Complex brain networks: From topological communities to clustered dynamics

Recent research has revealed a rich and complicated network topology in the cortical connectivity of mammalian brains. A challenging task is to understand the implications of such network structures on the functional organisation of the brain activities. We investigate synchronisation dynamics on the corticocortical network of the cat by modelling each node of the network (cortical area) with a subnetwork of interacting excitable neurons. We find that this network of networks displays clustered synchronisation behaviour and the dynamical clusters closely coincide with the topological community structures observed in the anatomical network. The correlation between the firing rate of the areas and the areal intensity is additionally examined. Our results provide insights into the relationship between the global organisation and the functional specialisation of the brain cortex.      

A model for social networks

Social networks are organized into communities with dense internal connections, giving rise to high values of the clustering coefficient. In addition, these networks have been observed to be assortative, i.e., highly connected vertices tend to connect to other highly connected vertices, and have broad degree distributions. We present a model for an undirected growing network which reproduces these characteristics, with the aim of producing efficiently very large networks to be used as platforms for studying sociodynamic phenomena. The communities arise from a mixture of random attachment and implicit preferential attachment. The structural properties of the model are studied analytically and numerically, using the k-clique method for quantifying the communities.     

Multi-component static model for social networks

The static model was introduced to generate a scale-free network. In the model, N number of vertices are present from the beginning. Each vertex has its own weight, representing how much the vertex is influential in a system. The static model, however, is not relevant, when a complex network is composed of many modules such as communities in social networks. An individual may belong to more than one community and has distinct weights for each community. Thus, we generalize the static model by assigning a q-component weight on each vertex. We first choose a component among the q components at random and a pair of vertices is linked with a color according to their weights of the component as in the static model. A (1-f) fraction of the entire edges is connected following this way. The remaining fraction f is added with (q + 1)-th color as in the static model but using the maximum weights among the q components each individual has. The social activity with such maximum weights is an essential ingredient to enhance the assortativity coefficient as large as the ones of real social networks.Received: 27 October 2003, Published online: 17 February 2004PACS: 89.65.-s Social and economic systems - 89.75.Hc Networks and genealogical trees - 89.75.Da Systems obeying scaling laws     

A spatial model for social networks

We study spatial embeddings of random graphs in which nodes are randomly distributed in geographical space. We let the edge probability between any two nodes to be dependent on the spatial distance between them and demonstrate that this model captures many generic properties of social networks, including the “small-world” properties, skewed degree distribution, and most distinctively the existence of community structures.     

System of mobile agents to model social networks

We propose a model of mobile agents to construct social networks, based on a system of moving particles by keeping track of the collisions during their permanence in the system. We reproduce not only the degree distribution, clustering coefficient, and shortest path length of a large database of empirical friendship networks recently collected, but also some features related with their community structure. The model is completely characterized by the collision rate, and above a critical collision rate we find the emergence of a giant cluster in the universality class of two-dimensional percolation. Moreover, we propose possible schemes to reproduce other networks of particular social contacts, namely, sexual contacts.     

Social and place-focused communities in location-based online social networks

Thanks to widely available, cheap Internet access and the ubiquity of smartphones,millions of people around the world now use online location-based social networkingservices. Understanding the structural properties of these systems and their dependenceupon users’ habits and mobility has many potential applications, including resourcerecommendation and link prediction. Here, we construct and characterise social andplace-focused graphs by using longitudinal information about declared social relationshipsand about users’ visits to physical places collected from a popular online location-basedsocial service. We show that although the social and place-focused graphs are constructedfrom the same data set, they have quite different structural properties. We find that thesocial and location-focused graphs have different global and meso-scale structure, and inparticular that social and place-focused communities have negligible overlap.Consequently, group inference based on community detection performed on the social graphalone fails to isolate place-focused groups, even though these do exist in the network. Bystudying the evolution of tie structure within communities, we show that the time periodover which location data are aggregated has a substantial impact on the stability ofplace-focused communities, and that information about place-based groups may be moreuseful for user-centric applications than that obtained from the analysis of socialcommunities alone.     

