An improved lower bound for (1,<=2)-identifying codes in the king grid

We call a subset $C$ of vertices of a graph $G$ a $(1,\leq \ell)$-identifying code if for all subsets $X$ of vertices with size at most $\ell$, the sets $\{c\in C |\exists u \in X, d(u,c)\leq 1\}$ are distinct. The concept of identifying codes was introduced in 1998 by Karpovsky, Chakrabarty and Levitin. Identifying codes have been studied in various grids. In particular, it has been shown that there exists a $(1,\leq 2)$-identifying code in the king grid with density 3/7 and that there are no such identifying codes with density smaller than 5/12. Using a suitable frame and a discharging procedure, we improve the lower bound by showing that any $(1,\leq 2)$-identifying code of the king grid has density at least 47/111

Continuous and discrete models of cooperation in complex bacterial colonies

We study the effect of discreteness on various models for patterning in bacterial colonies. In a bacterial colony with branching pattern, there are discrete entities - bacteria - which are only two orders of magnitude smaller than the elements of the macroscopic pattern. We present two types of models. The first is the Communicating Walkers model, a hybrid model composed of both continuous fields and discrete entities - walkers, which are coarse-graining of the bacteria. Models of the second type are systems of reaction diffusion equations, where the branching of the pattern is due to non-constant diffusion coefficient of the bacterial field. The diffusion coefficient represents the effect of self-generated lubrication fluid on the bacterial movement. We implement the discreteness of the biological system by introducing a cutoff in the growth term at low bacterial densities. We demonstrate that the cutoff does not improve the models in any way. Its only effect is to decrease the effective surface tension of the front, making it more sensitive to anisotropy. We compare the models by introducing food chemotaxis and repulsive chemotactic signaling into the models. We find that the growth dynamics of the Communication Walkers model and the growth dynamics of the Non-Linear diffusion model are affected in the same manner. From such similarities and from the insensitivity of the Communication Walkers model to implicit anisotropy we conclude that the increased discreteness, introduced be the coarse-graining of the walkers, is small enough to be neglected.Comment: 16 pages, 10 figures in 13 gif files, to be published in proceeding of CMDS

First-principles thermoelasticity of bcc iron under pressure

We investigate the elastic and isotropic aggregate properties of ferromagnetic bcc iron as a function of temperature and pressure by computing the Helmholtz free energies for the volume-conserving strained structures using the first-principles linear response linear-muffin-tin-orbital method and the generalized-gradient approximation. We include the electronic excitation contributions to the free energy from the band structures, and phonon contributions from quasi-harmonic lattice dynamics. We make detailed comparisons between our calculated elastic moduli and their temperature and pressure dependences with available experimental and theoretical data.Comment: 5 figures, 2 table

Viscosity of Colloidal Suspensions

Simple expressions are given for the Newtonian viscosity $\eta_N(\phi)$ as well as the viscoelastic behavior of the viscosity $\eta(\phi,\omega)$ of neutral monodisperse hard sphere colloidal suspensions as a function of volume fraction $\phi$ and frequency $\omega$ over the entire fluid range, i.e., for volume fractions $0 < \phi < 0.55$. These expressions are based on an approximate theory which considers the viscosity as composed as the sum of two relevant physical processes: $\eta (\phi,\omega) = \eta_{\infty}(\phi) + \eta_{cd}(\phi,\omega)$, where $\eta_{\infty}(\phi) = \eta_0 \chi(\phi)$ is the infinite frequency (or very short time) viscosity, with $\eta_0$ the solvent viscosity, $\chi(\phi)$ the equilibrium hard sphere radial distribution function at contact, and $\eta_{cd}(\phi,\omega)$ the contribution due to the diffusion of the colloidal particles out of cages formed by their neighbors, on the P\'{e}clet time scale $\tau_P$, the dominant physical process in concentrated colloidal suspensions. The Newtonian viscosity $\eta_N(\phi) = \eta(\phi,\omega = 0)$ agrees very well with the extensive experiments of Van der Werff et al and others. Also, the asymptotic behavior for large $\omega$ is of the form $\eta_{\infty}(\phi) + A(\phi)(\omega \tau_P)^{-1/2}$, in agreement with these experiments, but the theoretical coefficient $A(\phi)$ differs by a constant factor $2/\chi(\phi)$ from the exact coefficient, computed from the Green-Kubo formula for $\eta(\phi,\omega)$. This still enables us to predict for practical purposes the visco-elastic behavior of monodisperse spherical colloidal suspensions for all volume fractions by a simple time rescaling.Comment: 51 page

