In percolation theory, vertices within a graph have a binary state: either active or inactive. Furthermore, a percolation process decides how activation spreads within the graph. Firstly, we propose and analyse a simple data-driven percolation process in which percolations are preliminarily learnt from a graph with observed percolations. Secondly, we study a problem related to the one solved by...

The percolation process provides a simple picture of a critical point transition and has been of increasing recent theoretical interest. We refer to several review articles (1-a~ for a general survey of the subject. An important development first established by Kasteleyn and Fortuin (4,5~ is the connection between bond percolation and a lattice statistical model. This consideration leads to a f...

We test the universal finite-size scaling of the cluster mass order parameter in two-dimensional (2D) isotropic and directed continuum percolation models below the percolation threshold by computer simulations. We found that the simulation data in the 2D continuum models obey the same scaling expression of massM to sample size L as generally accepted for isotropic lattice problems, but with a p...

A new kind of percolation problem is described which differs from ordinary percolation theory in that it automatically finds the critical points of the system. The model is motivated by the problem of one fluid displacing another from a porous medium under the action of capillary forces, but in principle it may be applied to any kind of invasion process which proceeds along a path of least resi...

We formulate the Wolff algorithm as a site-bond percolation problem, apply it to the ferromagnetic and antiferromagnetic planar triangular spin models, and study the percolation critical behavior using Anite-size scaling. In the former case the Wold' algorithm is successful as an accelerating algorithm, whereas in the latter case it is not. We found the percolation temperatures and the cluster ...

Percolation theory is of interest in problems of phase transitions in condensed matter physics, and in biology and chemistry. More recently, concepts of percolation theory have been invoked in studies of color deconfinement at high temperatures in Quantum Chromodynamics. In the present paper we briefly review the basic concept of percolation theory, exemplify its application to the Ising model,...