Squaring and adding $\pm 1$ mod p generates a curiously intractable random walk. A similar process over the finite field $\mathbf{F}_q$ (with $q=2^d$) leads to novel connections between elementary Galois theory probability.

Fully reconfigurable add-drop filters (ADFs) have important applications in optical communication and information processing. Here we demonstrate a broadly tunable filter based on double-disk cavity optomechanical system, side-coupled with pair of tapered fiber waveguides. By varying the coupling rates between two waveguides, investigate dependence through (drop) efficiency rates, which agrees ...