Junctions and thin shells in general relativity using computer algebra I: The Darmois-Israel Formalism

We present the GRjunction package which allows boundary surfaces and thin-shells in general relativity to be studied with a computer algebra system. Implementing the Darmois-Israel thin shell formalism requires a careful selection of definitions and algorithms to ensure that results are generated in a straight-forward way. We have used the package to correctly reproduce a wide variety of examples from the literature. We present several of these verifications as a means of demonstrating the packages capabilities. We then use GRjunction to perform a new calculation - joining two Kerr solutions with differing masses and angular momenta along a thin shell in the slow rotation limit.Comment: Minor LaTeX error corrected. GRjunction for GRTensorII is available from http://astro.queensu.ca/~grtensor/GRjunction.htm

Book reviews

Teaching/Communication/Extension/Profession,

Invariants of the Riemann tensor for Class B Warped Product Spacetimes

We use the computer algebra system \textit{GRTensorII} to examine invariants polynomial in the Riemann tensor for class $B$ warped product spacetimes - those which can be decomposed into the coupled product of two 2-dimensional spaces, one Lorentzian and one Riemannian, subject to the separability of the coupling: $ds^2 = ds_{\Sigma_1}^2 (u,v) + C(x^\gamma)^2 ds_{\Sigma_2}^2 (\theta,\phi)$ with $C(x^\gamma)^2=r(u,v)^2 w(\theta,\phi)^2$ and $sig(\Sigma_1)=0, sig(\Sigma_2)=2\epsilon (\epsilon=\pm 1)$ for class $B_{1}$ spacetimes and $sig(\Sigma_1)=2\epsilon, sig(\Sigma_2)=0$ for class $B_{2}$. Although very special, these spaces include many of interest, for example, all spherical, plane, and hyperbolic spacetimes. The first two Ricci invariants along with the Ricci scalar and the real component of the second Weyl invariant $J$ alone are shown to constitute the largest independent set of invariants to degree five for this class. Explicit syzygies are given for other invariants up to this degree. It is argued that this set constitutes the largest functionally independent set to any degree for this class, and some physical consequences of the syzygies are explored.Comment: 19 pages. To appear in Computer Physics Communications Thematic Issue on "Computer Algebra in Physics Research". Uses Maple2e.st

Searching for the Kuhnian moment : the Black-Scholes-Merton formula and the evolution of modern finance theory

The Black-Scholes-Merton formula has been put to widespread use by options traders because it provides a means of calculating the theoretically 'correct' price of stock options. Traders can therefore see whether the market price of stock options undervalues or overvalues them compared with their hypothetical Black-Scholes-Merton price, before choosing to buy or sell options accordingly. As a consequence of this close relationship between options pricing theory and options pricing practice, a strong performativity loop was activated, whereby market prices quickly converged on the hypothetical Black-Scholes-Merton prices following the dissemination of the formula. The theory has therefore had significant real-world effects, but how should we characterize the initial instinct to derive the theory from a philosophy of science perspective? The two books under review suggest that a Kuhnian reading of the advancement of scientific knowledge might well be the most appropriate. But, on closer inspection, it becomes clear that the publication of the Black-Scholes-Merton formula should not be seen as a Kuhnian moment with paradigm-shaping attributes. It is shown that, at most, the formula acts as an important exemplar which, via its use in the training of options pricing theorists and options pricing practitioners, reinforces the entrenchment of finance theory within the orthodox economics worldview

Derivation and validation of a novel prognostic scale (modified–stroke subtype, Oxfordshire Community Stroke Project classification, age, and prestroke modified Rankin) to predict early mortality in acute stroke

Background and Purpose The stroke subtype, Oxfordshire Community Stroke Project classification, age, and prestroke modified Rankin (SOAR) score is a prognostic scale proposed for early mortality prediction after acute stroke. We aimed to evaluate whether including a measure of initial stroke severity (National Institutes of Health Stroke Scale and modified-SOAR [mSOAR] scores) would improve the prognostic accuracy. Methods Using Anglia Stroke and Heart Clinical Network data, 2008 to 2011, we assessed the performance of SOAR and mSOAR against in-hospital mortality using area under the receiver operating curve statistics. We externally validated the prognostic utility of SOAR and mSOAR using an independent cohort data set from Glasgow. We described calibration using Hosmer–Lemeshow goodness-of-fit test. Results A total of 1002 patients were included in the derivation cohort, and 105 (10.5%) died as inpatients. The area under the receiver operating curves for outcome of early mortality derived from the SOAR and mSOAR scores were 0.79 (95% confidence interval, 0.75–0.84) and 0.83 (95% confidence interval, 0.79–0.86), respectively (P=0.001). The external validation data set contained 1012 patients with stroke; of which, 121 (12.0%) patients died within 90 days. The mSOAR scores identified the risk of early mortality ranging from 3% to 42%. External validation of mSOAR score yielded an area under the receiver operating curve of 0.84 (95% confidence interval, 0.82–0.88) for outcome of early mortality. Calibration was good (P=0.70 for the Hosmer–Lemeshow test). Conclusions—Adding National Institutes of Health Stroke Scale data to create a modified-SOAR score improved prognostic utility in both derivation and validation data sets. The mSOAR may have clinical utility by using easily available data to predict mortality

