Boolean automata networks (BANs) are a generalisation of Boolean cellular automata. In such, any theorem describing the way BANs compute information is a strong tool that can be applied to a wide range of models of computation. In this paper we explore a way of working with BANs which involves adding external inputs to the base model (via modules), and more importantly, a way to link networks together using the above mentioned inputs (via wirings). Our aim is to develop a powerful formalism for BAN (de)composition. We formulate three results: the first one shows that our modules/wirings definition is complete; the second one uses modules/wirings to prove simulation results amongst BANs; the final one expresses the complexity of the relation between modularity and the dynamics of modules.

One of the first popular applications of Boolean networks for gene regulatory networks corresponds to the Mendoza & Alvarez-Buylla network of flower development. In this paper, we consider this model and a reduced version to reconstruct synthetic threshold Boolean networks that have the same asymptotic behavior as these base models. For this, we employ an evolution strategy to search for neighboring solutions. We were able to find solutions with fewer edges as well as networks with more balanced distributions of basins of attractions. Overall, our results show the effectiveness of using evolutionary computation in this application to explore alternative solutions with desired properties.

This paper aims at giving a general and precise method to achieve a good understanding of discrete dynamical systems by focusing on their attraction basins. This work is the result of a previous one which has permitted to show that the structural changes introduced by fixed boundary conditions on regulatory networks could directly and strongly influence the properties of their attraction basins. In this paper, we give an exhaustive stochastic study protocol to understand what happens on attraction basins of dynamical systems when the latter are subjected to state perturbations. Then, we give an application of this protocol by giving the results obtained on a specific system which is a model of the Arabidopsis thaliana flower’s morphogenesis, depending on a specific boundary condition.