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

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,

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

Proceedings of the 2nd International Workshop on Digital Language Archives: LangArc 2023

Article describe the approach which the authors are taking to access control and a design for a distributed access control system which can look after the A-is-for-accessible in FAIR data while respecting the CARE principles. It was presented at the 2nd International Workshop on Digital Language Archives held on June 30, 2023 as part of the ACM/IEEE Joint Conference on Digital Libraries 2023

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

Density Functional Theory Study of the Geometry, Energetics, and Reconstruction Process of Si(111) Surfaces

We report the structures and energies from first principles density functional calculations of 12 different reconstructed (111) surfaces of silicon, including the 3 × 3 to 9 × 9 dimer−adatom−stacking fault (DAS) structures. These calculations used the Perdew−Burke−Ernzerhof generalized gradient approximation of density functional theory and Gaussian basis functions. We considered fully periodic slabs of various thicknesses. We find that the most stable surface is the DAS 7 × 7 structure, with a surface energy of 1.044 eV/1 × 1 cell (1310 dyn/cm). To analyze the origins of the stability of these systems and to predict energetics for more complex, less-ordered systems, we develop a model in which the surface energy is partitioned into contributions from seven different types of atom environments. This analysis is used to predict the surface energy of larger DAS structures (including their asymptotic behavior for very large unit cells) and to study the energetics of the sequential size change (SSC) model proposed by Shimada and Tochihara for the observed dynamical reconstruction of the Si(111) 1 × 1 structure. We obtain an energy barrier at the 2 × 2 cell size and confirm that the 7 × 7 regular stage of the SSC model (corresponding to the DAS 7 × 7 reconstruction) provides the highest energy reduction per unit cell with respect to the unreconstructed Si(111) 1 × 1 surface

Density Functional Theory Study of the Geometry, Energetics, and Reconstruction Process of Si(111) Surfaces

We report the structures and energies from first principles density functional calculations of 12 different reconstructed (111) surfaces of silicon, including the 3 × 3 to 9 × 9 dimer−adatom−stacking fault (DAS) structures. These calculations used the Perdew−Burke−Ernzerhof generalized gradient approximation of density functional theory and Gaussian basis functions. We considered fully periodic slabs of various thicknesses. We find that the most stable surface is the DAS 7 × 7 structure, with a surface energy of 1.044 eV/1 × 1 cell (1310 dyn/cm). To analyze the origins of the stability of these systems and to predict energetics for more complex, less-ordered systems, we develop a model in which the surface energy is partitioned into contributions from seven different types of atom environments. This analysis is used to predict the surface energy of larger DAS structures (including their asymptotic behavior for very large unit cells) and to study the energetics of the sequential size change (SSC) model proposed by Shimada and Tochihara for the observed dynamical reconstruction of the Si(111) 1 × 1 structure. We obtain an energy barrier at the 2 × 2 cell size and confirm that the 7 × 7 regular stage of the SSC model (corresponding to the DAS 7 × 7 reconstruction) provides the highest energy reduction per unit cell with respect to the unreconstructed Si(111) 1 × 1 surface