Percolation threshold determines the optimal population density for public cooperation

Percolation threshold determines the optimal population density for public cooperation

While worldwide census data provide statistical evidence that firmly link the population density with several indicators of social welfare, the precise mechanisms underlying these observations are largely unknown. Here we study the impact of population density on the evolution of public cooperation in structured populations and find that the optimal density is uniquely related to the percolatio...

Node density , connectivity and the percolation threshold

Rigid-floppy percolation threshold.

The mathematical limits for the percolation of rigid and floppy clusters throughout continuous networks are considered. Results are compared to the previous prediction of Thorpe based on the assumption that the threshold condition is the equality of degrees of freedom and the number of constraints. It is demonstrated that, in two-dimensional systems, the thresholds values predicted here and in ...

Sharp Threshold for Percolation on Expanders

We study the appearance of the giant component in random subgraphs of a given finite graph G = (V, E) in which each edge is present independently with probability p. We show that if G is an expander with vertices of bounded degree, then for any c ∈]0, 1[, the property that the random subgraph contains a giant component of size c|V | has a sharp threshold.

Determination of the bond percolation threshold for the Kagomé lattice

The hull-gradient method is used to determine the critical threshold for bond percolation on the two-dimensional Kagomé lattice (and its dual, the dice lattice). For this system, the hull walk is represented as a self-avoiding trail, or mirror-model trajectory, on the (3,4,6,4)-Archimedean tiling lattice. The result pc = 0.524 4053 ± 0.000 0003 (one standard deviation of error) is not consisten...