A note on the Cops & Robber game on graphs embedded in non-orientable surfaces

The Cops and Robber game is played on undirected finite graphs. A number of cops and one robber are positioned on vertices and take turns in sliding along edges. The cops win if they can catch the robber. The minimum number of cops needed to win on a graph is called its cop number. It is known that the cop number of a graph embedded on a surface $X$ of genus $g$ is at most $3g/2 + 3$, if $X$ is orientable (Schroeder 2004), and at most $2g+1$, otherwise (Nowakowski & Schroeder 1997). We improve the bounds for non-orientable surfaces by reduction to the orientable case using covering spaces. As corollaries, using Schroeder's results, we obtain the following: the maximum cop number of graphs embeddable in the projective plane is 3; the cop number of graphs embeddable in the Klein Bottle is at most 4, and an upper bound is $3g/2 + 3/2$ for all other $g$.Comment: 5 pages, 1 figur

Hydrogen Sulfide and Radon in and Over the Western North Atlantic Ocean

Atmospheric measurements of radon and hydrogen sulfide, and seawater measurements of total sulfide, free sulfide, and carbonyl sulfide, were made on a cruise in the western North Atlantic Ocean (October 24 to November 9, 1989). Measured values for 222Rn ranged from 3 to 70 pCi m−3, those for atmospheric hydrogen sulfide from 1 to 85 parts per trillion, and those for dissolved total and free sulfide in seawater from 33 to 930 pmol L−1 and 0 to 73 pmol L−1, respectively. A positive correlation between 222Rn and atmospheric H2S was observed. Both 222Rn and H2S were high in air masses traced back to North America. Measurements in seawater showed that uncomplexed sulfides were approximately 13% of total sulfide at 2 m depth. Atmospheric H2S and dissolved H2S in seawater were usually not far from saturation equilibrium. Our results indicate that the ocean acted at some times as a source of atmospheric H2S but more frequently as a sink. Hydrolysis of COS and atmospheric deposition of H2S both may contribute to the budget of dissolved sulfide in seawater of the western North Atlantic Ocean. On a global scale the ocean/atmosphere exchange of H2S appears to play a minor role in the atmospheric sulfur cycle

Hitting all Maximal Independent Sets of a Bipartite Graph

We prove that given a bipartite graph G with vertex set V and an integer k, deciding whether there exists a subset of V of size k hitting all maximal independent sets of G is complete for the class Sigma_2^P.Comment: v3: minor chang

Nitrous oxide emissions from the Arabian Sea: A synthesis

We computed high-resolution (1º latitude x 1º longitude) seasonal and annual nitrous oxide (N2O) concentration fields for the Arabian Sea surface layer using a database containing more than 2400 values measured between December 1977 and July 1997. N2O concentrations are highest during the southwest (SW) monsoon along the southern Indian continental shelf. Annual emissions range from 0.33 to 0.70 Tg N2O and are dominated by fluxes from coastal regions during the SW and northeast monsoons. Our revised estimate for the annual N2O flux from the Arabian Sea is much more tightly constrained than the previous consensus derived using averaged in-situ data from a smaller number of studies. However, the tendency to focus on measurements in locally restricted features in combination with insufficient seasonal data coverage leads to considerable uncertainties of the concentration fields and thus in the flux estimates, especially in the coastal zones of the northern and eastern Arabian Sea. The overall mean relative error of the annual N2O emissions from the Arabian Sea was estimated to be at least 65%

The Partial Visibility Representation Extension Problem

For a graph $G$, a function $\psi$ is called a \emph{bar visibility representation} of $G$ when for each vertex $v \in V(G)$, $\psi(v)$ is a horizontal line segment (\emph{bar}) and $uv \in E(G)$ iff there is an unobstructed, vertical, $\varepsilon$-wide line of sight between $\psi(u)$ and $\psi(v)$. Graphs admitting such representations are well understood (via simple characterizations) and recognizable in linear time. For a directed graph $G$, a bar visibility representation $\psi$ of $G$, additionally, puts the bar $\psi(u)$ strictly below the bar $\psi(v)$ for each directed edge $(u,v)$ of $G$. We study a generalization of the recognition problem where a function $\psi'$ defined on a subset $V'$ of $V(G)$ is given and the question is whether there is a bar visibility representation $\psi$ of $G$ with $\psi(v) = \psi'(v)$ for every $v \in V'$. We show that for undirected graphs this problem together with closely related problems are \NP-complete, but for certain cases involving directed graphs it is solvable in polynomial time.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Transport of North African dust from the Bodélé depression to the Amazon Basin: a case study

