Many models have been proposed for spatial pattern formation in embryology and analyzed for the standard case of zero-flux boundary conditions. However, relatively little attention has been paid to the role of boundary conditions on the form of the final pattern. Here we investigate numerically, the effect of nonstandard boundary conditions on a model pattern generator, which we choose to be of...

Abstract The Fairlie-Gumbel-Morgenstern (FGM) family has been investigated in detail for various continuous marginals such as Cauchy, normal, exponential, gamma, Weibull, lognormal and others. It has been a popular model for the bivariate distribution with mild dependence. However, bivariate FGM’s with continuous marginals on a bounded support discussed in the literature are only those with uni...

Abstract We give some adequate extension, in the framework of a general Lévy process, of our previous construction of processes with one-dimensional martingale marginals, done originally in the set-up of Brownian motion. The Lévy process framework allows us to streamline our previous arguments, as well as to reach a larger class of such processes, even in the Brownian case. We give some illustr...

Drosophila, Wnt, FGF, Jak/Stat, Rho, Rac, RhoGEF, Pebble, Naked Cuticle The site for the latest installment of the Fly Meeting (March 7–11) was downtown Philadelphia. The conference offered an illustration of all that is great about the Drosophila field bringing together evolutionary biologists, immunologists and everyone in between. Here I will provide a small sample of several advances from t...