Regimes and mechanisms of transient amplification in abstract and biological networks

We use upper triangular matrices as abstract representations of neuronal networks and directly manipulate their eigenspectra and non-normality to explore different regimes of transient amplification. Counter–intuitively, manipulating the imaginary distribution can lead to highly amplifying regimes. This is noteworthy, because biological networks are constrained by Dale’s law and the non-existence of neuronal self-loops, limiting the range of manipulations in the real dimension. Within these constraints we can further manipulate transient amplification by controlling global inhibition.