On the construction of nested space-filling designs

Nested space-filling designs are nested designs with attractive low-dimensional stratification. Such designs are gaining popularity in statistics, applied mathematics and engineering. Their applications include multi-fidelity computer models, stochastic optimization problems, multi-level fitting of nonparametric functions, and linking parameters. We propose methods for constructing several new classes of nested space-filling designs. These methods are based on a new group projection and other algebraic techniques. The constructed designs can accommodate a nested structure with an arbitrary number of layers and are more flexible in run size than the existing families of nested space-filling designs. As a byproduct, the proposed methods can also be used to obtain sliced space-filling designs that are appealing for conducting computer experiments with both qualitative and quantitative factors.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1229 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Chemical Evolution of the Juvenile Universe

Only massive stars contribute to the chemical evolution of the juvenile universe corresponding to [Fe/H]<-1.5. If Type II supernovae (SNe II) are the only relevant sources, then the abundances in the interstellar medium of the juvenile epoch are simply the sum of different SN II contributions. Both low-mass (~8-11M_sun) and normal (~12-25M_sun) SNe II produce neutron stars, which have intense neutrino-driven winds in their nascent stages. These winds produce elements such as Sr, Y, and Zr through charged-particle reactions (CPR). Such elements are often called the light r-process elements, but are considered here as products of CPR and not the r-process. The observed absence of production of the low-A elements (Na through Zn including Fe) when the true r-process elements (Ba and above) are produced requires that only low-mass SNe II be the site if the r-process occurs in SNe II. Normal SNe II produce the CPR elements in addition to the low-A elements. This results in a two-component model that is quantitatively successful in explaining the abundances of all elements relative to hydrogen for -3<[Fe/H]<-1.5. This model explicitly predicts that [Sr/Fe]>-0.32. Recent observations show that there are stars with [Sr/Fe]<-2 and [Fe/H]<-3. This proves that the two-component model is not correct and that a third component is necessary to explain the observations. This leads to a simple three-component model including low-mass and normal SNe II and hypernovae (HNe), which gives a good description of essentially all the data for stars with [Fe/H]<-1.5. We conclude that HNe are more important than normal SNe II in the chemical evolution of the low-A elements, in sharp distinction to earlier models. (Abridged)Comment: 10 pages, 9 figures, to appear in Pub. Astron. Soc. Australi

Probing r-Process Production of Nuclei Beyond Bi209 with Gamma Rays

We estimate gamma-ray fluxes due to the decay of nuclei beyond Bi209 from a supernova or a supernova remnant assuming that the r-process occurs in supernovae. We find that a detector with a sensitivity of about 10**(-7) photons/cm**2/s at energies of 40 keV to 3 MeV may detect fluxes due to the decay of Ra226, Th229, Am241, Am243, Cf249, and Cf251 in the newly discovered supernova remnant near Vela. In addition, such a detector may detect fluxes due to the decay of Ac227 and Ra228 produced in a future supernova at a distance of about 1 kpc. As nuclei with mass numbers A > 209 are produced solely by the r-process, such detections are the best proof for a supernova r-process site. Further, they provide the most direct information on yields of progenitor nuclei with A > 209 at r-process freeze-out. Finally, detection of fluxes due to the decay of r-process nuclei over a range of masses from a supernova or a supernova remnant provides the opportunity to compare yields in a single supernova event with the solar r-process abundance pattern.Comment: 24 pages, 3 figures, to appear in the October 10, 1999 issue of Ap

High Fill-Out, Extreme Mass Ratio Overcontact Binary Systems. X. The new discovered binary XY Leonis Minoris

The new discovered short-period close binary star, XY LMi, was monitored photometrically since 2006. It is shown that the light curves are typical EW-type and show complete eclipses with an eclipse duration of about 80 minutes. By analyzing the complete B, V, R, and I light curves with the 2003 version of the W-D code, photometric solutions were determined. It is discovered that XY LMi is a high fill-out, extreme mass ratio overcontact binary system with a mass ratio of q=0.148 and a fill-out factor of f=74.1%, suggesting that it is on the late evolutionary stage of late-type tidal-locked binary stars. As observed in other overcontact binary stars, evidence for the presence of two dark spots on both components are given. Based on our 19 epoches of eclipse times, it is found that the orbital period of the overcontact binary is decreasing continuously at a rate of dP/dt=-1.67\times10^{-7}\,days/year, which may be caused by the mass transfer from the primary to the secondary or/and angular momentum loss via magnetic stellar wind. The decrease of the orbital period may result in the increase of the fill-out, and finally, it will evolve into a single rapid-rotation star when the fluid surface reaching the outer critical Roche Lobe.Comment: 19 pages, 4 figures, 9 table

Criticality and Continuity of Explosive Site Percolation in Random Networks

This Letter studies the critical point as well as the discontinuity of a class of explosive site percolation in Erd\"{o}s and R\'{e}nyi (ER) random network. The class of the percolation is implemented by introducing a best-of-m rule. Two major results are found: i). For any specific $m$, the critical percolation point scales with the average degree of the network while its exponent associated with $m$ is bounded by -1 and $\sim-0.5$. ii). Discontinuous percolation could occur on sparse networks if and only if $m$ approaches infinite. These results not only generalize some conclusions of ordinary percolation but also provide new insights to the network robustness.Comment: 5 pages, 5 figure