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.

Prevention of autoimmune demyelination in non-human primates by a cAMP-specific phosphodiesterase inhibitor.

Experimental allergic encephalomyelitis (EAE) is an autoimmune disease of the central nervous system that serves as a model for the human disease multiple sclerosis. We evaluated rolipram, a type IV phosphodiesterase inhibitor, for its efficacy in preventing EAE in the common marmoset Callithrix jacchus. In a blinded experimental design, clinical signs of EAE developed within 17 days of immunization with human white matter in two placebo-treated animals but in none of three monkeys that received rolipram (10 mg/kg s.c. every other day) beginning 1 week after immunization. In controls, signs of EAE were associated with development of cerebrospinal fluid pleocytosis and cerebral MRI abnormalities. In the treatment group, there was sustained protection from clinical EAE, transient cerebrospinal fluid pleocytosis in only one of three animals, no MRI abnormality, and marked reduction in histopathologic findings. Rolipram-treated and control animals equally developed circulating antibodies to myelin basic protein. Thus, inhibition of type IV phosphodiesterase, initiated after sensitization to central nervous system antigens, protected against autoimmune demyelinating disease.