Before revision:  By adapting percolation theory to directed bipartite graphs, evolving according to the AND logic dynamics, we are able to determine the region , in the network parameter space, where bipartite networks can support extensive gene expression , as required in stable cell types.
After revision:  By adapting percolation theory to directed bipartite graphs, evolving according to the AND logic dynamics, we are able to determine the necessary conditions , in the network parameter space, where bipartite networks can support extensive gene expression , as required in stable cell types.