On the multipacking number of grid graphs

In 2001, Erwin introduced broadcast domination in graphs. It is a variant of classical domination where selected vertices may have different domination powers. The minimum cost of a dominating broadcast in a graph $G$ is denoted $\gamma_b(G)$. The dual of this problem is called multipacking: a multipacking is a set $M$ of vertices such that for any vertex $v$ and any positive integer $r$, the ball of radius $r$ around $v$ contains at most $r$ vertices of $M$ . The maximum size of a multipacking in a graph $G$ is denoted mp(G). Naturally mp(G) $\leq \gamma_b(G)$. Earlier results by Farber and by Lubiw show that broadcast and multipacking numbers are equal for strongly chordal graphs. In this paper, we show that all large grids (height at least 4 and width at least 7), which are far from being chordal, have their broadcast and multipacking numbers equal

Helioseismology challenges models of solar convection

Convection is the mechanism by which energy is transported through the outermost 30% of the Sun. Solar turbulent convection is notoriously difficult to model across the entire convection zone where the density spans many orders of magnitude. In this issue of PNAS, Hanasoge et al. (2012) employ recent helioseismic observations to derive stringent empirical constraints on the amplitude of large-scale convective velocities in the solar interior. They report an upper limit that is far smaller than predicted by a popular hydrodynamic numerical simulation.Comment: Printed in the Proceedings of the National Academy of Sciences (2 pages, 1 figure). Available at http://www.pnas.org/cgi/doi/10.1073/pnas.120887510

IMAGES I, MD101: A coring cruise of the R/V Marion Dufresne in the North Atlantic Ocean and Norwegian Sea

IMAGES coordinated a first international cruise in June and July 1995 over the North Atlantic and Norwegian sea on board the French RN Mm'ion Dufresne (MD 10 I, Brest - Stornoway (Lewis Island) - St-Pierre - Azores - Marseille). Its main scientific objective was the collection of giant piston cores on rapidly sedimenting drifts and continental margins of the North Atlantic ocean and Norwegian Sea, along the track of the main thermohaline circulation. The cruise crossed the North-East Atlantic margins, the Feni Drift, the Scottish, North Faeroes and Norwegian margins (to nON), the Iceland South-East margins, the Gardar Drift, the NAMOC Channel, the Newfoundland margin, the Bermuda rise, the mid Atlantic ridge, and the Azores and Iberian margins. Additional objectives covered: - the contribution of Mediterranean waters to the North Atlantic intermediate waters, with 5 cores recovered across the slopes of the Iberian margin; - the evolution of the NAMOC channel, in the deep North-West Atlantic basin, in relation to the growths and decays of the Laurentide ice sheet (8 Kullenberg and gravity cores). This was the maiden cruise of the new Mm'ion Dujresne, just 2 weeks out from her Le Havre shipyard. The ship had a very small number of problems, taking into account the number of things which were not ready just a few days before the departure. Two days were lost for engine problems. 70 scientists, students and technicians from 22 institutions (13 countries) participated to at least one of the three legs. 43 cores (mean length over 30 meters) have been retrieved during the cruise, described and measured for magnetic susceptibility, p-wave velocity, y density and spectral light reflectance. The longest core, MD 95-2036 (52.64 m) was retrieved at 4461 m water depth on the Bermuda Rise. It covers about 150 kyr with a sedimentation rate over 30 cm/kyr. The Calypso corer worked properly, once a few problems encountered at the be"innin" of the cruise had been solved (i.e. sliced or imploded PVC liner). This report presents preliminary results, mostly obtained on board: core descriptions, physical properties and micro-paleontological stratigraphy. Color reflectance (between 40° and 55°N) and magnetic susceptibility (between 50° and 700N) have been used for direct tuning of the time scales by cyclo-stratigraphy in the precession and obliquity bands. Ocean-wide correlations have been established over the last 250 kyr

Chiral Perturbation Theory

An introduction to the methods and ideas of Chiral Perturbation Theory is presented in this talk. The discussion is illustrated with some phenomenological predictions that can be compared with available experimental results.Comment: 16 pages, 4 Postscript figures, uses epsf.sty. Talk presented at the International Conference on Particle Physics and Astrophysics in The Standard Model and Beyond, Bystra (Poland). Full Postscript file available at http://deneb.ugr.es/papers/ugft57.ps.g

Interpretation of Helioseismic Travel Times - Sensitivity to Sound Speed, Pressure, Density, and Flows

