Direct comparison of methionine restriction with leucine restriction on the metabolic health of C57BL/6J mice

EKL was the recipient of a BBSRC postgraduate studentship. This work was funded by Tenovus Scotland project grant to MD and NM (G13/07) and BBSRC DTG. MD is also supported by the British Heart Foundation (PG/09/048/27675, PG/11/8/28703 and PG/14/43/30889) and Diabetes UK (14/0004853). NM is funded by British Heart Foundation (PG/16/90/32518).Peer reviewedPublisher PD

New Differential Geometric Methods in Nonholonomic Path Finding

We outline three approaches for nonholonomic path finding ---nilpotent approximation, highly oscillatory inputs and path deformation--- that are based on the use of the techniques of modern geometric optimal control theory, as well as a more classical one ---optimal control--- where differential geometric methods are also beginning to play a significant role. x1. Introduction In this note we will outline and compare three approaches that have recently been pursued in our work on path finding for nonholonomic systems, and will suggest adding a fourth one to this list. One of the approaches --- optimal control--- is old, but has recently attracted renewed interest due to the fact that, by making systematic use of "differential geometric methods," it now appears possible to get explicit solutions of problems that could not be handled by means of the techniques developed in the era of "classical" control theory. Two others ---nilpotent approximation and highly oscillatory inputs--- have ..