An evolutionary model of social networks

Social networks in communities, markets, and societies self-organise through the interactions of many individuals. In this paper we use a well-known mechanism of social interactions — the balance of sentiment in triadic relations — to describe the development of social networks. Our model contrasts with many existing network models, in that people not only establish but also break up relations whilst the network evolves. The procedure generates several interesting network features such as a variety of degree distributions and degree correlations. The resulting network converges under certain conditions to a steady critical state where temporal disruptions in triangles follow a power-law distribution.     

A last updating evolution model for online social networks

As information technology has advanced, people are turning to electronic media more frequently for communication, and social relationships are increasingly found on online channels. However, there is very limited knowledge about the actual evolution of the online social networks. In this paper, we propose and study a novel evolution network model with the new concept of “last updating time”, which exists in many real-life online social networks. The last updating evolution network model can maintain the robustness of scale-free networks and can improve the network reliance against intentional attacks. What is more, we also found that it has the “small-world effect”, which is the inherent property of most social networks. Simulation experiment based on this model show that the results and the real-life data are consistent, which means that our model is valid.     

From semiconductors to superconductors: a simple model for pseudogaps

We consider a two-dimensional semiconductor with a local attraction among the carriers. We study the ground state of this system as a function of the semiconductor gap. We find a direct transition from a superconducting to an insulating phase for no doping at a critical value, the single particle excitations being always gapped. For finite doping we find a smooth crossover. We calculate the critical temperature due to both the particle excitations and the Berezinkii-Kosterlitz-Thouless transition. Received 8 December 1998     

Stochastic synchronization for time-varying complex dynamical networks

This paper studies the stochastic synchronization problem for time-varying complex dynamical networks. This model is totally different from some existing network models. Based on the Lyapunov stability theory, inequality techniques, and the properties of the Weiner process, some controllers and adaptive laws are designed to ensure achieving stochastic synchronization of a complex dynamical network model. A sufficient synchronization condition is given to ensure that the proposed network model is mean-square stable. Theoretical analysis and numerical simulation fully verify the main results.     

SIHR rumor spreading model in social networks

There are significant differences between rumor spreading and epidemic spreading in social networks, especially with consideration of the mutual effect of forgetting and remembering mechanisms. In this paper, a new rumor spreading model, Susceptible-Infected-Hibernator-Removed (SIHR) model, is developed. The model extends the classical Susceptible-Infected-Removed (SIR) rumor spreading model by adding a direct link from ignorants to stiflers and a new kind of people-Hibernators. We derive mean-field equations that describe the dynamics of the SIHR model in social networks. Then a steady-state analysis is conducted to investigate the final size of the rumor spreading under various spreading rate, stifling rate, forgetting rate, and average degree of the network. We discuss the spreading threshold and find the relationship between the final size of the rumor and two probabilities. Also Runge-Kutta method is used for numerical simulation which shows that the direct link from the ignorants to the stiflers advances the rumor terminal time and reduces the maximum rumor influence. Moreover, the forgetting and remembering mechanisms of hibernators postpone the rumor terminal time and reduce the maximum rumor influence.     

PageRank model of opinion formation on social networks

We propose the PageRank model of opinion formation and investigate its rich properties on real directed networks of the Universities of Cambridge and Oxford, LiveJournal, and Twitter. In this model, the opinion formation of linked electors is weighted with their PageRank probability. Such a probability is used by the Google search engine for ranking of web pages. We find that the society elite, corresponding to the top PageRank nodes, can impose its opinion on a significant fraction of the society. However, for a homogeneous distribution of two opinions, there exists a bistability range of opinions which depends on a conformist parameter characterizing the opinion formation. We find that the LiveJournal and Twitter networks have a stronger tendency to a totalitarian opinion formation than the university networks. We also analyze the Sznajd model generalized for scale-free networks with the weighted PageRank vote of electors.     

