Table 2.

Glossary of variables and expressions.

Variable	Description
$u$	Exogenous input
$x$	The i-th (neuronal) state in region j; e.g., mean depolarisation of a neuronal population
$\sigma \left(x\right)$	The neuronal firing rate – a sigmoid squashing function of depolarisation
$L$	Lead field vector mapping from (neuronal) states to measured (electrophysiological) responses
$g_v\left(\omega \right),g_o\left(\omega \right),g_y\left(\omega \right)$	Spectral density of (neuronal) state fluctuations, observation error and ensuing measurement, respectively
${\partial }_{x}f$	System Jacobian or derivative of system flow with respect to (neuronal) states
$k\left(t\right)=FT\left[K\left(\omega \right)\right]$	First order kernel mapping from inputs to responses; c.f., an impulse response function of time. This is the Fourier transform of the transfer function
$K\left(\omega \right)=FT\left[k\left(t\right)\right]$	Transfer function of frequency, modulating the power of endogenous neuronal fluctuations to produce a (cross spectral density) response. This is the Fourier transform of the kernel