests that the single quantity, maximal betweenness, may not give a comprehensive description of network synchronizability.

Immunization of susceptible-infected model on scale-free networks

In this paper, we investigate two major immunization strategies, random immunization and targeted immunization, of the susceptible–infected (SI) model on the Barabasi–Albert (BA) networks. For the heterogeneous structure, the random strategy is quite ineffective if the vaccinated proportion is small, while the targeted one which prefers to vaccinate the individuals with the largest degree can sharply depress the epidemic spreading even only a tiny fraction of population are vaccinated. The analytical solution is also obtained, which can capture the trend of velocity change vs. the amount of vaccinated population.

Continuous extremal optimization for Lennard-Jones clusters

We explore a general-purpose heuristic algorithm for finding high-quality solutions to continuous optimization problems. The method, called continuous extremal optimization (CEO), can be considered as an extension of extremal optimization and consists of two components, one which is responsible for global searching and the other which is responsible for local searching. The CEOs performance proves competitive with some more elaborate stochastic optimization procedures such as simulated annealing, genetic algorithms, and so on. We demonstrate it on a well-known continuous optimization problem: the Lennard-Jones cluster optimization problem.

Growing scale-free small-world networks with tunable assortative coefficient

In this paper, we propose a simple rule that generates scale-free small-world networks with tunable assortative coefficient. These networks are constructed by two-stage adding process for each new node. The model can reproduce scale-free degree distributions and small-world effect. The simulation results are consistent with the theoretical predictions approximately. Interestingly, we obtain the nontrivial clustering coefficient C and tunable degree assortativity r by adjusting the parameter: the preferential exponent β. The model can unify the characterization of both assortative and disassortative networks.

Geographical networks evolving with an optimal policy

In this article we propose a growing network model based on an optimal policy involving both topological and geographical measures. In this model, at each time step, a node, having randomly assigned coordinates in a 1x1 square, is added and connected to a previously existing node i, which minimizes the quantity ri2/kialpha, where ri is the geographical distance, ki the degree, and alpha a free parameter. The degree distribution obeys a power-law form when alpha=1, and an exponential form when alpha=0. When alpha is in the interval (0, 1), the network exhibits a stretched exponential distribution. We prove that the average topological distance increases in a logarithmic scale of the network size, indicating the existence of the small-world property. Furthermore, we obtain the geographical edge length distribution, the total geographical length of all edges, and the average geographical distance of the whole network. Interestingly, we found that the total edge length will sharply increase when alpha exceeds the critical value alphac=1, and the average geographical distance has an upper bound independent of the network size. All the results are obtained analytically with some reasonable approximations, which are well verified by simulations.

Electric Power Grids and Blackouts in Perspective of Complex Networks

In this paper, a brief review of blackouts on electric power grids is given. Firstly, we sum up the holistic topological characters of electric power grids, including their small- world effects, exponential degree distributions, power-law load distributions, and robustness intervenient between Possian and scale-free networks. And then, we investigate the self-organized criticality in electric transmission dynamics, and suggest a new measure, the time length of power shortage, to estimate the size of blackouts. The empirical results strongly support the recent theoretical hypothesis of the existence of self-organized critical behaviors. Finally, in perspective of complexity science, the mainstream theoretical and engineering models aiming at traffic and cascading dynamics on electric power grids are briefly reviewed.

INTERPLAY BETWEEN HIV/AIDS EPIDEMICS AND DEMOGRAPHIC STRUCTURES BASED ON SEXUAL CONTACT NETWORKS

In this article, we propose a network spreading model for HIV epidemics, wherein each individual is represented by a node of the transmission network and the edges are the connections between individuals along which the infection may spread. The sexual activity of each individual, measured by its degree, is not homogeneous but obeys a power-law distribution. Due to the heterogeneity of activity, the infection can persistently exist at a very low prevalence, which has been observed in the real data but cannot be illuminated by previous models with homogeneous mixing hypothesis. The model displays a clear picture of hierarchical spread: In the early stage the infection is adhered to these high-risk persons, and then, diffuses toward low-risk population. Furthermore, we find that to reduce the risky behaviors is much more effective in the fight against HIV/AIDS rather than the antiretroviral drug therapies. The prediction results show that the development of epidemics can be roughly categorized into three patterns for different countries, and the pattern of a given country is mainly determined by the average sex-activity and transmission probability per sexual partner. In most cases, the effect of HIV epidemics on demographic structure is very small. However, for some extremely countries, like Botswana, the number of sex-active people can be depressed to nearly a half by AIDS.

Boolean game on scale-free networks

Inspired by the local minority game, we propose a network Boolean game and investigate its dynamical properties on scale-free networks. The system can self-organize to a stable state with better performance than the random choice game, although only the local information is available to each agent. By introducing the heterogeneity of local interactions, we find that the system will achieve the best performance when each agents interaction frequency is linearly correlated with its information capacity. Generally, the agents with more information gain more than those with less information, while in the optimal case, each agent almost has the same average profit. In addition, we investigate the role of irrational factor and find an interesting symmetrical behavior.