Coalescence-fragmentation problems are of great interest across the physical, biological, and recently social sciences. They are typically studied from the perspective of the rate equations, at the heart of such models are the rules used for coalesce
nce and fragmentation. Here we discuss how changes in these microscopic rules affect the macroscopic cluster-size distribution which emerges from the solution to the rate equation. More generally, our work elucidates the crucial role that the fragmentation rule can play in such dynamical grouping models. We focus on two well-known models whose fragmentation rules lie at opposite extremes setting the models within the broader context of binary coalescence-fragmentation models. Further, we provide a range of generalizations and new analytic results for a well-known model of social group formation [V. M. Eguiluz and M. G. Zimmermann, Phys. Rev. Lett. 85, 5659 (2000)]. We develop analytic perturbation treatment of the original model, and extend the mathematical to the treatment of growing and declining populations.
We analyze the synchronous firings of the salamander ganglion cells from the perspective of the complex network viewpoint where the networks links reflect the correlated behavior of firings. We study the time-aggregated properties of the resulting ne
twork focusing on its topological features. The behavior of pairwise correlations has been inspected in order to construct an appropriate measure that will serve as a weight of network connection.
