Modulation of cognition-specific cortical activity by gonadal steroids: A positron-emission tomography study in women

There is considerable evidence from animal studies that gonadal steroid hormones modulate neuronal activity and affect behavior. To study this in humans directly, we used H215O positron-emission tomography to measure regional cerebral blood flow (rCBF) in young women during three pharmacologically controlled hormonal conditions spanning 4–5 months: ovarian suppression induced by the gonadotropin-releasing hormone agonist leuprolide acetate (Lupron), Lupron plus estradiol replacement, and Lupron plus progesterone replacement. Estradiol and progesterone were administered in a double-blind cross-over design. On each occasion positron-emission tomography scans were performed during (i) the Wisconsin Card Sorting Test, a neuropsychological test that physiologically activates prefrontal cortex (PFC) and an associated cortical network including inferior parietal lobule and posterior inferolateral temporal gyrus, and (ii) a no-delay matching-to-sample sensorimotor control task. During treatment with Lupron alone (i.e., with virtual absence of gonadal steroid hormones), there was marked attenuation of the typical Wisconsin Card Sorting Test activation pattern even though task performance did not change. Most strikingly, there was no rCBF increase in PFC. When either progesterone or estrogen was added to the Lupron regimen, there was normalization of the rCBF activation pattern with augmentation of the parietal and temporal foci and return of the dorsolateral PFC activation. These data directly demonstrate that the hormonal milieu modulates cognition-related neural activity in humans.

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.