This paper proposes a notion of smooth action on a manifold, and establishes a general integrability result for certain associated distributions. As corollaries, various classical and new results on manifold structures of orbits are established, and the main theorem on preservation of transitivity under sampling is shown to be a simple consequence.

The faithful segregation of DNA during mitosis is critical to the life of a cell. A complex molecular machine called the mitotic spindle mediates this task. The spindle is made up of microtubule-binding proteins and microtubules on which the chromosomes are segregated. A complete understanding of the formation of the bipolar spindle and the mechanism of chromosome movement on the spindle remain...

Consider a countable group Γ acting ergodically by measure preserving transformations on a probability space (X,μ), and let RΓ be the corresponding orbit equivalence relation on X. The following rigidity phenomenon is shown: there exist group actions such that the equivalence relation RΓ on X determines the group Γ and the action (X,μ,Γ) uniquely, up to finite groups. The natural action of SLn(...