The orbit rigidity matrix of a symmetric framework

A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides a matrix representation for fully symmetric infinitesimal flexes, and fully symmetric stresses of symmetric frameworks. The orbit matrix is a true analog of the standard rigidity matrix for general frameworks, and its analysis gives important insights into questions about the flexibility and rigidity of classes of symmetric frameworks, in all dimensions. With this narrower focus on fully symmetric infinitesimal motions, comes the power to predict symmetry-preserving finite mechanisms - giving a simplified analysis which covers a wide range of the known mechanisms, and generalizes the classes of known mechanisms. This initial exploration of the properties of the orbit matrix also opens up a number of new questions and possible extensions of the previous results, including transfer of symmetry based results from Euclidean space to spherical, hyperbolic, and some other metrics with shared symmetry groups and underlying projective geometry.Comment: 41 pages, 12 figure

Asteroids in the Inner Solar System II - Observable Properties

This paper presents synthetic observations of long-lived, coorbiting asteroids of Mercury, Venus, the Earth and Mars. Our sample is constructed by taking the limiting semimajor axes, differential longitudes and inclinations for long-lived stability provided by simulations. The intervals are randomly populated with values to create initial conditions. These orbits are re-simulated to check that they are stable and then re-sampled every 2.5 years for 1 million years. The Mercurian sample contains only horseshoe orbits, the Martian sample only tadpoles. For both Venus and the Earth, the greatest concentration of objects on the sky occurs close to the classical Lagrange points at heliocentric ecliptic longitudes of 60 and 300 degrees. The distributions are broad especially if horseshoes are present in the sample. The full-width half maximum (FWHM) in heliocentric longitude for Venus is 325 degrees and for the Earth is 328 degrees. The mean and most common velocity of these coorbiting satellites coincides with the mean motion of the parent planet, but again the spread is wide with a FWHM for Venus of 27.8 arcsec/hr and for the Earth of 21.0 arcsec/hr. For Mars, the greatest concentration on the sky occurs at heliocentric ecliptic latitudes of 12 degrees. The peak of the velocity distribution occurs at 65 arcsec/hr, significantly less than the Martian mean motion, while its FWHM is 32.3 arcsec/hr. The case of Mercury is the hardest of all, as the greatest concentration occurs at heliocentric longitudes close to the Sun.Comment: 16 pages, 11 figures, Monthly Notices (in press). Higher quality figures available at http://www-thphys.physics.ox.ac.uk/users/WynEvans/home.htm

Political brand identity: an examination of the complexities of Conservative brand and internal market engagement during the 2010 UK General Election campaign

This paper seeks to build an understanding of the importance of internal communications when building a strong political brand. Using Kapferer’s brand prism as a conceptual framework, the paper explores UK Conservative Party members’ attitudes towards the development of the Conservative brand as personified by David Cameron. There are clear implications for political strategists as the findings suggest that it is crucial to engage the internal market in the co-creation of the marketing communications strategy for as brand evangelists they interpret the brand promise at the local level

Asteroids in the Inner Solar System I - Existence

Ensembles of in-plane and inclined orbits in the vicinity of the Lagrange points of the terrestrial planets are integrated for up to 100 million years. The integrations incorporate the gravitational effects of Sun and the eight planets (Pluto is neglected). Mercury is the least likely planet, as it is unable to retain tadpole orbits over 100 million year timescales. Both Venus and the Earth are much more promising, as they possess rich families of stable tadpole and horseshoe orbits. Our survey of Trojans in the orbital plane of Venus is undertaken for 25 million years. Some 40% of the survivors are on tadpole orbits. For the Earth, the integrations are pursued for 50 million years. The stable zones in the orbital plane are larger for the Earth than for Venus, but fewer of the survivors are tadpoles. Both Venus and the Earth also have regions in which inclined test particles can endure near the Lagrange points. For Venus, only test particles close to the orbital plane are stable. For the Earth, there are two bands of stability, one at low inclinations (i < 16 degrees) and one at moderate inclinations (between 24 degrees and 34 degrees). The inclined test particles that evade close encounters are primarily moving on tadpole orbits. Our survey of in-plane test particles near the Martian Lagrange points shows no survivors after 60 million years. Low inclination test particles do not persist, as their inclinations are quickly increased until the effects of a secular resonance with Jupiter cause de-stabilisation. Numerical integrations of inclined test particles for timespans of 25 million years show stable zones for inclinations between 14 and 40 degrees.Comment: 20 pages, 21 figures, Monthly Notices (in press

Effects of antiplatelet therapy after stroke due to intracerebral haemorrhage (RESTART): a randomised, open-label trial

