Homotopy Lie algebras, lower central series and the Koszul property

Let X and Y be finite-type CW-complexes (X connected, Y simply connected), such that the rational cohomology ring of Y is a k-rescaling of the rational cohomology ring of X. Assume H^*(X,Q) is a Koszul algebra. Then, the homotopy Lie algebra pi_*(Omega Y) tensor Q equals, up to k-rescaling, the graded rational Lie algebra associated to the lower central series of pi_1(X). If Y is a formal space, this equality is actually equivalent to the Koszulness of H^*(X,Q). If X is formal (and only then), the equality lifts to a filtered isomorphism between the Malcev completion of pi_1(X) and the completion of [Omega S^{2k+1}, Omega Y]. Among spaces that admit naturally defined homological rescalings are complements of complex hyperplane arrangements, and complements of classical links. The Rescaling Formula holds for supersolvable arrangements, as well as for links with connected linking graph.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper30.abs.htm

SUSY Simplified Models at 14, 33, and 100 TeV Proton Colliders

Results are presented for a variety of SUSY Simplified Models at the 14 TeV LHC as well as a 33 and 100 TeV proton collider. Our focus is on models whose signals are driven by colored production. We present projections of the upper limit and discovery reach in the gluino-neutralino (for both light and heavy flavor decays), squark-neutralino, and gluino-squark Simplified Model planes. Depending on the model a jets + MET, mono-jet, or same-sign di-lepton search is applied. The impact of pileup is explored. This study utilizes the Snowmass backgrounds and combined detector. Assuming 3000 fb^{-1} of integrated luminosity, a gluino that decays to light flavor quarks can be discovered below 2.3 TeV at the 14 TeV LHC and below 11 TeV at a 100 TeV machine.Comment: 81 pages, 55 figures; v2 journal versio

There are laterality effects in memory functioning in children/adolescents with focal epilepsy.

In a sample of individuals with childhood focal epilepsy, children/adolescents with left hemisphere foci outperformed those with right foci on both measures of nonverbal learning. Participants with left foci performed worse than controls on paired associate delayed recall and semantic memory, and they had greater laterality effects in IQ. Participants with right foci performed worse than controls on delayed facial recognition. Both groups displayed reduced focused attention and poor passage retention over time. Although participants with bilateral foci displayed poor learning and lower IQ than controls, they did not have worse impairment than those with a unilateral focus

A Large Sample Study of Red Giants in the Globular Cluster Omega Centauri (NGC 5139)

We present abundances of several light, alpha, Fe-peak, and neutron-capture elements for 66 red giant branch (RGB) stars in the Galactic globular cluster Omega Centauri. Our observations lie in the range 12.0<V<13.5 and focus on the intermediate and metal-rich RGBs. We find that there are at least four peaks in the metallicity distribution function at [Fe/H]=-1.75, -1.45, -1.05, and -0.75, which correspond to about 55%, 30%, 10%, and 5% of our sample, respectively. Additionally, the most metal-rich stars are the most centrally located. Na and Al are correlated despite exhibiting star-to-star dispersions of more than a factor of 10, but the distribution of those elements appears to be metallicity dependent and are divided at [Fe/H]~-1.2. About 40-50% of stars with [Fe/H]<-1.2 have Na and Al abundances consistent with production solely in Type II supernovae and match observations of disk and halo stars at comparable metallicity. The remaining metal-poor stars are enhanced in Na and Al compared to their disk and halo counterparts and are mostly consistent with predicted yields from >5 M_sun asymptotic giant branch (AGB) stars. At [Fe/H]>-1.2, more than 75% of the stars are Na/Al enhanced and may have formed almost exclusively from AGB ejecta. Most of these stars are enhanced in Na by at least 0.2 dex for a given Al abundance than would be expected based on "normal" globular cluster values. All stars in our sample are alpha-rich and have solar-scaled Fe-peak abundances. Eu does not vary extensively as a function of metallicity; however, [La/Fe] varies from about -0.4 to +2 and stars with [Fe/H]>-1.5 have [La/Eu] values indicating domination by the s-process. A quarter of our sample have [La/Eu]>+1 and may be the result of mass transfer in a binary system.Comment: ApJ Accepted; 90 pages, 16 Figures, 5 Table

Multiple populations in Omega Centauri: a cluster analysis of spectroscopic data

Omega Cen is composed of several stellar populations. Their history might allow us to reconstruct the evolution of this complex object. We performed a statistical cluster analysis on the large data set provided by Johnson and Pilachowski (2010). Stars in Omega Cen divide into three main groups. The metal-poor group includes about a third of the total. It shows a moderate O-Na anticorrelation, and similarly to other clusters, the O-poor second generation stars are more centrally concentrated than the O-rich first generation ones. This whole population is La-poor, with a pattern of abundances for n-capture elements which is very close to a scaled r-process one. The metal-intermediate group includes the majority of the cluster stars. This is a much more complex population, with an internal spread in the abundances of most elements. It shows an extreme O-Na anticorrelation, with a very numerous population of extremely O-poor and He-rich second generation stars. This second generation is very centrally concentrated. This whole population is La-rich, with a pattern of the abundances of n-capture elements that shows a strong contribution by the s-process. The spread in metallicity within this metal-intermediate population is not very large, and we might attribute it either to non uniformities of an originally very extended star forming region, or to some ability to retain a fraction of the ejecta of the core collapse SNe that exploded first, or both. As previously noticed, the metal-rich group has an Na-O correlation, rather than anticorrelation. There is evidence for the contribution of both massive stars ending their life as core-collapse SNe, and intermediate/low mass stars, producing the s-capture elements. Kinematics of this population suggests that it formed within the cluster rather than being accreted.Comment: Accepted for publication in Astronomy and Astrophysic