Significant changes have occurred in the developmental role of Hox genes, even within groups of arthropods that already have complex body plans and many different segment types. This is hard to reconcile with the 'selector gene' model for Hox gene function. Selector genes act as stable binary switches that direct lineages of cells to adopt alternative developmental fates. This model suggests th...

We construct a minimax selector for eventually quadratic hamiltonians on cotangent bundles. We use it to give a relation between Hofer’s energy and Mather’s action minimizing function. We also study the local flatness of the set of twist maps.

In this paper we establish under suitable conditions the existence of measurable selectors for Gs-valued multifunctions. In particular we prove that a measurable partition of a Polish space into G6 sets admits a Borel selector.