How Important is the Detection of Changes in Active Constraints in Real-Time Optimization?

In real-time optimization, enforcing the constraints that need to be active is important for optimality. In fact, it has been established in the context of parametric variations that, if these constraints are not satisfied, the optimality loss would be O($\eta^2$) – denoting the magnitude of the parametric variations. In contrast, the loss of optimality upon enforcing the correct set of active constraints would be O($\eta^2$). However, no result is available when the set of active constraints changes due to parametric variations, which forms the subject of this paper. Herein it is shown that, if the optimal solution is unique for each , keeping only the strictly active constraints of the nominal solution active will lead to O($\eta^2$) loss in optimality, even when the remaining active constraints of the perturbed system are different from that of the nominal system. This, in turn, means that, in any input adaptation scheme for real-time optimization, identifying changes in active constraints is not important as long as it is possible to enforce the strictly active constraints of the nominal solution to remain active

LSST Science Book, Version 2.0

A survey that can cover the sky in optical bands over wide fields to faint magnitudes with a fast cadence will enable many of the exciting science opportunities of the next decade. The Large Synoptic Survey Telescope (LSST) will have an effective aperture of 6.7 meters and an imaging camera with field of view of 9.6 deg^2, and will be devoted to a ten-year imaging survey over 20,000 deg^2 south of +15 deg. Each pointing will be imaged 2000 times with fifteen second exposures in six broad bands from 0.35 to 1.1 microns, to a total point-source depth of r~27.5. The LSST Science Book describes the basic parameters of the LSST hardware, software, and observing plans. The book discusses educational and outreach opportunities, then goes on to describe a broad range of science that LSST will revolutionize: mapping the inner and outer Solar System, stellar populations in the Milky Way and nearby galaxies, the structure of the Milky Way disk and halo and other objects in the Local Volume, transient and variable objects both at low and high redshift, and the properties of normal and active galaxies at low and high redshift. It then turns to far-field cosmological topics, exploring properties of supernovae to z~1, strong and weak lensing, the large-scale distribution of galaxies and baryon oscillations, and how these different probes may be combined to constrain cosmological models and the physics of dark energy.Comment: 596 pages. Also available at full resolution at http://www.lsst.org/lsst/sciboo

Enrichment of genetic markers of recent human evolution in educational and cognitive traits

Higher cognitive functions are regarded as one of the main distinctive traits of humans. Evidence for the cognitive evolution of human beings is mainly based on fossil records of an expanding cranium and an increasing complexity of material culture artefacts. However, the molecular genetic factors involved in the evolution are still relatively unexplored. Here, we investigated whether genomic regions that underwent positive selection in humans after divergence from Neanderthals are enriched for genetic association with phenotypes related to cognitive functions. We used genome wide association data from a study of college completion (N = 111,114), one of educational attainment (N = 293,623) and two different studies of general cognitive ability (N = 269,867 and 53,949). We found nominally significant polygenic enrichment of associations with college completion (p = 0.025), educational attainment (p = 0.043) and general cognitive ability (p = 0.015 and 0.025, respectively), suggesting that variants influencing these phenotypes are more prevalent in evolutionarily salient regions. The enrichment remained significant after controlling for other known genetic enrichment factors, and for affiliation to genes highly expressed in the brain. These findings support the notion that phenotypes related to higher order cognitive skills typical of humans have a recent genetic component that originated after the separation of the human and Neanderthal lineages