Localized cell shape change initiates epithelial folding, while neighboring cell invagination determines the final depth of an epithelial fold. The mechanism that controls the extent of invagination remains unknown. During Drosophila gastrulation, a higher number of cells undergo invagination to form the deep posterior dorsal fold, whereas far fewer cells become incorporated into the initially ...

Given a linear isometry A0 : Rn → Rn of finite order on Rn , a general 〈A0〉-invariant closed subset M of Rn is considered with Lipschitz boundary. Under suitable topological restrictions the existence of A0-invariant geodesics of M is proven.

[1] We have identified a dust storm deposit in the GISP2 ice core that most likely originated from the Great Plains region of the United States during the 1930’s ‘Dust Bowl’ era. These results indicate that the Central U.S. can be a significant source of dust to the Greenland ice sheet, especially when the source area is affected by intense drought conditions.

We describe a new proof of the complete integrability of the two related dynamical systems: the billiard inside the ellipsoid and the geodesic flow on the ellipsoid (in Euclidean, spherical or hyperbolic space). The proof is based on the construction of a metric on the ellipsoid whose nonparameterized geodesics coincide with those of the standard metric. This new metric is induced by the hyperb...