Towards a mathematical definition of functional connectivity

Functional connectivity is a neurobiological notion, informally stating that there would be strong dependence between neurons and this might useful in understanding the way brain encodes stimuli, programs actions, etc. However, practice such dependencies are often reconstructed via Hawkes processes based on an amazingly small number of neurons, because very scarce observation complex huge network. We derive new simple equations, which explain how ideal reconstruction linked to covariance observed neurons. These equations help us particular understand what does two settings, synchronization classical point process asymptotics. Moreover they also qualitatively happening at scale unobserved network, paving path for possible mathematical definition functional connectivity.