On the controllability of distributed systems

To “control” a system is to make it behave (hopefully) according to our “wishes,” in a way compatible with safety and ethics, at the least possible cost. The systems considered here are distributed—i.e., governed (modeled) by partial differential equations (PDEs) of evolution. Our “wish” is to drive the system in a given time, by an adequate choice of the controls, from a given initial state to a final given state, which is the target. If this can be achieved (respectively, if we can reach any “neighborhood” of the target) the system, with the controls at our disposal, is exactly (respectively, approximately) controllable. A very general (and fuzzy) idea is that the more a system is “unstable” (chaotic, turbulent) the “simplest,” or the “cheapest,” it is to achieve exact or approximate controllability. When the PDEs are the Navier–Stokes equations, it leads to conjectures, which are presented and explained. Recent results, reported in this expository paper, essentially prove the conjectures in two space dimensions. In three space dimensions, a large number of new questions arise, some new results support (without proving) the conjectures, such as generic controllability and cases of decrease of cost of control when the instability increases. Short comments are made on models arising in climatology, thermoelasticity, non-Newtonian fluids, and molecular chemistry. The Introduction of the paper and the first part of all sections are not technical. Many open questions are mentioned in the text.

Introduction of the transposable element Minos into the germ line of Drosophila melanogaster.

A transposon based on the transposable element Minos from Drosophila hydei was introduced into the genome of Drosophila melanogaster using transformation mediated by the Minos transposase. The transposon carries a wild-type version of the white gene (w) of Drosophila inserted into the second exon of Minos. Transformation was obtained by injecting the transposon into preblastoderm embryos that were expressing transposase either from a Hsp70-Minos fusion inserted into the genome via P-element-mediated transformation or from a coinjected plasmid carrying the Hsp70-Minos fusion. Between 1% and 6% of the fertile injected individuals gave transformed progeny. Four of the insertions were cloned and the DNA sequences flanking the transposon ends were determined. The "empty" sites corresponding to three of the insertions were amplified from the recipient strain by PCR, cloned, and sequenced. In all cases, the transposon has inserted into a TA dinucleotide and has created the characteristic TA target site duplication. In the absence of transposase, the insertions were stable in the soma and the germ line. However, in the presence of the Hsp70-Minos gene the Minos-w transposon excises, resulting in mosaic eyes and germ-line reversion to the white phenotype. Minos could be utilized as an alternative to existing systems for transposon tagging and enhancer trapping in Drosophila; it might also be of use as a germ-line transformation vector for non-Drosophila insects.