Impact of network activity on noise delayed spiking for a Hodgkin-Huxley model

In a Hodgkin-Huxley neuron model driven just above threshold, external noise can increase both jitter and latency of the first spike, an effect called “noise delayed decay” (NDD). This phenomenon is important when considering how neuronal information is represented, thus by the precise timing of spikes or by their rate. We examine how NDD can be affected by network activity by varying the model's membrane time constant, τ_m. We show that NDD is significant for small τ_m or high network activity, and decreases for large τ_m, or low network activity. Our results suggest that for inputs just above threshold, the activity of the network constrains the neuronal coding strategy due to, at least in part, the NDD effect.     

Stochastic epidemics and rumours on finite random networks

In this paper, we investigate the stochastic spread of epidemics and rumours on networks. We focus on the general stochastic (SIR) epidemic model and a recently proposed rumour model on networks in Nekovee et al. (2007) [3], and on networks with different random structures, taking into account the structure of the underlying network at the level of the degree–degree correlation function. Using embedded Markov chain techniques and ignoring density correlations between neighbouring nodes, we derive a set of equations for the final size of the epidemic/rumour on a homogeneous network that can be solved numerically, and compare the resulting distribution with the solution of the corresponding mean-field deterministic model. The final size distribution is found to switch from unimodal to bimodal form (indicating the possibility of substantial spread of the epidemic/rumour) at a threshold value that is higher than that for the deterministic model. However, the difference between the two thresholds decreases with the network size, n, following a n^−1/3 behaviour. We then compare results (obtained by Monte Carlo simulation) for the full stochastic model on a homogeneous network, including density correlations at neighbouring nodes, with those for the approximating stochastic model and show that the latter reproduces the exact simulation results with great accuracy. Finally, further Monte Carlo simulations of the full stochastic model are used to explore the effects on the final size distribution of network size and structure (using homogeneous networks, simple random graphs and the Barabasi–Albert scale-free networks).     

Stochastic resonance on Newman-Watts networks of Hodgkin-Huxley neurons with local periodic driving

We study the phenomenon of stochastic resonance on Newman-Watts small-world networks consisting of biophysically realistic Hodgkin-Huxley neurons with a tunable intensity of intrinsic noise via voltage-gated ion channels embedded in neuronal membranes. Importantly thereby, the subthreshold periodic driving is introduced to a single neuron of the network, thus acting as a pacemaker trying to impose its rhythm on the whole ensemble. We show that there exists an optimal intensity of intrinsic ion channel noise by which the outreach of the pacemaker extends optimally across the whole network. This stochastic resonance phenomenon can be further amplified via fine-tuning of the small-world network structure, and depends significantly also on the coupling strength among neurons and the driving frequency of the pacemaker. In particular, we demonstrate that the noise-induced transmission of weak localized rhythmic activity peaks when the pacemaker frequency matches the intrinsic frequency of subthreshold oscillations. The implications of our findings for weak signal detection and information propagation across neural networks are discussed.     

Semantic networks based on titles of scientific papers

In this paper we study the topological structure of semantic networks based on titles of papers published in scientific journals. It discusses its properties and presents some reflections on how the use of social and complex network models can contribute to the diffusion of knowledge. The proposed method presented here is applied to scientific journals where the titles of papers are in English or in Portuguese. We show that the topology of studied semantic networks are small-world and scale-free.     

The spreading of opposite opinions on online social networks with authoritative nodes

The study of opinion dynamics, such as spreading and controlling of rumors, has become an important issue on social networks. Numerous models have been devised to describe this process, including epidemic models and spin models, which mainly focus on how opinions spread and interact with each other, respectively. In this paper, we propose a model that combines the spreading stage and the interaction stage for opinions to illustrate the process of dispelling a rumor. Moreover, we set up authoritative nodes, which disseminate positive opinion to counterbalance the negative opinion prevailing on online social networking sites. With analysis of the relationship among positive opinion proportion, opinion strength and the density of authoritative nodes in networks with different topologies, we demonstrate that the positive opinion proportion grows with the density of authoritative nodes until the positive opinion prevails in the entire network. In particular, the relationship is linear in homogeneous topologies. Besides, it is also noteworthy that initial locations of the negative opinion source and authoritative nodes do not influence positive opinion proportion in homogeneous networks but have a significant impact on heterogeneous networks. The results are verified by numerical simulations and are helpful to understand the mechanism of two different opinions interacting with each other on online social networking sites.     

Synchronization speed of identical oscillators on community networks

Synchronizability of complex oscillators networks has attracted much research interest in recent years. In contrast, in this paper we investigate numerically the synchronization speed, rather than the synchronizability or synchronization stability, of identical oscillators on complex networks with communities. A new weighted community network model is employed here, in which the community strength could be tunable by one parameter δ. The results showed that the synchronization speed of identical oscillators on community networks could reach a maximal value when δ is around 0.1. We argue that this is induced by the competition between the community partition and the scale-free property of the networks. Moreover, we have given the corresponding analysis through the second least eigenvalue λ₂ of the Laplacian matrix of the network which supports the previous result that the synchronization speed is determined by the value of λ₂.     

