public · active

Exactly the same, Except

AndreyAnastasiya

What makes an apparently perfect copy meaningfully different?

Move 1
Andrey
x˙(t)=−∂V(x)∂x+A0sin⁡(ω0t)+ξ(t)⟨ξ(t)ξ(t′)⟩=2Dδ(t−t′)In non-linear systems, sub-threshold signals fail to trigger a responseon their own. Adding a tiny amount of Gaussian noise ξ(t) boostssignal-to-noise ratio by periodically pushing the signal over theactivation threshold. In nature, paddlefish use this mechanism todetect faint electrical fields of prey amid turbulent water.\begin{aligned} &\dot{x}(t) = -\frac{\partial V(x)}{\partial x} + A_0 \sin(\omega_0 t) + \xi(t) \\[1.5em] &\langle \xi(t)\xi(t') \rangle = 2D\delta(t - t') \\[1.6em] &{\scriptsize \text{In non-linear systems, sub-threshold signals fail to trigger a response}} \\ &{\scriptsize \text{on their own. Adding a tiny amount of Gaussian noise } \xi(t) \text{ boosts}} \\ &{\scriptsize \text{signal-to-noise ratio by periodically pushing the signal over the}} \\ &{\scriptsize \text{activation threshold. In nature, paddlefish use this mechanism to}} \\ &{\scriptsize \text{detect faint electrical fields of prey amid turbulent water.}} \end{aligned}

Read the complete history