Unlimited simultaneous discrimination intervals in regression Technical report no. 90

Unlimited simultaneous discrimination intervals in linear regression

Binary Encounters With Supermassive Black Holes: Zero-Eccentricity LISA Events

Current simulations of the rate at which stellar-mass compact objects merge with supermassive black holes (called extreme mass ratio inspirals, or EMRIs) focus on two-body capture by emission of gravitational radiation. The gravitational wave signal of such events will likely involve a significant eccentricity in the sensitivity range of the Laser Interferometer Space Antenna (LISA). We show that tidal separation of stellar-mass compact object binaries by supermassive black holes will instead produce events whose eccentricity is nearly zero in the LISA band. Compared to two-body capture events, tidal separations have a high cross section and result in orbits that have a large pericenter and small apocenter. Therefore, the rate of interactions per binary is high and the resulting systems are very unlikely to be perturbed by other stars into nearly radial plunges. Depending on the fraction of compact objects that are in binaries within a few parsecs of the center, the rate of low-eccentricity LISA events could be comparable to or larger than the rate of high-eccentricity events.Comment: Final accepted version: ApJ Letters 2005, 631, L11

Four-Body Effects in Globular Cluster Black Hole Coalescence

In the high density cores of globular clusters, multibody interactions are expected to be common, with the result that black holes in binaries are hardened by interactions. It was shown by Sigurdsson & Hernquist (1993) and others that 10 solar mass black holes interacting exclusively by three-body encounters do not merge in the clusters themselves, because recoil kicks the binaries out of the clusters before the binaries are tight enough to merge. Here we consider a new mechanism, involving four-body encounters. Numerical simulations by a number of authors suggest that roughly 20-50% of binary-binary encounters will eject one star but leave behind a stable hierarchical triple. If the orbital plane of the inner binary is strongly tilted with respect to the orbital plane of the outer object, a secular Kozai resonance, first investigated in the context of asteroids in the Solar System, can increase the eccentricity of the inner body significantly. We show that in a substantial fraction of cases the eccentricity is driven to a high enough value that the inner binary will merge by gravitational radiation, without a strong accompanying kick. Thus the merged object remains in the cluster; depending on the binary fraction of black holes and the inclination distribution of newly-formed hierarchical triples, this mechanism may allow massive black holes to accumulate through successive mergers in the cores of globular clusters. It may also increase the likelihood that stellar-mass black holes in globular clusters will be detectable by their gravitational radiation.Comment: Submitted to ApJ Letters (includes emulateapj.sty

Gadolinium scandium germanide, Gd2Sc3Ge4

Gd2Sc3Ge4 adopts the ortho­rhom­bic Pu5Rh4-type structure. The crystal structure contains six sites in the asymmetric unit: two sites are statistically occupied by rare-earth atoms with Gd:Sc ratios of 0.967 (4):0.033 (4) and 0.031 (3):0.969 (3), one site (.m. symmetry) is occupied by Sc atoms, and three distinct sites (two of which with .m. symmetry) are occupied by Ge atoms. The rare-earth atoms form two-dimensional slabs with Ge atoms occupying the trigonal-prismatic voids

Three-body equations of motion in successive post-Newtonian approximations

There are periodic solutions to the equal-mass three-body (and N-body) problem in Newtonian gravity. The figure-eight solution is one of them. In this paper, we discuss its solution in the first and second post-Newtonian approximations to General Relativity. To do so we derive the canonical equations of motion in the ADM gauge from the three-body Hamiltonian. We then integrate those equations numerically, showing that quantities such as the energy, linear and angular momenta are conserved down to numerical error. We also study the scaling of the initial parameters with the physical size of the triple system. In this way we can assess when general relativistic results are important and we determine that this occur for distances of the order of 100M, with M the total mass of the system. For distances much closer than those, presumably the system would completely collapse due to gravitational radiation. This sets up a natural cut-off to Newtonian N-body simulations. The method can also be used to dynamically provide initial parameters for subsequent full nonlinear numerical simulations.Comment: 8 pages, 9 figure