Localization of diffusion sources in complex networks with sparse observations

Locating sources in a large network is of paramount importance to reduce the spreading of disruptive behavior. Based on the backward diffusion-based method and integer programming, we propose an efficient approach to locate sources in complex networks with limited observers. The results on model networks and empirical networks demonstrate that, for a certain fraction of observers, the accuracy of our method for source localization will improve as the increase of network size. Besides, compared with the previous method (the maximum–minimum method), the performance of our method is much better with a small fraction of observers, especially in heterogeneous networks. Furthermore, our method is more robust against noise environments and strategies of choosing observers.     

Modelling of discrete-time SIS models with awareness interactions on degree-uncorrelated networks

Many epidemic models ignored the impact of awareness on epidemics in a population, though it is not the case from the real viewpoints. In this paper, a discrete-time SIS model with awareness interactions on degree-uncorrelated networks is considered. We study three kinds of awareness, including local awareness and global awareness which are originated from the epidemic-dependent information, and individual awareness which is epidemic-independent and determined by the individual information. We demonstrate analytically that awareness of the epidemic-dependent information cannot change the epidemic threshold regardless of the global or local spreading information. In contrast, epidemic-independent awareness to individual information increases the epidemic threshold in finite scale-free networks, but cannot halt the absence of epidemic threshold in an infinite scale-free network. By numerical simulations, we find that local awareness has a stronger impact on epidemic prevalence than global awareness. Our findings explore the effects of various types of awareness on epidemic spreading and address their roles in the epidemic control.     

Exponential synchronization of complex networks with nonidentical time-delayed dynamical nodes

In this Letter, exponential synchronization of a complex network with nonidentical time-delayed dynamical nodes is considered. Two effective control schemes are proposed to drive the network to synchronize globally exponentially onto any smooth goal dynamics. By applying open-loop control to all nodes and adding some intermittent controllers to partial nodes, some simple criteria for exponential synchronization of such network are established. Meanwhile, a pinning scheme deciding which nodes need to be pinned and a simply approximate formula for estimating the least number of pinned nodes are also provided. By introducing impulsive effects to the open-loop controlled network, another synchronization scheme is developed for the network with nonidentical time-delayed dynamical nodes, and an estimate of the upper bound of impulsive intervals ensuring global exponential stability of the synchronization process is also given. Numerical simulations are presented finally to demonstrate the effectiveness of the theoretical results.     

Models and synchronization of time-delayed complex dynamical networks with multi-links based on adaptive control

In this Letter, time-delay has been introduced in to split the networks, upon which a model of complex dynamical networks with multi-links has been constructed. Moreover, based on Lyapunov stability theory and some hypotheses, we achieve synchronization between two complex networks with different structures by designing effective controllers. The validity of the results was proved through numerical simulations of this Letter.     

Synchronization of mobile chaotic agents on connected networks

This work studies the synchronization of a number of mobile agents on a substrate network. Each agent carries a chaotic map and randomly walks on a connected network. The collection of agents consists of another time-varying network derived from the substrate network. It is found that the synchronization conditions of this agent network depend on the average degree of the substrate network’s connectivity, the coupling strength between interacting agents, and the agent density in the network. Synchronization of the agent network on scale-free and ER networks is considered here, and it is found that the scale-free topology is more applicable to synchronize mobile chaotic agents. To get analytical insights, the star graph is taken and considered as a substrate network.     

On the efficiency of data representation on the modeling and characterization of complex networks

Specific choices about how to represent complex networks can have a substantial impact on the execution time required for the respective construction and analysis of those structures. In this work we report a comparison of the effects of representing complex networks statically by adjacency matrices or dynamically by adjacency lists. Three theoretical models of complex networks are considered: two types of Erd?s-Rényi as well as the Barabási-Albert model. We investigated the effect of the different representations with respect to the construction and measurement of several topological properties (i.e. degree, clustering coefficient, shortest path length, and betweenness centrality). We found that different forms of representation generally have a substantial effect on the execution time, with the sparse representation frequently resulting in remarkably superior performance.     

Study of a market model with conservative exchanges on complex networks

Many models of market dynamics make use of the idea of conservative wealth exchanges among economic agents. A few years ago an exchange model using extremal dynamics was developed and a very interesting result was obtained: a self-generated minimum wealth or poverty line. On the other hand, the wealth distribution exhibited an exponential shape as a function of the square of the wealth. These results have been obtained both considering exchanges between nearest neighbors or in a mean field scheme. In the present paper we study the effect of distributing the agents on a complex network. We have considered archetypical complex networks: Erdös–Rényi random networks and scale-free networks. The presence of a poverty line with finite wealth is preserved but spatial correlations are important, particularly between the degree of the node and the wealth. We present a detailed study of the correlations, as well as the changes in the Gini coefficient, that measures the inequality, as a function of the type and average degree of the considered networks.     

