The two properties of the radial mass distribution a gravitational lens that are well-constrained by Einstein rings radius R_E and xi2 = alpha''(R_E)/(1-kappa_E), where alpha''(R_E) kappa_E second derivative deflection profile convergence at R_E. However, if there is tight mathematical relationship between angular structure, as true ellipsoids, an ring can appear to strongly distinguish distrib...

Web-building spiders are important models for sexual selection. While our understanding of post-copulatory mechanisms including sperm competition and cryptic female choice is considerable, our knowledge of courtship and how it influences male and female mating decisions is still extremely poor. Here, we provide the first comprehensive description of male courtship behaviour and vibrations gener...

Informal models have always been used in biology to guide thinking and devise experiments. In recent years, formal mathematical models have also been widely introduced. It is sometimes suggested that formal models are inherently superior to informal ones and that biology should develop along the lines of physics or economics by replacing the latter with the former. Here I suggest to the contrar...