We study the convergence rate of Bergman metrics on class polarized pointed Kähler n-manifolds (M, L, g, x) with $$\textrm{Vol}\left( B_1 (x) \right) >v $$ and $$|\!\sec \!|\le K M. Relying Tian’s peak section method (Tian in J Differ Geom 32(1):99–130, 1990), we show that $$C^{1,\alpha }$$ is uniform. In end, discuss sharpness our estimates.

We present an original ant model to solve the foraging problem. We describe simulations and provide a convergence analysis. We prove the convergence of the model in the discrete and in the continuous cases. We show that the ant population computes the solution of an optimal control problem and converges in a well defined sense. We discuss the rate of convergence with respect to the number of an...