Category: Neuroscience

Summary: Estimating how much selective excitatory synaptic depression is needed to quench a localized transient-amplification mode in a Dale-law neural network.

Transient amplification in excitatory-inhibitory circuits can make a network respond strongly to perturbations even when it remains linearly stable overall. This experiment asks when short-term depression acting on excitatory structure is strong enough to suppress that behavior, specifically for a localized reactive mode concentrated on an excitatory assembly in a strict Dale-law random network.

The script builds dense symmetric reactivity operators for excitatory and inhibitory populations, then uses iterative deepening with repeated eigensolves to bisect the depression-strength threshold across increasing system sizes. It tracks whether the dominant reactive mode remains assembly-localized, how much of the mode stays on excitatory cells, and how sharply the threshold bracket closes as the network grows.

The scientific value is in treating synaptic depression as a structural control on transient amplification rather than only as a modulation of firing rates. The output helps locate where localized amplification stops being sustainable in finite dense E/I networks.

Method: Dense symmetric reactivity eigensolves with iterative deepening and bisection on depression strength rho across network sizes up to N=3072.

What is measured: Critical depression threshold, maximum reactive eigenvalue, assembly mass, excitatory mass, participation ratio, and bracket width.