We show that in the mapping class group of a surface any relation between Dehn twists of the form T j xT k y = M (M a multitwist) is the lantern relation, and any relation of the form (TxTy) k = M (where Tx commutes with M ) is the 2-chain relation. AMS Classification 57M07; 20F38, 57N05

Photonic lanterns allow the decomposition of highly multimodal light into a simplified modal basis such as single-moded and/or few-moded. They are increasingly finding uses in astronomy, optics and telecommunications. Calculating propagation through photonic lantern using traditional algorithms takes $\sim 1$ hour per simulation on modern CPU. This paper demonstrates that neural networks can br...

The success of insects arises partly from extraordinary biochemical and physiological specializations. For example, most species lack glutathione peroxidase, glutathione reductase and respiratory-gas transport proteins and thus allow oxygen to diffuse directly into cells. To counter the increased potential for oxidative damage, insect tissues rely on the indirect protection of the thioredoxin r...

The biogenic amine, octopamine, has been proposed as the transmitter in the firefly light organ (Evans, 1980; Robertson, 1981). Whereas initial studies implicated adrenaline (Smalley, 1965; Carlson, 1968a), octopamine was found to be more potent in inducing luminescence than any amine other than synephrine (Carlson, 19686). Octopamine, but not synephrine, was found in adult lantern segments (Ro...