Synchronization in an array of linearly stochastically coupled networks with time delays

In this paper, the complete synchronization problem is investigated in an array of linearly stochastically coupled identical networks with time delays. The stochastic coupling term, which can reflect a more realistic dynamical behavior of coupled systems in practice, is introduced to model a coupled system, and the influence from the stochastic noises on the array of coupled delayed neural networks is studied thoroughly. Based on a simple adaptive feedback control scheme and some stochastic analysis techniques, several sufficient conditions are developed to guarantee the synchronization in an array of linearly stochastically coupled neural networks with time delays. Finally, an illustrate example with numerical simulations is exploited to show the effectiveness of the theoretical results.     

Research on the search ability of Brownian particles on networks with an adaptive mechanism

In this paper, we focus on the search ability of Brownian particles with an adaptive mechanism. In the adaptive mechanism, nodes are allowed to be able to change their own accepting probability according to their congestion states. Two searching-traffic models, the static one in which nodes have fixed accepting probability to the incoming particles and the adaptive one in which nodes have adaptive accepting probability to the incoming particles are presented for testing the adaptive mechanism. Instead of number of hops, we use the traveling time, which includes not only the number of hops for a particle to jump from the source node to the destination but also the time that the particle stays in the queues of nodes, to evaluate the search ability of Brownian particles. We apply two models to different networks. The experiment results show that the adaptive mechanism can decrease the network congestion and the traveling time of the first arriving particle. Furthermore, we investigate the influence of network topologies on the congestion of networks by addressing several main properties: degree distribution, average path length, and clustering coefficient. We show the reason why random topologies are more able to deal with congested traffic states than others. We also propose an absorption strategy to deal with the additional Brownian particles in networks. The experiment results on Barabási–Albert (BA) scale-free networks show that the absorption strategy can increase the probability of a successful search and decrease the average per-node particles overhead for our models.     

Impact of media coverage on epidemic spreading in complex networks

An SIS network model incorporating the influence of media coverage on transmission rate is formulated and analyzed. We calculate the basic reproduction number _R0$R_0$ by utilizing the local stability of the disease-free equilibrium. Our results show that the disease-free equilibrium is globally asymptotically stable and that the disease dies out if _R0$R_0$ is below 1; otherwise, the disease will persist and converge to a unique positive stationary state. This result may suggest effective control strategies to prevent disease through media coverage and education activities in finite-size scale-free networks. Numerical simulations are also performed to illustrate our results and to give more insights into the dynamical process.     

Attack structural vulnerability of power grids: A hybrid approach based on complex networks

Power grids have been studied as a typical example of real-world complex networks. Different from previous methods, this paper proposes a hybrid approach for structural vulnerability analysis of power transmission networks, in which a DC power flow model with hidden failures is embedded into the traditional error and attack tolerance methodology to form a new scheme for power grids vulnerability assessment and modeling. The new approach embodies some important characteristics of power transmission networks. Furthermore, the simulation on the standard IEEE 118 bus system demonstrates that a critical region might exist and when the power grid operates in the region, it is vulnerable to both random and intentional attacks. Finally, a brief theoretical analysis is presented to explain the new phenomena.     

Research on the relationships of the domestic mutual investment of China based on the cross-shareholding networks of the listed companies

Enterprises are the core power and the carriers to promote the country’s economy developing sustainably and rapidly; the listed enterprises are the outstanding companies which can represent the economic level at the places where the enterprises are located, so we establish the cross-shareholding networks of the listed companies between 2002 and 2009, and then analyze the mutual investment at company-level, province-level and region-level. We have researched the overall trend of economic development and the overall tendency of capital flow of China in the recent 8 years based on the cross-shareholding networks, the influence of a global economic crisis on the stock markets and the overall economics of China in 2008 and the recovery of the economy after the economic crisis. Moreover, we analyze the variations of the cross-shareholding networks and the influence of the state-owned large and medium enterprises listing frequently on Chinese stock markets. We divide the provinces of China into 3 main categories according to their industrial situations. Though the analysis, we find that the wealth gap between the different areas is not significantly reduced even though the government has carried out strategies such as the Development of the West Regions and the Rejuvenation of Old Industrial Bases in Northeastern China. We analyze the cumulative distribution function of the degree of the vertices and use large amounts of data to do empirical analysis. The methods used include the hierarchical cluster analysis, regression analysis, etc.     

Effects of delayed recovery and nonuniform transmission on the spreading of diseases in complex networks

We investigate the effects of delaying the time to recovery (delayed recovery) and of nonuniform transmission on the propagation of diseases on structured populations. Through a mean-field approximation and large-scale numerical simulations, we find that postponing the transition from the infectious to the recovered states can largely reduce the epidemic threshold, therefore promoting the outbreak of epidemics. On the other hand, if we consider nonuniform transmission among individuals, the epidemic threshold increases, thus inhibiting the spreading process. When both mechanisms are at work, the latter might prevail, hence resulting in an increase of the epidemic threshold with respect to the standard case, in which both ingredients are absent. Our findings are of interest for a better understanding of how diseases propagate on structured populations and to a further design of efficient immunization strategies.