A classification of spherically symmetric spacetimes

A complete classification of locally spherically symmetric four-dimensional Lorentzian spacetimes is given in terms of their local conformal symmetries. The general solution is given in terms of canonical metric types and the associated conformal Lie algebras. The analysis is based upon the local conformal decomposition into 2+2 reducible spacetimes and the Petrov type. A variety of physically meaningful example spacetimes are discussed

Killing tensors in pp-wave spacetimes

The formal solution of the second order Killing tensor equations for the general pp-wave spacetime is given. The Killing tensor equations are integrated fully for some specific pp-wave spacetimes. In particular, the complete solution is given for the conformally flat plane wave spacetimes and we find that irreducible Killing tensors arise for specific classes. The maximum number of independent irreducible Killing tensors admitted by a conformally flat plane wave spacetime is shown to be six. It is shown that every pp-wave spacetime that admits an homothety will admit a Killing tensor of Koutras type and, with the exception of the singular scale-invariant plane wave spacetimes, this Killing tensor is irreducible.Comment: 18 page

Calcisponges have a ParaHox gene and dynamic expression of dispersed NK homeobox genes

This study was funded by the Sars Centre core budget to M. Adamska. Sequencing was performed at the Norwegian High Throughput Sequencing Centre funded by the Norwegian Research Council. O.M.R. and D.E.K.F. acknowledge support from the BBSRC and the School of Biology, University of St Andrews.Sponges are simple animals with few cell types, but their genomes paradoxically contain a wide variety of developmental transcription factors1,2,3,4, including homeobox genes belonging to the Antennapedia (ANTP) class5,6, which in bilaterians encompass Hox, ParaHox and NK genes. In the genome of the demosponge Amphimedon queenslandica, no Hox or ParaHox genes are present, but NK genes are linked in a tight cluster similar to the NK clusters of bilaterians5. It has been proposed that Hox and ParaHox genes originated from NK cluster genes after divergence of sponges from the lineage leading to cnidarians and bilaterians5,7. On the other hand, synteny analysis lends support to the notion that the absence of Hox and ParaHox genes in Amphimedon is a result of secondary loss (the ghost locus hypothesis)8. Here we analysed complete suites of ANTP-class homeoboxes in two calcareous sponges, Sycon ciliatum and Leucosolenia complicata. Our phylogenetic analyses demonstrate that these calcisponges possess orthologues of bilaterian NK genes (Hex, Hmx and Msx), a varying number of additional NK genes and one ParaHox gene, Cdx. Despite the generation of scaffolds spanning multiple genes, we find no evidence of clustering of Sycon NK genes. All Sycon ANTP-class genes are developmentally expressed, with patterns suggesting their involvement in cell type specification in embryos and adults, metamorphosis and body plan patterning. These results demonstrate that ParaHox genes predate the origin of sponges, thus confirming the ghost locus hypothesis8, and highlight the need to analyse the genomes of multiple sponge lineages to obtain a complete picture of the ancestral composition of the first animal genome.PostprintPeer reviewe

Conformal invariance: from Weyl to SO(2,d)

The present work deals with two different but subtilely related kinds of conformal mappings: Weyl rescaling in $d>2$ dimensional spaces and SO(2,d) transformations. We express how the difference between the two can be compensated by diffeomorphic transformations. This is well known in the framework of String Theory but in the particular case of $d=2$ spaces. Indeed, the Polyakov formalism describes world-sheets in terms of two-dimensional conformal field theory. On the other hand, B. Zumino had shown that a classical four-dimensional Weyl-invariant field theory restricted to live in Minkowski space leads to an SO(2,4)-invariant field theory. We extend Zumino's result to relate Weyl and SO(2,d) symmetries in arbitrary conformally flat spaces (CFS). This allows us to assert that a classical $SO(2,d)$-invariant field does not distinguish, at least locally, between two different $d$-dimensional CFSs.Comment: 5 pages, no figures. There are slight modifications to match with the published versio

Synchronisation in networks of delay-coupled type-I excitable systems

We use a generic model for type-I excitability (known as the SNIPER or SNIC model) to describe the local dynamics of nodes within a network in the presence of non-zero coupling delays. Utilising the method of the Master Stability Function, we investigate the stability of the zero-lag synchronised dynamics of the network nodes and its dependence on the two coupling parameters, namely the coupling strength and delay time. Unlike in the FitzHugh-Nagumo model (a model for type-II excitability), there are parameter ranges where the stability of synchronisation depends on the coupling strength and delay time. One important implication of these results is that there exist complex networks for which the adding of inhibitory links in a small-world fashion may not only lead to a loss of stable synchronisation, but may also restabilise synchronisation or introduce multiple transitions between synchronisation and desynchronisation. To underline the scope of our results, we show using the Stuart-Landau model that such multiple transitions do not only occur in excitable systems, but also in oscillatory ones.Comment: 10 pages, 9 figure

