Individual versus social benefit on heterogeneous networks.

The focus of structural balance theory is dedicated to social benefits, while in a real network individual benefits sometimes are the focus as well. The Strauss's model addresses individual benefits besides the social one with a simple assumption that all individual benefits are equivalent. Therefore, the results show that the competition between two terms leads to a phase transition between individual and social benefits and there is a critical point CP that represents a first-order phase transition in the network.

Robustness of functional networks at criticality against structural defects.

The robustness of dynamical properties of neuronal networks against structural damages is a central problem in computational and experimental neuroscience. Research has shown that the cortical network of a healthy brain works near a critical state and, moreover, that functional neuronal networks often have scale-free and small-world properties. In this work, we study how the robustness of simple functional networks at criticality is affected by structural defects.

Functional scale-free networks in the two-dimensional Abelian sandpile model.

Recently, the similarity of the functional network of the brain and the Ising model was investigated by Chialvo [Nat. Phys. 6, 744 (2010)].

Taylor's frozen-flow hypothesis in Burgers turbulence.

By detailed analytical treatment of the shock dynamics in the Burgers turbulence with large scale forcing we calculate the velocity structure functions between pairs of points displaced both in time and space. Our analytical treatment verifies the so-called Taylor's frozen-flow hypothesis without relying on any closure and under very general assumptions. We discuss the limitation of the hypothesis and show that it is valid up to time scales smaller than the correlation time scale of temporal velocity correlation function.