Through long-range transport of dust, the North-African desert supplies essential minerals to the Amazon rain forest. Since North African dust reaches South America mostly during the Northern Hemisphere winter, the dust sources active during winter are the main contributors to the forest. Given that the Bodélé depression area in southwestern Chad is the main winter dust source, a close link is expected between the Bodélé emission patterns and volumes and the mineral supply flux to the Amazon. <br><br> Until now, the particular link between the Bodélé and the Amazon forest was based on sparse satellite measurements and modeling studies. In this study, we combine a detailed analysis of space-borne and ground data with reanalysis model data and surface measurements taken in the central Amazon during the Amazonian Aerosol Characterization Experiment (AMAZE-08) in order to explore the validity and the nature of the proposed link between the Bodélé depression and the Amazon forest. <br><br> This case study follows the dust events of 11–16 and 18–27 February 2008, from the emission in the Bodélé over West Africa (most likely with contribution from other dust sources in the region) the crossing of the Atlantic Ocean, to the observed effects above the Amazon canopy about 10 days after the emission. The dust was lifted by surface winds stronger than 14 m s<sup>−1</sup>, usually starting early in the morning. The lofted dust, mixed with biomass burning aerosols over Nigeria, was transported over the Atlantic Ocean, and arrived over the South American continent. The top of the aerosol layer reached above 3 km, and the bottom merged with the boundary layer. The arrival of the dusty air parcel over the Amazon forest increased the average concentration of aerosol crustal elements by an order of magnitude

On the link between ocean biota emissions, aerosol, and maritime clouds: Airborne, ground, and satellite measurements off the coast of California

Surface, airborne, and satellite measurements over the eastern Pacific Ocean off the coast of California during the period between 2005 and 2007 are used to explore the relationship between ocean chlorophyll a, aerosol, and marine clouds. Periods of enhanced chlorophyll a and wind speed are coincident with increases in particulate diethylamine and methanesulfonate concentrations. The measurements indicate that amines are a source of secondary organic aerosol in the marine atmosphere. Subsaturated aerosol hygroscopic growth measurements indicate that the organic component during periods of high chlorophyll a and wind speed exhibit considerable water uptake ability. Increased average cloud condensation nucleus (CCN) activity during periods of increased chlorophyll a levels likely results from both size distribution and aerosol composition changes. The available data over the period of measurements indicate that the cloud microphysical response, as represented by either cloud droplet number concentration or cloud droplet effective radius, is likely influenced by a combination of atmospheric dynamics and aerosol perturbations during periods of high chlorophyll a concentrations

Additional global climate cooling by clouds due to ice crystal complexity

Ice crystal submicron structures have a large impact on the optical properties of cirrus clouds and consequently on their radiative effect. Although there is growing evidence that atmospheric ice crystals are rarely pristine, direct in situ observations of the degree of ice crystal complexity are largely missing. Here we show a comprehensive in situ data set of ice crystal complexity coupled with measurements of the cloud angular scattering functions collected during a number of observational airborne campaigns at diverse geographical locations. Our results demonstrate that an overwhelming fraction (between 61 % and 81 %) of atmospheric ice crystals sampled in the different regions contain mesoscopic deformations and, as a consequence, a similar flat and featureless angular scattering function is observed. A comparison between the measurements and a database of optical particle properties showed that severely roughened hexagonal aggregates optimally represent the measurements in the observed angular range. Based on this optical model, a new parameterization of the cloud bulk asymmetry factor was introduced and its effects were tested in a global climate model. The modelling results suggest that, due to ice crystal complexity, ice-containing clouds can induce an additional short-wave cooling effect of −1.12 W m2 on the top-of-the-atmosphere radiative budget that has not yet been considered

Seasonal variation of ozone deposition to a tropical rain forest in southwest Amazonia

International audienceWithin the project EUropean Studies on Trace gases and Atmospheric CHemistry as a contribution to Large-scale Biosphere-atmosphere experiment in Amazonia (LBA-EUSTACH), we performed tower-based eddy covariance measurements of O3 flux above an Amazonian primary rain forest at the end of the wet and dry season. Ozone deposition revealed distinct seasonal differences in the magnitude and diel variation. In the wet season, the rain forest was an effective O3 sink with a mean daytime (midday) maximum deposition velocity of 2.3 cm s?1, and a corresponding O3 flux of ?11 nmol m?2 s?1. At the end of the dry season, the ozone mixing ratio was about four times higher (up to maximum values of 80 ppb) than in the wet season, as a consequence of strong regional biomass burning activity. However, the typical maximum daytime deposition flux was very similar to the wet season. This results from a strong limitation of daytime O3 deposition due to reduced plant stomatal aperture as a response to large values of the specific humidity deficit. As a result, the average midday deposition velocity in the dry burning season was only 0.5 cm s?1. The large diel ozone variation caused large canopy storage effects that masked the true diel variation of ozone deposition mechanisms in the measured eddy covariance flux, and for which corrections had to be made. In general, stomatal aperture was sufficient to explain the largest part of daytime ozone deposition. However, during nighttime, chemical reaction with nitrogen monoxide (NO) was found to contribute substantially to the O3 sink in the rain forest canopy. Further contributions were from non-stomatal plant uptake and other processes that could not be clearly identified. Measurements, made simultaneously on a 22 years old cattle pasture enabled the spatially and temporally direct comparison of O3 dry deposition values from this site with typical vegetation cover of deforested land in southwest Amazonia to the results from the primary rain forest. The mean ozone deposition to the pasture was found to be systematically lower than that to the forest by 30% in the wet and 18% in the dry season