The Construction of Sorkin Triangulations

Some time ago, Sorkin (1975) reported investigations of the time evolution and initial value problems in Regge calculus, for one triangulation each of the manifolds $R*S^3$ and $R^4$. Here we display the simple, local characteristic of those triangulations which underlies the structure found by Sorkin, and emphasise its general applicability, and therefore the general validity of Sorkin's conclusions. We also make some elementary observations on the resulting structure of the time evolution and initial value problems in Regge calculus, and add some comments and speculations.Comment: 5 pages (plus one figure not included, available from author on request), Plain Tex, no local preprint number (Only change: omitted "\magnification" command now replaced

A comparison of intramuscular diamorphine and intramuscular pethidine for labour analgesia: a two-centre randomised blinded controlled trial.

Intramuscular (i.m.) pethidine is used worldwide for labour analgesia and i.m. diamorphine usage has increased in the UK in the last 15 years. This trial aims to ascertain the relative efficacy and adverse effects of diamorphine and pethidine for labour pain

Regge calculus in the canonical form

(3+1) (continuous time) Regge calculus is reduced to Hamiltonian form. The constraints are classified, classical and quantum consequences are discussed. As basic variables connection matrices and antisymmetric area tensors are used supplemented with appropriate bilinear constraints. In these variables the action can be made quasipolinomial with $\arcsin$ as the only deviation from polinomiality. In comparison with analogous formalism in the continuum theory classification of constraints changes: some of them disappear, the part of I class constraints including Hamiltonian one become II class (and vice versa, some new constraints arise and some II class constraints become I class). As a result, the number of the degrees of freedom coincides with the number of links in 3-dimensional leaf of foliation. Moreover, in empty space classical dynamics is trivial: the scale of timelike links become zero and spacelike links are constant.Comment: 24 pages,Plain LaTeX,BINP 93-4

Discrete quantum gravity in the framework of Regge calculus formalism

An approach to the discrete quantum gravity based on the Regge calculus is discussed which was developed in a number of our papers. Regge calculus is general relativity for the subclass of general Riemannian manifolds called piecewise flat ones. Regge calculus deals with the discrete set of variables, triangulation lengths, and contains continuous general relativity as a particular limiting case when the lengths tend to zero. In our approach the quantum length expectations are nonzero and of the order of Plank scale $10^{-33}cm$. This means the discrete spacetime structure on these scales.Comment: LaTeX, 16 pages, to appear in JET

Regge Calculus as a Fourth Order Method in Numerical Relativity

The convergence properties of numerical Regge calculus as an approximation to continuum vacuum General Relativity is studied, both analytically and numerically. The Regge equations are evaluated on continuum spacetimes by assigning squared geodesic distances in the continuum manifold to the squared edge lengths in the simplicial manifold. It is found analytically that, individually, the Regge equations converge to zero as the second power of the lattice spacing, but that an average over local Regge equations converges to zero as (at the very least) the third power of the lattice spacing. Numerical studies using analytic solutions to the Einstein equations show that these averages actually converge to zero as the fourth power of the lattice spacing.Comment: 14 pages, LaTeX, 8 figures mailed in separate file or email author directl

The IDvIP Trial: A two-centre randomised double-blind controlled trial comparing intramuscular diamorphine and intramuscular pethidine for labour analgesia

