Category: Neuroscience

Summary: Estimating how Dale’s law shifts the critical interaction strength for instability in dense excitatory-inhibitory neural networks.

Classical random-matrix theory predicts a simple instability threshold for unconstrained networks, but biological neural circuits obey Dale’s law: each neuron is either purely excitatory or purely inhibitory. This sign constraint changes the spectrum and can create outlier modes that alter when recurrent activity becomes unstable.

The experiment generates dense non-symmetric matrices with a fixed excitatory-inhibitory split and then bisects coupling strength across increasing system sizes. By tracking the leading eigenvalue, it estimates how the stability boundary moves away from the unconstrained May-theorem prediction.

That is relevant because sign structure is one of the most basic biological constraints on cortical models. The computation turns that structural difference into a quantitative finite-size threshold map.

Method: Dense non-symmetric eigensolves with iterative deepening and bisection on coupling strength in Dale-law random networks.

What is measured: Critical coupling threshold, leading-eigenvalue stability indicator, finite-size scaling, inhibitory-fraction setting, and bracket width.