  The cortex is a very large network characterized by a complex connectivity
including at least two scales: a microscopic scale at which the
interconnections are non-specific and very dense, while macroscopic
connectivity patterns connecting different regions of the brain at larger scale
are extremely sparse. This motivates to analyze the behavior of networks with
multiscale coupling, in which a neuron is connected to its $v(N)$
nearest-neighbors where $v(N)=o(N)$, and in which the probability of
macroscopic connection between two neurons vanishes. These are called singular
multi-scale connectivity patterns. We introduce a class of such networks and
derive their continuum limit. We show convergence in law and propagation of
chaos in the thermodynamic limit. The limit equation obtained is an intricate
non-local McKean-Vlasov equation with delays which is universal with respect to
the type of micro-circuits and macro-circuits involved.
