The airborne lava-seawater interaction plume at Kilauea Volcano, Hawaii

Petrology igneous metamorphic and volcanic studies; medm0

Fidelity threshold for long-range entanglement in quantum networks

We present a strategy to generate long-range entanglement in noisy quantum networks. We consider a cubic lattice whose bonds are partially entangled mixed states of two qubits, and where quantum operations can be applied perfectly at the nodes. In contrast to protocols designed for one- or two-dimensional regular lattices, we find that entanglement can be created between arbitrarily distant qubits if the fidelity of the bonds is higher than a critical value, independent of the system size. Therefore, we show that a constant overhead of local resources, together with connections of finite fidelity, is sufficient to achieve long-distance quantum communication in noisy networks.Comment: published versio

Models and seroepidemiology of co-existing virus strains

Imperial Users onl

Partitioning of light lithophile elements during basalt eruptions on Earth and application to Martian shergottites

An enigmatic record of light lithophile element (LLE) zoning in pyroxenes in basaltic shergottite meteorites, whereby LLE concentrations decrease dramatically from the cores to the rims, has been interpreted as being due to partitioning of LLE into a hydrous vapor during magma ascent to the surface on Mars. These trends are used as evidence that Martian basaltic melts are water-rich (McSween et al., 2001). Lithium and boron are light lithophile elements (LLE) that partition into volcanic minerals and into vapor from silicate melts, making them potential tracers of degassing processes during magma ascent to the surface of Earth and of other planets. While LLE degassing behavior is relatively well understood for silica-rich melts, where water and LLE concentrations are relatively high, very little data exists for LLE abundance, heterogeneity and degassing in basaltic melts. The lack of data hampers interpretation of the trends in the shergottite meteorites. Through a geochemical study of LLE, volatile and trace elements in olivine-hosted melt inclusions from Kilauea Volcano, Hawaii, it can be demonstrated that lithium behaves similarly to the light to middle rare Earth elements during melting, magma mixing and fractionation. Considerable heterogeneity in lithium and boron is inherited from mantle-derived primary melts, which is dominant over the fractionation and degassing signal. Lithium and boron are only very weakly volatile in basaltic melt erupted from Kilauea Volcano, with vapor-melt partition coefficients 4 wt%. The observed terrestrial LLE partitioning behavior is extrapolated to Martian primitive melts through modeling. The zoning observed in the shergottite pyroxenes is only consistent with degassing of LLE from a Martian melt near its liquidus temperature if the vapor-melt partition coefficient was an order of magnitude larger than observed on Earth. The range in LLE and trace elements observed in shergottite pyroxenes are instead consistent with concurrent mixing and fractionation of heterogeneous melts from the mantle.This work was funded by NERC through the Ion Microprobe facility (IMF grants IMF376/0509 and 429/0511).This is the accepted manuscript. The final version is available from Elsevier at http://dx.doi.org/10.1016/j.epsl.2014.11.03

Hypergraphic LP Relaxations for Steiner Trees

We investigate hypergraphic LP relaxations for the Steiner tree problem, primarily the partition LP relaxation introduced by Koenemann et al. [Math. Programming, 2009]. Specifically, we are interested in proving upper bounds on the integrality gap of this LP, and studying its relation to other linear relaxations. Our results are the following. Structural results: We extend the technique of uncrossing, usually applied to families of sets, to families of partitions. As a consequence we show that any basic feasible solution to the partition LP formulation has sparse support. Although the number of variables could be exponential, the number of positive variables is at most the number of terminals. Relations with other relaxations: We show the equivalence of the partition LP relaxation with other known hypergraphic relaxations. We also show that these hypergraphic relaxations are equivalent to the well studied bidirected cut relaxation, if the instance is quasibipartite. Integrality gap upper bounds: We show an upper bound of sqrt(3) ~ 1.729 on the integrality gap of these hypergraph relaxations in general graphs. In the special case of uniformly quasibipartite instances, we show an improved upper bound of 73/60 ~ 1.216. By our equivalence theorem, the latter result implies an improved upper bound for the bidirected cut relaxation as well.Comment: Revised full version; a shorter version will appear at IPCO 2010