Instances and connectors : issues for a second generation process language

This work is supported by UK EPSRC grants GR/L34433 and GR/L32699Over the past decade a variety of process languages have been defined, used and evaluated. It is now possible to consider second generation languages based on this experience. Rather than develop a second generation wish list this position paper explores two issues: instances and connectors. Instances relate to the relationship between a process model as a description and the, possibly multiple, enacting instances which are created from it. Connectors refers to the issue of concurrency control and achieving a higher level of abstraction in how parts of a model interact. We believe that these issues are key to developing systems which can effectively support business processes, and that they have not received sufficient attention within the process modelling community. Through exploring these issues we also illustrate our approach to designing a second generation process language.Postprin

Evaluation of stroke services in Anglia Stroke Clinical Network to examine the variation in acute services and stroke outcomes.

BACKGROUND: Stroke is the third leading cause of death in developed countries and the leading cause of long-term disability worldwide. A series of national stroke audits in the UK highlighted the differences in stroke care between hospitals. The study aims to describe variation in outcomes following stroke and to identify the characteristics of services that are associated with better outcomes, after accounting for case mix differences and individual prognostic factors. METHODS/DESIGN: We will conduct a cohort study in eight acute NHS trusts within East of England, with at least one year of follow-up after stroke. The study population will be a systematically selected representative sample of patients admitted with stroke during the study period, recruited within each hospital. We will collect individual patient data on prognostic characteristics, health care received, outcomes and costs of care and we will also record relevant characteristics of each provider organisation. The determinants of one year outcome including patient reported outcome will be assessed statistically with proportional hazards regression models. Self (or proxy) completed EuroQol (EQ-5D) questionnaires will measure quality of life at baseline and follow-up for cost utility analyses. DISCUSSION: This study will provide observational data about health service factors associated with variations in patient outcomes and health care costs following hospital admission for acute stroke. This will form the basis for future RCTs by identifying promising health service interventions, assessing the feasibility of recruiting and following up trial patients, and provide evidence about frequency and variances in outcomes, and intra-cluster correlation of outcomes, for sample size calculations. The results will inform clinicians, public, service providers, commissioners and policy makers to drive further improvement in health services which will bring direct benefit to the patients.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

GRLite and GRTensorJ: Graphical user interfaces to the computer algebra system GRTensorII

GRLite and GRTensorJ are first and second generation graphical user interfaces to the computer algebra system GRTensorII. Current development centers on GRTensorJ, which provides fully customizable symbolic procedures that reduce many complex calculations to "elementary functions". Although still in development, GRTensorJ, which is now available (free of charge) over the internet, is sufficiently advanced to be of interest to researchers in general relativity and related fields.Comment: To appear in the Proceedings of the Eighth Canadian Conference on General Relativity and Relativistic Astrophysics . Requires two figures, grliteview.png and grtensorjview.pn

Conventional direction to unconventional measures: using quantitative easing to shape Eurozone fiscal capacity

Eight years after the outbreak of the crisis, the Eurozone (EZ) fiscal policy remains fragmented at the national level. This paper fills the structural gap between the monetary and fiscal dimensions of EZ economic policy by suggesting a ‘conventional’ direction to the unconventional Quantitative Easing (QE) policy of the European Central Bank (ECB). We propose an evolution for QE to tackle the shortcomings of the current ‘decentralized’ fiscal policy in the EZ. In a nutshell, we suggest a change in the composition of QE asset purchases, focusing on buying European Investment Bank (EIB) bonds that, in turn, would be used to finance real investments through the Juncker Plan programme. The rationale of our proposal is legitimised by an overview of the gloomy macroeconomic conditions of the EZ, and the situation in ongoing policies. The mechanism is described in detail, with a discussion of both its strengths and possible limitations

Climate Process Team on Internal-Wave Driven Ocean Mixing

Diapycnal mixing plays a primary role in the thermodynamic balance of the ocean, and consequently, in oceanic heat and carbon uptake and storage. Though observed mixing rates are on average consistent with values required by inverse models, recent attention has focused on the dramatic spatial variability, spanning several orders of magnitude, of mixing rates in both the upper and deep ocean. Climate models have been shown to be very sensitive not only to the overall level but to the detailed distribution of mixing; sub-grid-scale parameterizations based on accurate physical processes will allow model forecasts to evolve with a changing climate. Spatio-temporal patterns of mixing are largely driven by the geography of generation, propagation and destruction of internal waves, which are thought to supply much of the power for turbulent mixing. Over the last five years and under the auspices of US CLIVAR, a NSF and NOAA supported Climate Process Team has been engaged in developing, implementing and testing dynamics-base parameterizations for internal-wave driven turbulent mixing in global ocean models. The work has primarily focused on turbulence 1) near sites of internal tide generation, 2) in the upper ocean related to wind-generated near inertial motions, 3) due to internal lee waves generated by low-frequency mesoscale flows over topography, and 4) at ocean margins. Here we review recent progress, describe the tools developed, and discuss future directions