  Some recent papers relate the criticality of complex systems to their maximal
capacity of information processing. In the present paper, we consider high
dimensional point processes, known as age-dependent Hawkes processes, which
have been used to model spiking neural networks. Using mean-field
approximation, the response of the network to a stimulus is computed and we
provide a notion of stimulus sensitivity. It appears that the maximal
sensitivity is achieved in the sub-critical regime, yet almost critical for a
range of biologically relevant parameters.
