  In neural circuits, statistical connectivity rules strongly depend on
neuronal type. Here we study dynamics of neural networks with cell-type
specific connectivity by extending the dynamic mean field method, and find that
these networks exhibit a phase transition between silent and chaotic activity.
By analyzing the locus of this transition, we derive a new result in random
matrix theory: the spectral radius of a random connectivity matrix with
block-structured variances. We apply our results to show how a small group of
hyper-excitable neurons within the network can significantly increase the
network's computational capacity.
