Spacetime Groups

A spacetime group is a connected 4-dimensional Lie group G endowed with a left invariant Lorentz metric h and such that the connected component of the isometry group of h is G itself. The Newman-Penrose formalism is used to give an algebraic classification of spacetime groups, that is, we determine a complete list of inequivalent spacetime Lie algebras, which are pairs, (g, n), with g being a 4-dimensional Lie algebra and n being a Lorentzian inner product on g. A full analysis of the equivalence problem for spacetime Lie algebras is given which leads to a completely algorithmic solution to the problem of determining when two spacetime Lie algebras are isomorphic. The utility of our classification is demonstrated by a number of applications. The results of a detailed study of the Einstein field equations for various matter fields on spacetime groups are given, which resolve a number of open cases in the literature. The possible Petrov types of spacetime groups that, generically, are algebraically special are completely characterized. Several examples of conformally Einstein spacetime groups are exhibited. Finally, we describe some novel features of a software package created to support the computations and applications of this paper

The DifferentialGeometry Package

This is the entire DifferentialGeometry package, a zip file (DifferentialGeometry.zip) containing (1) a Maple Library file, DifferentialGeometryUSU.mla, (2) a Maple help file DifferentialGeometry.help, (3) a Maple Library file, DGApplicatons.mla. This is the latest version of the DifferentialGeometry software; it supersedes what is released with Maple. Installation instruction

A New Non-Inheriting Homogeneous Solution of the Einstein-Maxwell Equations with Cosmological Term

We find a new homogeneous solution to the Einstein-Maxwell equations with a cos- mological term. The spacetime manifold is R × S3. The spacetime metric admits a simply transitive isometry group G = R × SU(2) and is Petrov type I. The spacetime is geodesically complete and globally hyperbolic. The electromagnetic field is non- null and non-inheriting: it is only invariant with respect to the SU(2) subgroup and is time-dependent in a stationary reference frame

The importance of DNA methylation in prostate cancer development.

After briefly reviewing the nature of DNA methylation, its general role in cancer and the tools available to interrogate it, we consider the literature surrounding DNA methylation as relating to prostate cancer. Specific consideration is given to recurrent alterations. A list of frequently reported genes is synthesized from 17 studies that have reported on methylation changes in malignant prostate tissue, and we chart the timing of those changes in the diseases history through amalgamation of several previously published data sets. We also review associations with genetic alterations and hormone signalling, before the practicalities of investigating prostate cancer methylation using cell lines are assessed. We conclude by outlining the interplay between DNA methylation and prostate cancer metabolism and their regulation by androgen receptor, with a specific discussion of the mitochondria and their associations with DNA methylation.CEM is funded by an ERC grant. IGM is supported in Oslo by funding from the Norwegian Research Council, Helse Sor-Ost and the University of Oslo through the Centre for Molecular Medicine (Norway), which is a part of the Nordic EMBL (European Molecular Biology Laboratory) partnership. IGM holds a visiting scientist position with Cancer Research UK through the Cambridge Research Institute and a Senior Honorary Visiting Research Fellowship with Cambridge University through the Department of Oncology. IGM is supported in Belfast by the Belfast-Manchester Movember Centre of Excellence (CE013_2-004), funded in partnership with Prostate Cancer UK. AGL is supported by a Cancer Research UK programme grant (C14303/A20406) to Simon Tavaré and by the European Commission through the Horizon 2020 project SOUND (Grant Agreement no. 633974). CEM and AGL acknowledge the support of the University of Cambridge, Cancer Research UK and Hutchison Whampoa Limited.This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.jsbmb.2016.04.00

Terrain classification using circular polarimetric features

Conventional representations of polarization response are referred to a horizontally and vertically polarized basis. Recent studies by Freeman and Durden, van Zyl, and others suggest that alternative polarimetric features which more easily resolve the contributions of simple scattering mechanisms such as odd-bounce, even-bounce, and diffuse scattering could offer several advantages in terrain classification. The circular polarization covariance matrix is a potential source of such features. In this paper, we derive its relationship to the Stokes matrix, describe some of its properties, and compare the utility of linear and circular polarimetric features in classifying an AIRSAR scene containing urban, park, and ocean terrain

Radiation damage to nucleoprotein complexes in macromolecular crystallography

Significant progress has been made in macromolecular crystallography over recent years in both the understanding and mitigation of X-ray induced radiation damage when collecting diffraction data from crystalline proteins. In contrast, despite the large field that is productively engaged in the study of radiation chemistry of nucleic acids, particularly of DNA, there are currently very few X-ray crystallographic studies on radiation damage mechanisms in nucleic acids. Quantitative comparison of damage to protein and DNA crystals separately is challenging, but many of the issues are circumvented by studying pre-formed biological nucleoprotein complexes where direct comparison of each component can be made under the same controlled conditions. Here a model protein-DNA complex C.Esp1396I is employed to investigate specific damage mechanisms for protein and DNA in a biologically relevant complex over a large dose range (2.07-44.63 MGy). In order to allow a quantitative analysis of radiation damage sites from a complex series of macromolecular diffraction data, a computational method has been developed that is generally applicable to the field. Typical specific damage was observed for both the protein on particular amino acids and for the DNA on, for example, the cleavage of base-sugar N1-C and sugar-phosphate C-O bonds. Strikingly the DNA component was determined to be far more resistant to specific damage than the protein for the investigated dose range. At low doses the protein was observed to be susceptible to radiation damage while the DNA was far more resistant, damage only being observed at significantly higher doses

Group Invariant Solutions Without Transversality

We present a generalization of Lie\u27s method for finding the group invariant solutions to a system of partial differential equations. Our generalization relaxes the standard transversality assumption and encompasses the common situation where the reduced differential equations for the group invariant solutions involve both fewer dependent and independent variables. The theoretical basis for our method is provided by a general existence theorem for the invariant sections, both local and global, of a bundle on which a finite dimensional Lie group acts. A simple and natural extension of our characterization of invariant sections leads to an intrinsic characterization of the reduced equations for the group invariant solutions for a system of differential equations. The characterization of both the invariant sections and the reduced equations are summarized schematically by the kinematic and dynamic reduction diagrams and are illustrated by a number of examples from fluid mechanics, harmonic maps, and general relativity. This work also provides the theoretical foundations for a further detailed study of the reduced equations for group invariant solutions

Sub-seismic scale folding and thrusting within an exposed mass transport deposit : A case study from NW Argentina

This work was carried out with support from CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) - Brazil, BG - Brazil and the University of Aberdeen. We would like to thank the following geologists for their support, camaraderie and countless hours of fieldwork: Arthur Giovannini, Claus Fallgatter, Victoria Valdez, Qun Liu, Carla Puigdomenech, Guilherme Bozetti and Roberto Noll Filho. We thank Christopher Jackson and an anonymous reviewer, whose constructive comments and criticism helped to improve the manuscript.Peer reviewedPostprin

Symmetric Criticality in Classical Field Theory

This is a brief overview of work done by Ian Anderson, Mark Fels, and myself on symmetry reduction of Lagrangians and Euler-Lagrange equations, a subject closely related to Palais’ Principle of Symmetric Criticality. After providing a little history, I describe necessary and sufficient conditions on a group action such that reduction of a group-invariant Lagrangian by the symmetry group yields the correct symmetry-reduced Euler-Lagrange equations