Node-balancing by edge-increments

Suppose you are given a graph $G=(V,E)$ with a weight assignment $w:V\rightarrow\mathbb{Z}$ and that your objective is to modify $w$ using legal steps such that all vertices will have the same weight, where in each legal step you are allowed to choose an edge and increment the weights of its end points by $1$. In this paper we study several variants of this problem for graphs and hypergraphs. On the combinatorial side we show connections with fundamental results from matching theory such as Hall's Theorem and Tutte's Theorem. On the algorithmic side we study the computational complexity of associated decision problems. Our main results are a characterization of the graphs for which any initial assignment can be balanced by edge-increments and a strongly polynomial-time algorithm that computes a balancing sequence of increments if one exists.Comment: 10 page

Particle geochemistry in the Rainbow hydrothermal plume, Mid-Atlantic Ridge1

We report the analysis of 18 large volume (500-1500 L) in situ filtered samples of particulate material from the largest hydrothermal plume on the Mid-Atlantic Ridge, overlying the ultramafic-hosted Rainbow hydrothermal field at 36[deg] 14'N. Measured particulate iron concentrations reach 614 nM. High concentrations of particulate Fe oxyhydroxides result from the extremely high Fe concentration (~24 mM) and Fe/H2S ratio (~24) of the vent fluids, and persist to at least 10 km away from the vent site due to the advection of plume material with the ambient along-axis flow. Two of the nine pairs of pump deployments appear to have intercepted the buoyant or otherwise very young portion of the hydrothermal plume. These samples are characterized by anomalously (compared to neutrally buoyant plume samples) high concentrations of Mg, U, and chalcophile elements, and low concentrations of Mn, Ca, V, Y, and the rare earth elements (REE). Within the neutrally buoyant plume, elemental distributions are largely consistent with previously observed behaviors: preferential removal of chalcophile elements, conservative behavior of oxyanions (P, V, and U), and continuous scavenging of Y and the REE. This consistency is particularly significant in light of the underlying differences in fluid chemistry between Rainbow and other studied sites. Chalcophile elements are preferentially removed from the plume in the order Cd>Zn>Co>Cu. Phosphorus/iron and vanadium/iron ratios for the neutrally buoyant plume are consistent with global trends with respect to the concentration of dissolved phosphate in ambient seawater. Comparison of buoyant and neutrally buoyant plume ratios with data from hydrothermal sediments underlying the Rainbow plume (Cave et al., 2002) indicates, however, that while P/Fe ratios are indeed constant V/Fe ratios increase progressively from early stage plume particles to sediments. REE distributions in the buoyant and neutrally buoyant plume appear most consistent with a continuous scavenging process during dispersion through the water colum

Matching Algorithms Are Fast in Sparse Random Graphs

We present an improved average case analysis of the maximum cardinality matching problem. We show that in a bipartite or general random graph on n vertices, with high probability every non-maximum matching has an augmenting path of length O(log n). This implies that augmenting path algorithms like the Hopcroft–Karp algorithm for bipartite graphs and the Micali–Vazirani algorithm for general graphs, which have a worst case running time of O(m √ n), run in time O(m log n) with high probability, where m is the number of edges in the graph. Motwani proved these results for random graphs when the average degree is at least ln(n

Heat, volume and chemical fluxes from submarine venting: A synthesis of results from the Rainbow hydrothermal field, 36°N MAR

International audienceHigh-temperature hydrothermal activity occurs in all ocean basins and along ridge crests of all spreading rates. While it has long been recognized that the fluxes associated with such venting are large, precise quantification of their impact on ocean biogeochemistry has proved elusive. Here, we report a comprehensive study of heat, fluid and chemical fluxes from a single submarine hydrothermal field. To achieve this, we have exploited the integrating nature of the non-buoyant plume dispersing above the Rainbow hydrothermal field, a long-lived and tectonically hosted high-temperature vent site on the Mid-Atlantic Ridge. Our calculations yield heat and volume fluxes for high-temperature fluids exiting the seafloor of 0.5 GW and 450 L s −1 , together with accompanying chemical fluxes, for Fe, Mn and CH 4 of 10, 1 and 1 mol s −1 , respectively. Accompanying fluxes for 25 additional chemical species that are associated with Fe-rich plume particles have also been calculated as they are transported away from the Rainbow vent site before settling to the seabed. High-temperature venting has been found to recur at least once every 100 km along all slow-spreading ridges investigated to-date, with half of all known sites on the Mid-Atlantic Ridge occurring as long-lived and tectonically hosted systems. If these patterns persist along all slow-and ultraslow-spreading ridges, high-temperature venting of the kind reported here could account for 50% of the on-axis hydrothermal heat flux along 30,000 km of the 55,000 km global ridge crest

The effect of plume processes on the Fe-isotope composition of hydrothermally derived Fe in the deep ocean as inferred from the Rainbow vent site, Mid-Atlantic Ridge, 36,14'N

The Rainbow hydrothermal vent site, which is the largest known point source for dissolved Fe delivered to the deep North Atlantic ocean, has remained invariant in its Fe isotope composition over at least the past 16,000 years, based on analysis of metalliferous sediments beneath the plume. Because of the conservative behavior of Fe in the Rainbow plume, 56Fe values of particles in the neutrally buoyant plume (?0.18±0.05‰) and underlying sediments (?0.19±0.05‰) are indistinguishable from the 56Fe values of the high-temperature fluid sources (?0.23±0.04‰). Particles from the near-vent, buoyant stage of the plume, however, have higher 56Fe values (+0.15‰ to +1.20‰) relative to the original vent fluid, consistent with fractionation during oxidation of Fe(II)aq to Fe(III)aq. Isotope compositions become invariant in the plume once all Fe(II)aq is fully oxidized, preserving the original composition of the vent fluid. The constant Fe isotope compositions of the vent fluids over time implies that changes in seawater Fe isotope composition of the North Atlantic ocean, as they are recorded in Fe–Mn crusts, requires changes in the relative fluxes of Fe to the ocean