Periodically intermittent controlling complex dynamical networks with time-varying delays to a desired orbit

This Letter investigates the problem of synchronization in complex dynamical networks with time-varying delays. A periodically intermittent control scheme is proposed to achieve global exponential synchronization for a general complex network with both time-varying delays dynamical nodes and time-varying delays coupling. It is shown that the sates of the general complex network with both time-varying delays dynamical nodes and time-varying delays coupling can globally exponentially synchronize with a desired orbit under the designed intermittent controllers. Moreover, a typical network consisting of the time-delayed Chua oscillator with nearest-neighbor unidirectional time-varying delays coupling is given as an example to verify the effectiveness of the proposed control methodology.     

Explosive synchronization: From synthetic to real-world networks

Synchronization is a widespread phenomenon in both synthetic and real-world networks. This collective behavior of simple and complex systems has been attracting much research during the last decades. Two different routes to synchrony are defined in networks; first-order, characterized as explosive, and second-order, characterized as continuous transition. Although pioneer researches explained that the transition type is a generic feature in the networks, recent studies proposed some frameworks in which different phase and even chaotic oscillators exhibit explosive synchronization. The relationship between the structural properties of the network and the dynamical features of the oscillators is mainly proclaimed because some of these frameworks show abrupt transitions. Despite different theoretical analyses about the appearance of the first-order transition, studies are limited to the mean-field theory, which cannot be generalized to all networks. There are different real-world and man-made networks whose properties can be characterized in terms of explosive synchronization, e.g., the transition from unconsciousness to wakefulness in the brain and spontaneous synchronization of power-grid networks. In this review article, explosive synchronization is discussed from two main aspects. First, pioneer articles are categorized from the dynamical-structural framework point of view. Then, articles that considered different oscillators in the explosive synchronization frameworks are studied. In this article, the main focus is on the explosive synchronization in networks with chaotic and neuronal oscillators. Also, efforts have been made to consider the recent articles which proposed new frameworks of explosive synchronization.     

Self-contained algorithms to detect communities in networks

The investigation of community structures in networks is an important issue in many domains and disciplines. In this paper we present a new class of local and fast algorithms which incorporate a quantitative definition of community. In this way the algorithms for the identification of the community structure become fully self-contained and one does not need additional non-topological information in order to evaluate the accuracy of the results. The new algorithms are tested on artificial and real-world graphs. In particular we show how the new algorithms apply to a network of scientific collaborations both in the unweighted and in the weighted version. Moreover we discuss the applicability of these algorithms to other non-social networks and we present preliminary results about the detection of community structures in networks of interacting proteins.Received: 7 November 2003, Published online: 14 May 2004PACS: 89.75.Hc Networks and genealogical trees - 87.23.Ge Dynamics of social systems - 87.90. + y Other topics in biological and medical physics     

Stability conditions for Cohen-Grossberg neural networks with time-varying delays

Global asymptotic stability for Cohen-Grossberg neural networks (CGNNs) with time-varying delays is investigated. Criteria are proposed to guarantee the stability and uniqueness of equilibrium point of CGNNs via LMI approach. A numerical example is illustrated to show the effectiveness of our results.     

Improved stability criteria for neural networks with time-varying delay

The problem of the stability analysis of neural networks with time-varying delay is considered in this Letter. By constructing a new augmented Lyapunov functional which contains a triple-integral term, an improved delay-dependent stability criterion is derived in terms of LMI using the free-weighting matrices method. The rate-range of the delay is also considered in the derivation of the criterion. Numerical examples are presented to illustrate the effectiveness of the proposed method.     

Exponential convergence for a class of delayed cellular neural networks with time-varying coefficients

In this Letter, we consider a class of delayed cellular neural networks with time-varying coefficients. By applying Lyapunov functional method and differential inequality techniques, we establish new results to ensure that all solutions of the networks converge exponentially to zero point.     

Using feature vectors to detect frog calls in wireless sensor networks

A method for detecting vocalization of giant barred frogs (Mixophyes iteratus) in noisy audio is proposed. Audio recordings from remote wireless sensor nodes were segmented into individual sounds and from each sound a small set of features was extracted. Feature vectors were compared to those of example calls using a Euclidean distance formula as a detection system. The system achieved a sensitivity of 0.85 with specificity of 0.92 when distinguishing M. iteratus calls from other species' calls and sensitivity of 0.88 with specificity 0.82 against background noise.