Boolean Internal Structure Reconstruction from Collapsed Small-Scale Networks

Dynamic network reconstruction aims to infer network structure from input-output data. Dynamical structure functions (DSFs) have been introduced to represent structural information between observable nodes of linear time-invariant systems. However, reconstructing large-scale DSFs can be difficult since most existing methods do not scale. Instead of inferring large DSFs directly, an alternative approach is to reconstruct many small-scale DSFs that are easier to infer. Given a sparsity constraint on the network, this paper proposes a necessary and sufficient condition for perfect reconstruction of the Boolean network using collapsed small-scale networks. For sparse networks, such as gene regulatory networks, this method can significantly reduce time and computational costs of Boolean network inference for most links in the network, especially when using parallel computing.