Implications of the PSR 1257+12 Planetary System for Isolated Millisecond Pulsars

The first extrasolar planets were discovered in 1992 around the millisecond pulsar PSR 1257+12. We show that recent developments in the study of accretion onto magnetized stars, plus the existence of the innermost, moon-sized planet in the PSR 1257+12 system, suggest that the pulsar was born with approximately its current rotation frequency and magnetic moment. If so, this has important implications for the formation and evolution of neutron star magnetic fields as well as for the formation of planets around pulsars. In particular, it suggests that some and perhaps all isolated millisecond pulsars may have been born with high spin rates and low magnetic fields instead of having been recycled by accretion.Comment: 17 pages including one figure, uses aaspp4, accepted by Ap

Chemical variation in a dominant tree species: population divergence, selection and genetic stability across environments

Understanding among and within population genetic variation of ecologically important plant traits provides insight into the potential evolutionary processes affecting those traits. The strength and consistency of selection driving variability in traits would be affected by plasticity in differences among genotypes across environments (G×E). We investigated population divergence, selection and environmental plasticity of foliar plant secondary metabolites (PSMs) in a dominant tree species, Eucalyptus globulus. Using two common garden trials we examined variation in PSMs at multiple genetic scales; among 12 populations covering the full geographic range of the species and among up to 60 families within populations. Significant genetic variation in the expression of many PSMs resides both among and within populations of E. globulus with moderate (e.g., sideroxylonal A h2op = 0.24) to high (e.g., macrocarpal G h2op = 0.48) narrow sense heritabilities and high coefficients of additive genetic variation estimated for some compounds. A comparison of Qst and Fst estimates suggest that variability in some of these traits may be due to selection. Importantly, there was no genetic by environment interaction in the expression of any of the quantitative chemical traits despite often significant site effects. These results provide evidence that natural selection has contributed to population divergence in PSMs in E. globulus, and identifies the formylated phloroglucinol compounds (particularly sideroxylonal) and a dominant oil, 1,8-cineole, as candidates for traits whose genetic architecture has been shaped by divergent selection. Additionally, as the genetic differences in these PSMs that influence community phenotypes is stable across environments, the role of plant genotype in structuring communities is strengthened and these genotypic differences may be relatively stable under global environmental changes

Phytochemical Activation of Nrf2 Protects Human Coronary Artery Endothelial Cells against an Oxidative Challenge

Activation of NF-E2-related factor 2 (Nrf2) is a potential therapeutic intervention against endothelial cell oxidative stress and associated vascular disease. We hypothesized that treatment with the phytochemicals in the patented dietary supplement Protandim would induce Nrf2 nuclear localization and phase II antioxidant enzyme protein in human coronary artery endothelial cells (HCAECs), protecting against an oxidant challenge in an Nrf2- dependent manner. Protandim treatment induced Nrf2 nuclear localization, and HO-1 (778% of control ± 82.25 P < 0.01), SOD1 (125.9% of control ± 6.05 P < 0.01), NQO1 (126% of control ± 6.5 P < 0.01), and GR (119.5% of control ± 7.00 P < 0.05) protein expression in HCAEC. Treatment of HCAEC with H2O2 induced apoptosis in 34% of cells while pretreatment with Protandim resulted in only 6% apoptotic cells (P < 0.01). Nrf2 silencing significantly decreased the Protandim-induced increase in HO-1 protein (P < 0.01). Nrf2 silencing also significantly decreased the protection afforded by Protandim against H2O2- induced apoptosis (P < 0.01 compared to no RNA, and P < 0.05 compared to control RNA). These results show that Protandim induces Nrf2 nuclear localization and antioxidant enzyme expression, and protection of HCAEC from an oxidative challenge is Nrf2 dependent