Time-distance helioseismology uses cross-covariances of wave motions on the solar surface to determine the travel times of wave packets moving from one surface location to another. We review the methodology to interpret travel-time measurements in terms of small, localized perturbations to a horizontally homogeneous reference solar model. Using the first Born approximation, we derive and compute 3D travel-time sensitivity (Fr\'echet) kernels for perturbations in sound-speed, density, pressure, and vector flows. While kernels for sound speed and flows had been computed previously, here we extend the calculation to kernels for density and pressure, hence providing a complete description of the effects of solar dynamics and structure on travel times. We treat three thermodynamic quantities as independent and do not assume hydrostatic equilibrium. We present a convenient approach to computing damped Green's functions using a normal-mode summation. The Green's function must be computed on a wavenumber grid that has sufficient resolution to resolve the longest lived modes. The typical kernel calculations used in this paper are computer intensive and require on the order of 600 CPU hours per kernel. Kernels are validated by computing the travel-time perturbation that results from horizontally-invariant perturbations using two independent approaches. At fixed sound-speed, the density and pressure kernels are approximately related through a negative multiplicative factor, therefore implying that perturbations in density and pressure are difficult to disentangle. Mean travel-times are not only sensitive to sound-speed, density and pressure perturbations, but also to flows, especially vertical flows. Accurate sensitivity kernels are needed to interpret complex flow patterns such as convection

A Simple Method to Reconstruct Firing Rates from Dendritic Calcium Signals

Calcium imaging using fluorescent reporters is the most widely used optical approach to investigate activity in intact neuronal circuits with single-cell resolution. Calcium signals, however, are often difficult to interpret, especially if the desired output quantity is membrane voltage or instantaneous firing rates. Combining dendritic intracellular electrophysiology and multi-photon calcium imaging in vivo, we recently investigated the relationship between optical signals recorded with the fluorescent calcium indicator Oregon Green BAPTA-1 (OGB-1) and spike output in principal neurons in the locust antennal lobe. We derived from these experiments a simple, empirical and easily adaptable method requiring minimal calibration to reconstruct firing rates from calcium signals with good accuracy and 50-ms temporal resolution

Hunting for Runaways from the Orion Nebula Cluster

We use Gaia DR2 to hunt for runaway stars from the Orion Nebula Cluster (ONC). We search a region extending 45{\deg} around the ONC and out to 1 kpc to find sources that overlapped in angular position with the cluster in the last ~10 Myr. We find ~17,000 runaway/walkaway candidates satisfy this 2D traceback condition. Most of these are expected to be contaminants, e.g., caused by Galactic streaming motions of stars at different distances. We thus examine six further tests to help identify real runaways, namely: (1) possessing young stellar object (YSO) colors and magnitudes based on Gaia optical photometry; (2) having IR excess consistent with YSOs based on 2MASS and WISE photometry; (3) having a high degree of optical variability; (4) having closest approach distances well constrained to within the cluster half-mass radius; (5) having ejection directions that avoid the main Galactic streaming contamination zone; and (6) having a required radial velocity (RV) for 3D overlap of reasonable magnitude (or, for the 7% of candidates with measured RVs, satisfying 3D traceback). Thirteen sources, not previously noted as Orion members, pass all these tests, while another twelve are similarly promising, except they are in the main Galactic streaming contamination zone. Among these 25 ejection candidates, ten with measured RVs pass the most restrictive 3D traceback condition. We present full lists of runaway/walkaway candidates, estimate the high-velocity population ejected from the ONC and discuss its implications for cluster formation theories via comparison with numerical simulations.Comment: 22 pages, 10 figures, and 5 tables. Accepted for publication in Ap

Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids

We study holomorphic Poisson manifolds and holomorphic Lie algebroids from the viewpoint of real Poisson geometry. We give a characterization of holomorphic Poisson structures in terms of the Poisson Nijenhuis structures of Magri-Morosi and describe a double complex which computes the holomorphic Poisson cohomology. A holomorphic Lie algebroid structure on a vector bundle $A\to X$ is shown to be equivalent to a matched pair of complex Lie algebroids $(T^{0,1}X,A^{1,0})$, in the sense of Lu. The holomorphic Lie algebroid cohomology of $A$ is isomorphic to the cohomology of the elliptic Lie algebroid $T^{0,1}X\bowtie A^{1,0}$. In the case when $(X,\pi)$ is a holomorphic Poisson manifold and $A=(T^*X)_\pi$, such an elliptic Lie algebroid coincides with the Dirac structure corresponding to the associated generalized complex structure of the holomorphic Poisson manifold.Comment: 29 pages, v2: paper split into two, part 1 of 2, v3: two references added, v4: final version to appear in International Mathematics Research Notice