An Update on the 0Z Project

We give an update on our 0Z Survey to find more extremely metal poor (EMP) stars with [Fe/H] < -3 dex through mining the database of the Hamburg/ESO Survey. We present the most extreme such stars we have found from ~1550 moderate resolution follow up spectra. One of these, HE1424-0241, has highly anomalous abundance ratios not seen in any previously known halo giant, with very deficient Si, moderately deficient Ca and Ti, highly enhanced Mn and Co, and low C, all with respect to Fe. We suggest a SNII where the nucleosynthetic yield for explosive alpha-burning nuclei was very low compared to that for the hydrostatic alpha-burning element Mg, which is normal in this star relative to Fe. A second, less extreme, outlier star with high [Sc/Fe] has also been found. We examine the extremely metal-poor tail of the HES metallicity distribution function (MDF). We suggest on the basis of comparison of our high resolution detailed abundance analyses with [Fe/H](HES) for stars in our sample that the MDF inferred from follow up spectra of the HES sample of candidate EMP stars is heavily contaminated for [Fe/H](HES) < -3 dex; many of the supposed EMP stars below that metallicity are of substantially higher Fe-metallicity, including most of the very C-rich stars, or are spurious objects.Comment: to appear in conference proceedings "First Stars III", ed. B. O'Shea, A. Heger & T.Abel, 4 pages, 2 figure

Self-adjusting advertisement of cache indicators with bandwidth constraints

Cache advertisements reduce the access cost by allowing users to skip the cache when it does not contain their datum. Such advertisements are used in multiple networked domains such as 5G networks, wide area networks, and information-centric networking. The selection of an advertisement strategy exposes a trade-off between the access cost and bandwidth consumption. Still, existing works mostly apply a trial-and-error approach for selecting the best strategy, as the rigorous foundations required for optimizing such decisions is lacking.Our work shows that the desired advertisement policy depends on numerous parameters such as the cache policy, the workload, the cache size, and the available bandwidth. In particular, we show that there is no ideal single configuration. Therefore, we design an adaptive, self-adjusting algorithm that periodically selects an advertisement policy. Our algorithm does not require any prior information about the cache policy, cache size, or work-load, and does not require any apriori configuration. Through extensive simulations, using several state-of-the-art cache policies, and real workloads, we show that our approach attains a similar cost to that of the best static configuration (which is only identified in retrospect) in each case

Shock Geometry and Spectral Breaks in Large SEP Events

Solar energetic particle (SEP) events are traditionally classified as "impulsive" or "gradual." It is now widely accepted that in gradual SEP events, particles are accelerated at coronal mass ejection-driven (CME-driven) shocks. In many of these large SEP events, particle spectra exhibit double power law or exponential rollover features, with the break energy or rollover energy ordered as (Q/A)^α, with Q being the ion charge in e and A the ion mass in units of proton mass m_p . This Q/A dependence of the spectral breaks provides an opportunity to study the underlying acceleration mechanism. In this paper, we examine how the Q/A dependence may depend on shock geometry. Using the nonlinear guiding center theory, we show that α ~ 1/5 for a quasi-perpendicular shock. Such a weak Q/A dependence is in contrast to the quasi-parallel shock case where α can reach 2. This difference in α reflects the difference of the underlying parallel and perpendicular diffusion coefficients κ_(||) and κ ⊥. We also examine the Q/A dependence of the break energy for the most general oblique shock case. Our analysis offers a possible way to remotely examine the geometry of a CME-driven shock when it is close to the Sun, where the acceleration of particle to high energies occurs