Measurement of the in-flight pusher density of an indirect drive capsule implosion core using x-ray backlighting

Both the efficiency of an implosion and the growth rate of hydrodynamic instability increase with the aspect ratio of an implosion. In order to study the physics of implosions with high Rayleigh-Taylor growth factors, we use doped ablators which should minimize x-ray preheat and shell decompression, and hence increase in- flight aspect ratio. We use x-ray backlighting techniques to image the indirectly-driven capsules. We record backlit 4.7 KeV images of the full capsule throughout the implosion phase with 55 ps and 15{mu}m resolution. We use these images to measure the in-flight aspect ratios for doped ablators, and we infer the radial density profile as a function of time by Abel inverting the transmission profiles

Rapid genotype imputation from sequence without reference panels

Inexpensive genotyping methods are essential for genetic studies requiring large sample sizes. In human studies, array-based microarrays and high-density haplotype reference panels allow efficient genotype imputation for this purpose. However, these resources are typically unavailable in non-human settings. Here we describe a method (STITCH) for imputation based only on sequencing read data, without requiring additional reference panels or array data. We demonstrate its applicability even in settings of extremely low sequencing coverage, by accurately imputing 5.7 million SNPs at a mean r(2) value of 0.98 in 2,073 outbred laboratory mice (0.15× sequencing coverage). In a sample of 11,670 Han Chinese (1.7× coverage), we achieve accuracy similar to that of alternative approaches that require a reference panel, demonstrating that our approach can work for genetically diverse populations. Our method enables straightforward progression from low-coverage sequence to imputed genotypes, overcoming barriers that at present restrict the application of genome-wide association study technology outside humans

Inequality, Fiscal Capacity and the Political Regime: Lessons from the Post-Communist Transition

Using panel data for twenty-seven post-communist economies between 1987-2003, we examine the nexus of relationships between inequality, fiscal capacity (defined as the ability to raise taxes efficiently) and the political regime. Investigating the impact of political reform we find that full political freedom is associated with lower levels of income inequality. Under more oligarchic (authoritarian) regimes, the level of inequality is conditioned by the state’s fiscal capacity. Specifically, oligarchic regimes with more developed fiscal systems are able to defend the prevailing vested interests at a lower cost in terms of social injustice. This empirical finding is consistent with the model developed by Acemoglu (2006). We also find that transition countries undertaking early macroeconomic stabilisation now enjoy lower levels of inequality; we confirm that education fosters equality and the suggestion of Commander et al (1999) that larger countries are prone to higher levels of inequality.http://deepblue.lib.umich.edu/bitstream/2027.42/57211/1/wp831 .pd

Impact of shortened crop rotation of oilseed rape on soil and rhizosphere microbial diversity in relation to yield decline

Oilseed rape (OSR) grown in monoculture shows a decline in yield relative to virgin OSR of up to 25%, but the mechanisms responsible are unknown. A long term field experiment of OSR grown in a range of rotations with wheat was used to determine whether shifts in fungal and bacterial populations of the rhizosphere and bulk soil were associated with the development of OSR yield decline. The communities of fungi and bacteria in the rhizosphere and bulk soil from the field experiment were profiled using terminal restriction fragment length polymorphism (TRFLP) and sequencing of cloned internal transcribed spacer regions and 16S rRNA genes, respectively. OSR cropping frequency had no effect on rhizosphere bacterial communities. However, the rhizosphere fungal communities from continuously grown OSR were significantly different to those from other rotations. This was due primarily to an increase in abundance of two fungi which showed 100% and 95% DNA identity to the plant pathogens Olpidium brassicae and Pyrenochaeta lycopersici, respectively. Real-time PCR confirmed that there was significantly more of these fungi in the continuously grown OSR than the other rotations. These two fungi were isolated from the field and used to inoculate OSR and Brassica oleracea grown under controlled conditions in a glasshouse to determine their effect on yield. At high doses, Olpidium brassicae reduced top growth and root biomass in seedlings and reduced branching and subsequent pod and seed production. Pyrenochaeta sp. formed lesions on the roots of seedlings, and at high doses delayed flowering and had a negative impact on seed quantity and quality