properties on criticality. It was shown here that a high κ (high percentage of internal inputs) and a low µ (node-to- module ratio) promote criticality in what otherwise would be a chaotic regime. However, is there an “optimal” value of κ and/or µ for particular systems? It would be also interesting to measure the modularity of real GRNs, and measure to what extent the modularity plays a role in their criticality [5]. Modularity might help explain why real GRNs tend to have a high average connectivity that would set them in the chaotic regime [21], while exhibiting critical behavior [5]. The results presented here are encouraging to study modularity at multiple scales, i.e. nested modules or hierarchies. RBNs have two scales: nodes and network, with no modularity. MRBNs have three scales: nodes, modules, and networks. The MRBN model can be generalized to have an arbitrary number of intermediate scales, i.e. modules of modules, with different coupling pref- erences. In this way, a multi-scaled modular network could have in principle different dynamical regimes at different scales, i.e. damage could propagate at one scale but not at another. A general way of defining multiple scales might be with recursive RBNs. A scale-free topology has been shown to promote criticality in what otherwise would be ordered networks [1]. Scale-free topology and criticality are also present in natural networks [2, 34]. It would be interesting to study how modular and scale free topologies could be combined, and whether their effects on criticality are cummulative: for abstract RBNs and for real GRNs. For example, in our present studies N is constant for all modules, while the module size could have a scale-free distribution (few large modules and several small modules). The redundancy of nodes [20] and modules [7] has shown to promote robustness in RBNs. MRBNs can be general models to study the relationship between modularity, robustness, evolv- ability, and criticality. Also, degeneracy can play an important role in robustness [46, 47] and evolvability [51], although the role of degeneracy in the criticality of RBNs still remains to be explored. The potential avenues of research are several. The topics related to modularity and criticality are many. We believe that MRBNs can contribute to illuminate these interesting questions. 25