Relative categories: Another model for the homotopy theory of homotopy theories

We lift Charles Rezk's complete Segal space model structure on the category of simplicial spaces to a Quillen equivalent one on the category of relative categories.Comment: 27 pages. Updated to correct typographical error

Declining Rotation Curve and Brown Dwarf MACHOs

If the Galactic rotation speed at the Solar circle is $\sim 200$ km s$^{-1}$ or smaller, which is supported by several recent studies, the rotation curve of the Galaxy could be declining in the outermost region. Motivated by this, we investigate the effect of such declining rotation curve on the estimate of the MACHO mass and the fractional contribution of the MACHOs to the Galactic dark halo. Using Hernquist and Plummer halo models instead of the standard halo model, we find that the MACHO mass could be significantly smaller than that for the standard halo case. In particular, there exists a certain set of halo parameters for which the MACHO mass is 0.1$M_\odot$ or less and at the same time the MACHO contribution to the total mass of the halo is almost 100 %. This result indicates that a halo which consists solely of brown dwarfs can be consistent with both of the observed microlensing properties and the constraints from the rotation curve, provided the outer rotation curve is indeed declining.Comment: 8 pages and 4 figures, accepted for publication in ApJ Letter

Order statistics and the linear assignment problem

Under mild conditions on the distribution functionF, we analyze the asymptotic behavior in expectation of the smallest order statistic, both for the case thatF is defined on (–, +) and for the case thatF is defined on (0, ). These results yield asymptotic estimates of the expected optiml value of the linear assignment problem under the assumption that the cost coefficients are independent random variables with distribution functionF.asymptotic analysis;linear assignment problem;order statistic

Stabilizing intrinsic defects in SnO2_{2}

TThe magnetism and electronic structure of Li-doped SnO$_{2}$ are investigated using first-principles LDA/LDA$+U$ calculations. We find that Li induces magnetism in SnO$_{2}$ when doped at the Sn site but becomes non-magnetic when doped at the O and interstitial sites. The calculated formation energies show that Li prefers the Sn site as compared with the O site, in agreement with previous experimental works. The interaction of Li with native defects (Sn V$_\mathrm{Sn}$ and O V$_\mathrm{O}$ vacancies) is also studied, and we find that Li not only behaves as a spin polarizer, but also a vacancy stabilizer, i.e. Li significantly reduces the defect formation energies of the native defects and helps the stabilization of magnetic oxygen vacancies. The electronic densities of states reveals that these systems, where the Fermi level touches the conduction (valence) band, are non-magnetic (magnetic).cancies. The electronic densities of states reveal that those systems, where the Fermi levels touch the conduction (valence) band, are non-magnetic (magnetic).Comment: Phys. Rev. B (2013), Accepte