Antiplatelet therapy reduces the risk of major vascular events for people with occlusive vascular disease, although it might increase the risk of intracranial haemorrhage. Patients surviving the commonest subtype of intracranial haemorrhage, intracerebral haemorrhage, are at risk of both haemorrhagic and occlusive vascular events, but whether antiplatelet therapy can be used safely is unclear. We aimed to estimate the relative and absolute effects of antiplatelet therapy on recurrent intracerebral haemorrhage and whether this risk might exceed any reduction of occlusive vascular events

Inflammatory Markers and Outcomes in Cardiovascular Disease

In a commentary on two new research studies in PLoS Medicine, Leonard Kritharides discusses the role of inflammatory markers in predicting cardiovascular outcomes and patients' responses to treatment

Popular music, psychogeography, place identity and tourism: The case of Sheffield

Tourism and cultural agencies in some English provincial cities are promoting their popular music ‘heritage’ and, in some cases, contemporary musicians through the packaging of trails, sites, ‘iconic’ venues and festivals. This article focuses on Sheffield, a ‘post-industrial’ northern English city which is drawing on its associations with musicians past and present in seeking to attract tourists. This article is based on interviews with, among others, recording artists, promoters, producers and venue managers, along with reflective observational and documentary data. Theoretical remarks are made on the representations of popular musicians through cultural tourism strategies, programmes and products and also on the ways in which musicians convey a ‘psychogeographical’ sense of place in the ‘soundscape’ of the city

Incidental findings on brain magnetic resonance imaging: systematic review and meta-analysis

Objective To quantify the prevalence of incidental findings on magnetic resonance imaging (MRI) of the brain

Small grid embeddings of 3-polytopes

We introduce an algorithm that embeds a given 3-connected planar graph as a convex 3-polytope with integer coordinates. The size of the coordinates is bounded by $O(2^{7.55n})=O(188^{n})$. If the graph contains a triangle we can bound the integer coordinates by $O(2^{4.82n})$. If the graph contains a quadrilateral we can bound the integer coordinates by $O(2^{5.46n})$. The crucial part of the algorithm is to find a convex plane embedding whose edges can be weighted such that the sum of the weighted edges, seen as vectors, cancel at every point. It is well known that this can be guaranteed for the interior vertices by applying a technique of Tutte. We show how to extend Tutte's ideas to construct a plane embedding where the weighted vector sums cancel also on the vertices of the boundary face

Evaluating the Quality of Research into a Single Prognostic Biomarker: A Systematic Review and Meta-analysis of 83 Studies of C-Reactive Protein in Stable Coronary Artery Disease

Background Systematic evaluations of the quality of research on a single prognostic biomarker are rare. We sought to evaluate the quality of prognostic research evidence for the association of C-reactive protein (CRP) with fatal and nonfatal events among patients with stable coronary disease. Methods and Findings We searched MEDLINE (1966 to 2009) and EMBASE (1980 to 2009) and selected prospective studies of patients with stable coronary disease, reporting a relative risk for the association of CRP with death and nonfatal cardiovascular events. We included 83 studies, reporting 61,684 patients and 6,485 outcome events. No study reported a prespecified statistical analysis protocol; only two studies reported the time elapsed (in months or years) between initial presentation of symptomatic coronary disease and inclusion in the study. Studies reported a median of seven items (of 17) from the REMARK reporting guidelines, with no evidence of change over time. The pooled relative risk for the top versus bottom third of CRP distribution was 1.97 (95% confidence interval [CI] 1.78–2.17), with substantial heterogeneity (I2 = 79.5). Only 13 studies adjusted for conventional risk factors (age, sex, smoking, obesity, diabetes, and low-density lipoprotein [LDL] cholesterol) and these had a relative risk of 1.65 (95% CI 1.39–1.96), I2 = 33.7. Studies reported ten different ways of comparing CRP values, with weaker relative risks for those based on continuous measures. Adjusting for publication bias (for which there was strong evidence, Egger's p<0.001) using a validated method reduced the relative risk to 1.19 (95% CI 1.13–1.25). Only two studies reported a measure of discrimination (c-statistic). In 20 studies the detection rate for subsequent events could be calculated and was 31% for a 10% false positive rate, and the calculated pooled c-statistic was 0.61 (0.57–0.66). Conclusion Multiple types of reporting bias, and publication bias, make the magnitude of any independent association between CRP and prognosis among patients with stable coronary disease sufficiently uncertain that no clinical practice recommendations can be made. Publication of prespecified statistical analytic protocols and prospective registration of studies, among other measures, might help improve the quality of prognostic biomarker research