Empirical analysis of the Lieb-Oxford bound in ions and molecules

Universal properties of the Coulomb interaction energy apply to all many-electron systems. Bounds on the exchange-correlation energy, inparticular, are important for the construction of improved density functionals. Here we investigate one such universal property -- the Lieb-Oxford lower bound -- for ionic and molecular systems. In recent work [J. Chem. Phys. 127, 054106 (2007)], we observed that for atoms and electron liquids this bound may be substantially tightened. Calculations for a few ions and molecules suggested the same tendency, but were not conclusive due to the small number of systems considered. Here we extend that analysis to many different families of ions and molecules, and find that for these, too, the bound can be empirically tightened by a similar margin as for atoms and electron liquids. Tightening the Lieb-Oxford bound will have consequences for the performance of various approximate exchange-correlation functionals.Comment: 8 pages, 3 color figure

The first high-density genetic map of common cockle (Cerastoderma edule) reveals a major QTL controlling shell color variation

Shell color shows broad variation within mollusc species and despite information on the genetic pathways involved in shell construction and color has recently increased, more studies are needed to understand its genetic architecture. The common cockle ( Cerastoderma edule) is a valuable species from ecological and commercial perspectives which shows important variation in shell color across Northeast Atlantic. In this study, we constructed a high-density genetic map, as a tool for screening common cockle genome, which was applied to ascertain the genetic basis of color variation in the species. The consensus genetic map comprised 19 linkage groups (LGs) in accordance with the cockle karyotype (2n = 38) and spanned 1073 cM, including 730 markers per LG and an inter-marker distance of 0.13 cM. Five full-sib families showing segregation for several color-associated traits were used for a genome-wide association study and a major QTL on chromosome 13 associated to different color-traits was detected. Mining on this genomic region revealed several candidate genes related to shell construction and color. A genomic region previously reported associated with divergent selection in cockle distribution overlapped with this QTL suggesting its putative role on adaptationInterreg Atlantic Area | Ref. EAPA_458/2016Ministerio de Economía, Industria y Competitividad | Ref. BES2016/078166Roslin Institute | Ref. BBS/E/D/20002172Roslin Institute | Ref. BBS/E/D/30002275Roslin Institute | Ref. BBS/E/D/1000207

Coloring random graphs online without creating monochromatic subgraphs

Consider the following random process: The vertices of a binomial random graph $G_{n,p}$ are revealed one by one, and at each step only the edges induced by the already revealed vertices are visible. Our goal is to assign to each vertex one from a fixed number $r$ of available colors immediately and irrevocably without creating a monochromatic copy of some fixed graph $F$ in the process. Our first main result is that for any $F$ and $r$, the threshold function for this problem is given by $p_0(F,r,n)=n^{-1/m_1^*(F,r)}$, where $m_1^*(F,r)$ denotes the so-called \emph{online vertex-Ramsey density} of $F$ and $r$. This parameter is defined via a purely deterministic two-player game, in which the random process is replaced by an adversary that is subject to certain restrictions inherited from the random setting. Our second main result states that for any $F$ and $r$, the online vertex-Ramsey density $m_1^*(F,r)$ is a computable rational number. Our lower bound proof is algorithmic, i.e., we obtain polynomial-time online algorithms that succeed in coloring $G_{n,p}$ as desired with probability $1-o(1)$ for any $p(n) = o(n^{-1/m_1^*(F,r)})$.Comment: some minor addition

Asymptotic Orbits in Barred Spiral Galaxies

We study the formation of the spiral structure of barred spiral galaxies, using an $N$-body model. The evolution of this $N$-body model in the adiabatic approximation maintains a strong spiral pattern for more than 10 bar rotations. We find that this longevity of the spiral arms is mainly due to the phenomenon of stickiness of chaotic orbits close to the unstable asymptotic manifolds originated from the main unstable periodic orbits, both inside and outside corotation. The stickiness along the manifolds corresponding to different energy levels supports parts of the spiral structure. The loci of the disc velocity minima (where the particles spend most of their time, in the configuration space) reveal the density maxima and therefore the main morphological structures of the system. We study the relation of these loci with those of the apocentres and pericentres at different energy levels. The diffusion of the sticky chaotic orbits outwards is slow and depends on the initial conditions and the corresponding Jacobi constant.Comment: 17 pages, 24 figure

Methods for Estimating Fluxes and Absorptions of Faint X-ray Sources

X-ray sources with very few counts can be identified with low-noise X-ray detectors such as ACIS onboard the Chandra X-ray Observatory. These sources are often too faint for parametric spectral modeling using well-established methods such as fitting with XSPEC. We discuss the estimation of apparent and intrinsic broad-band X-ray fluxes and soft X-ray absorption from gas along the line of sight to these sources, using nonparametric methods. Apparent flux is estimated from the ratio of the source count rate to the instrumental effective area averaged over the chosen band. Absorption, intrinsic flux, and errors on these quantities are estimated from comparison of source photometric quantities with those of high S/N spectra that were simulated using spectral models characteristic of the class of astrophysical sources under study. The concept of this method is similar to the long-standing use of color-magnitude diagrams in optical and infrared astronomy, with X-ray median energy replacing color index and X-ray source counts replacing magnitude. Our nonparametric method is tested against the apparent spectra of 2000 faint sources in the Chandra observation of the rich young stellar cluster in the M17 HII region. We show that the intrinsic X-ray properties can be determined with little bias and reasonable accuracy using these observable photometric quantities without employing often uncertain and time-consuming methods of non-linear parametric spectral modeling. Our method is calibrated for thermal spectra characteristic of stars in young stellar clusters, but recalibration should be possible for some other classes of faint X-ray sources such as extragalactic AGN.Comment: Accepted for publication in The Astrophysical Journal. 39 pages, 15 figure