We show that the low-frequency regime of the density of states of structural glass formers is crucially sensitive to the stress-ensemble from which the configurations are sampled. Specifically, in two dimensions, an exactly isotropic ensemble with zero shear stress fluctuations, displays a $D(omega_{min}) sim omega^{5}_{min}$ regime, as opposed to the $omega^{4}_{min}$ regime observed under unstrained conditions. We also study an ensemble of strained amorphous solids near a plastic event. We show that the minimum eigenvalue distribution at a strain $gamma$ near the plastic event occurring at $gamma_{P}$, displays a collapse when scaled by $sqrt{gamma_P - gamma}$, and with the number of particles as $N^{-0.22}$. Notably, at low-frequencies, this scaled distribution displays a robust $D(omega_{min}) sim omega^{6}_{min}$ power-law regime, which survives in the large $N$ limit. Finally, we probe the universal properties of this ensemble through a characterization of the second and third eigenvalues of the Hessian matrix near a plastic event.
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