(A) Firing rates of the excitatory (blue) and inhibitory population (red) in the presence of spike-frequency adaptation (SFA). During stimulation (gray bar) additional input is injected into the excitatory population. The inset shows a cartoon of how SFA affects spiking neuronal dynamics in response to a step current input. (B) Left: Same as (A) but in the presence of E-to-E short-term depression (STD). Right: Same as left but inactivating inhibition in the period marked in purple. (C) 3D plot of the excitatory activity , inhibitory activity , and the STD variable of the network in B left. The orange and green points mark the fixed points before/after and during stimulation. (D) Characteristic function in networks with E-to-E STD. Different brightness levels correspond to different time points in B left. (E) Same as (B) but in the presence of E-to-I short-term facilitation (STF). (F) Inhibition-stabilized network (ISN) index, which corresponds to the largest real part of the eigenvalues of the Jacobian matrix of the E-E subnetwork with STD, as a function of time for the network with E-to-E STD in B left. For values above zero (dashed line), the ensemble is an ISN. (G) Analytical solution of non-ISN (magenta), ISN (green), paradoxical, and non-paradoxical regions for different parameter combinations and the STD variable . The solid line separates the non-ISN and ISN regions, whereas the dashed line separates the non-paradoxical and paradoxical regions. (H) The normalized firing rates of the excitatory (blue) and inhibitory population (red) when injecting additional excitatory current into the inhibitory population before stimulation (left; orange bar in B), and during stimulation (right; green bar in B). Initially, the ensemble is in the non-ISN regime and injecting excitatory current into the inhibitory population increases its firing rate. During stimulation, however, the ensemble is an ISN. In this case, excitatory current injection into the inhibitory population results in a reduction of its firing rate, also known as the paradoxical effect.