On tree-decompositions of one-ended graphs

A graph is one-ended if it contains a ray (a one way infinite path) and whenever we remove a finite number of vertices from the graph then what remains has only one component which contains rays. A vertex $v$ {\em dominates} a ray in the end if there are infinitely many paths connecting $v$ to the ray such that any two of these paths have only the vertex $v$ in common. We prove that if a one-ended graph contains no ray which is dominated by a vertex and no infinite family of pairwise disjoint rays, then it has a tree-decomposition such that the decomposition tree is one-ended and the tree-decomposition is invariant under the group of automorphisms. This can be applied to prove a conjecture of Halin from 2000 that the automorphism group of such a graph cannot be countably infinite and solves a recent problem of Boutin and Imrich. Furthermore, it implies that every transitive one-ended graph contains an infinite family of pairwise disjoint rays

Deuterium toward the WD0621-376 sight line: Results from the Far Ultraviolet Spectroscopic Explorer (FUSE) Mission

Far Ultraviolet Spectroscopic Explorer observations are presented for WD0621-376, a DA white dwarf star in the local interstellar medium (LISM) at a distance of about 78 pc. The data have a signal-to-noise ratio of about 20-40 per 20 km/s resolution element and cover the wavelength range 905-1187 \AA. LISM absorption is detected in the lines of D I, C II, C II*, C III, N I, N II, N III, O I, Ar I, and Fe II. This sight line is partially ionized, with an ionized nitrogen fraction of > 0.23. We determine the ratio $D/O = (3.9 \pm ^{1.3}_{1.0})\times 10^{-2}$ (2$\sigma$). Assuming a standard interstellar oxygen abundance, we derive ${\rm D/H} \approx 1. 3 \times 10^{-5}$. Using the value of N(H I) derived from EUVE data gives a similar D/H ratio. The D I/N I ratio is $(3.3 \pm ^{1.0}_{0.8})\times 10^{-1}$ (2$\sigma$).Comment: accepted for publication in the ApJ

A first-draft human protein-interaction map

BACKGROUND: Protein-interaction maps are powerful tools for suggesting the cellular functions of genes. Although large-scale protein-interaction maps have been generated for several invertebrate species, projects of a similar scale have not yet been described for any mammal. Because many physical interactions are conserved between species, it should be possible to infer information about human protein interactions (and hence protein function) using model organism protein-interaction datasets. RESULTS: Here we describe a network of over 70,000 predicted physical interactions between around 6,200 human proteins generated using the data from lower eukaryotic protein-interaction maps. The physiological relevance of this network is supported by its ability to preferentially connect human proteins that share the same functional annotations, and we show how the network can be used to successfully predict the functions of human proteins. We find that combining interaction datasets from a single organism (but generated using independent assays) and combining interaction datasets from two organisms (but generated using the same assay) are both very effective ways of further improving the accuracy of protein-interaction maps. CONCLUSIONS: The complete network predicts interactions for a third of human genes, including 448 human disease genes and 1,482 genes of unknown function, and so provides a rich framework for biomedical research

Early stage investing in green SMEs: the case of the UK

How might a Green New Deal be applied to the early stage financing of Cleantechs? Amidst rising interest and adoption of Green New Deals in the US, the paper explores the need for more focused policy to address early stage long horizon financing of Cleantechs. We argue that insufficient focus has been applied to early stage investing into these types of innovative SMEs that could lower CO2 emissions across a range of sectors (including renewable energy, recycling, advanced manufacturing, transport and bio-science). Adopting a resource complementarity lens and borrowing from transaction cost theory, we illustrate and build theory through longitudinal UK case studies. These demonstrate how government policy can scale-up through international collaboration public-private, principally venture capital, cofinance to facilitate cleantech innovation with potentially game changing impacts on reducing CO2 emissions in order to meet the Paris 2015 Climate Change targets

Dimension-Dependence of the Critical Exponent in Spherically Symmetric Gravitational Collapse

We study the critical behaviour of spherically symmetric scalar field collapse to black holes in spacetime dimensions other than four. We obtain reliable values for the scaling exponent in the supercritical region for dimensions in the range $3.5\leq D\leq 14$. The critical exponent increases monotonically to an asymptotic value at large $D$ of $\gamma\sim0.466$. The data is well fit by a simple exponential of the form: $\gamma \sim 0.466(1-e^{-0.408 D})$.Comment: 5 pages, including 7 figures New version contains more data points, one extra graph and more accurate error bars. No changes to result

AMR, stability and higher accuracy

Efforts to achieve better accuracy in numerical relativity have so far focused either on implementing second order accurate adaptive mesh refinement or on defining higher order accurate differences and update schemes. Here, we argue for the combination, that is a higher order accurate adaptive scheme. This combines the power that adaptive gridding techniques provide to resolve fine scales (in addition to a more efficient use of resources) together with the higher accuracy furnished by higher order schemes when the solution is adequately resolved. To define a convenient higher order adaptive mesh refinement scheme, we discuss a few different modifications of the standard, second order accurate approach of Berger and Oliger. Applying each of these methods to a simple model problem, we find these options have unstable modes. However, a novel approach to dealing with the grid boundaries introduced by the adaptivity appears stable and quite promising for the use of high order operators within an adaptive framework

The epsilon expansion at next-to-next-to-leading order with small imaginary chemical potential

We discuss chiral perturbation theory for two and three quark flavors in the epsilon expansion at next-to-next-to-leading order (NNLO) including a small imaginary chemical potential. We calculate finite-volume corrections to the low-energy constants $\Sigma$ and $F$ and determine the non-universal modifications of the theory, i.e., modifications that cannot be mapped to random matrix theory (RMT). In the special case of two quark flavors in an asymmetric box we discuss how to minimize the finite-volume corrections and non-universal modifications by an optimal choice of the lattice geometry. Furthermore we provide a detailed calculation of a special version of the massless sunset diagram at finite volume.Comment: 21 pages, 5 figure