Uniform synchronous criticality of diversely random complex networks

We investigate collective synchronous behaviors in random complex networks of limit-cycle oscillators with the non-identical asymmetric coupling scheme, and find a uniform coupling criticality of collective synchronization which is independent of complexity of network topologies. Numerically simulations on categories of random complex networks have verified this conclusion.Comment: 8 pages, 4 figure

Topological fractal networks introduced by mixed degree distribution

Several fundamental properties of real complex networks, such as the small-world effect, the scale-free degree distribution, and recently discovered topological fractal structure, have presented the possibility of a unique growth mechanism and allow for uncovering universal origins of collective behaviors. However, highly clustered scale-free network, with power-law degree distribution, or small-world network models, with exponential degree distribution, are not self-similarity. We investigate networks growth mechanism of the branching-deactivated geographical attachment preference that learned from certain empirical evidence of social behaviors. It yields high clustering and spectrums of degree distribution ranging from algebraic to exponential, average shortest path length ranging from linear to logarithmic. We observe that the present networks fit well with small-world graphs and scale-free networks in both limit cases (exponential and algebraic degree distribution respectively), obviously lacking self-similar property under a length-scale transformation. Interestingly, we find perfect topological fractal structure emerges by a mixture of both algebraic and exponential degree distributions in a wide range of parameter values. The results present a reliable connection among small-world graphs, scale-free networks and topological fractal networks, and promise a natural way to investigate universal origins of collective behaviors.Comment: 14 pages, 6 figure

Empirical studies on the network of social groups: the case of Tencent QQ

Participation in social groups are important but the collective behaviors of human as a group are difficult to analyze due to the difficulties to quantify ordinary social relation, group membership, and to collect a comprehensive dataset. Such difficulties can be circumvented by analyzing online social networks. In this paper, we analyze a comprehensive dataset obtained from Tencent QQ, an instant messenger with the highest market share in China. Specifically, we analyze three derivative networks involving groups and their members -- the hypergraph of groups, the network of groups and the user network -- to reveal social interactions at microscopic and mesoscopic level. Our results uncover interesting behaviors on the growth of user groups, the interactions between groups, and their relationship with member age and gender. These findings lead to insights which are difficult to obtain in ordinary social networks.Comment: 18 pages, 9 figure

Multiscale modeling of oscillations and spiral waves in Dictyostelium populations

Unicellular organisms exhibit elaborate collective behaviors in response to environmental cues. These behaviors are controlled by complex biochemical networks within individual cells and coordinated through cell-to-cell communication. Describing these behaviors requires new mathematical models that can bridge scales -- from biochemical networks within individual cells to spatially structured cellular populations. Here, we present a family of multiscale models for the emergence of spiral waves in the social amoeba Dictyostelium discoideum. Our models exploit new experimental advances that allow for the direct measurement and manipulation of the small signaling molecule cAMP used by Dictyostelium cells to coordinate behavior in cellular populations. Inspired by recent experiments, we model the Dictyostelium signaling network as an excitable system coupled to various pre-processing modules. We use this family of models to study spatially unstructured populations by constructing phase diagrams that relate the properties of population-level oscillations to parameters in the underlying biochemical network. We then extend our models to include spatial structure and show how they naturally give rise to spiral waves. Our models exhibit a wide range of novel phenomena including a density dependent frequency change, bistability, and dynamic death due to slow cAMP dynamics. Our modeling approach provides a powerful tool for bridging scales in modeling of Dictyostelium populations