<p>Abstract</p> <p>Background</p> <p>Intramuscular pethidine is routinely used throughout the UK for labour analgesia. Studies have suggested that pethidine provides little pain relief in labour and has a number of side effects affecting mother and neonate. It can cause nausea, vomiting and dysphoria in mothers and can cause reduced fetal heart rate variability and accelerations. Neonatal effects include respiratory depression and impaired feeding. There are few large studies comparing the relative side effects and efficacy of different opioids in labour. A small trial comparing intramuscular pethidine with diamorphine, showed diamorphine to have some benefits over pethidine when used for labour analgesia but the study did not investigate the adverse effects of either opioid.</p> <p>Methods</p> <p>The Intramuscular Diamorphine versus Intramuscular Pethidine (IDvIP) trial is a randomised double-blind two centre controlled trial comparing intramuscular diamorphine and pethidine regarding their analgesic efficacy in labour and their side effects in mother, fetus and neonate. Information about the trial will be provided to women in the antenatal period or in early labour. Consent and recruitment to the trial will be obtained when the mother requests opioid analgesia. The sample size requirement is 406 women with data on primary outcomes. The maternal primary outcomes are pain relief during the first 3 hours after trial analgesia and specifically pain relief after 60 minutes. The neonatal primary outcomes are need for resuscitation and Apgar Score <7 at 1 minute. The secondary outcomes are an additional measure of pain relief, maternal sedation, nausea and vomiting, maternal oxygen saturation, satisfaction with analgesia, whether method of analgesia would be used again, use of Entonox, umbilical arterial and venous pH, fetal heart rate, meconium staining, time from delivery to first breath, Apgar scores at 5 mins, naloxone requirement, transfer to neonatal intensive care unit, neonatal haemoglobin oxygen saturation at 30, 60, 90, and 120 mins after delivery, and neonatal sedation and feeding behaviour during first 2 hours.</p> <p>Discussion</p> <p>If the trial demonstrates that diamorphine provides better analgesia with fewer side effects in mother and neonate this could lead to a change in national practice and result in diamorphine becoming the preferred intramuscular opioid for analgesia in labour.</p> <p>Trial Registration</p> <p><a href="http://www.controlled-trials.com/ISRCTN14898678">ISRCTN14898678</a></p> <p>Eudra No: 2006-003250-18, REC Reference No: 06/Q1702/95, MHRA Authorisation No: 1443/0001/001-0001, NIHR UKCRN reference 6895, RfPB grant PB-PG-0407-13170_IR5</p

A fully (3+1)-D Regge calculus model of the Kasner cosmology

We describe the first discrete-time 4-dimensional numerical application of Regge calculus. The spacetime is represented as a complex of 4-dimensional simplices, and the geometry interior to each 4-simplex is flat Minkowski spacetime. This simplicial spacetime is constructed so as to be foliated with a one parameter family of spacelike hypersurfaces built of tetrahedra. We implement a novel two-surface initial-data prescription for Regge calculus, and provide the first fully 4-dimensional application of an implicit decoupled evolution scheme (the ``Sorkin evolution scheme''). We benchmark this code on the Kasner cosmology --- a cosmology which embodies generic features of the collapse of many cosmological models. We (1) reproduce the continuum solution with a fractional error in the 3-volume of 10^{-5} after 10000 evolution steps, (2) demonstrate stable evolution, (3) preserve the standard deviation of spatial homogeneity to less than 10^{-10} and (4) explicitly display the existence of diffeomorphism freedom in Regge calculus. We also present the second-order convergence properties of the solution to the continuum.Comment: 22 pages, 5 eps figures, LaTeX. Updated and expanded versio

(Broken) Gauge Symmetries and Constraints in Regge Calculus

We will examine the issue of diffeomorphism symmetry in simplicial models of (quantum) gravity, in particular for Regge calculus. We find that for a solution with curvature there do not exist exact gauge symmetries on the discrete level. Furthermore we derive a canonical formulation that exactly matches the dynamics and hence symmetries of the covariant picture. In this canonical formulation broken symmetries lead to the replacements of constraints by so--called pseudo constraints. These considerations should be taken into account in attempts to connect spin foam models, based on the Regge action, with canonical loop quantum gravity, which aims at implementing proper constraints. We will argue that the long standing problem of finding a consistent constraint algebra for discretized gravity theories is equivalent to the problem of finding an action with exact diffeomorphism symmetries. Finally we will analyze different limits in which the pseudo constraints might turn into proper constraints. This could be helpful to infer alternative discretization schemes in which the symmetries are not broken.Comment: 32 pages, 15 figure

Brief Report: Schema Consistent Misinformation Effects in Eyewitnesses with Autism Spectrum Disorder

A number of studies have demonstrated schema-related misinformation effects in typical individuals, but no research to date has examined this with witnesses with autism spectrum disorder (ASD), despite their impaired ability to generate core elements that define everyday events. After witnessing slides depicting a bank robbery, 16 adults with ASD and 16 matched comparison individuals were exposed to post-event misinformation that was either schema typical or atypical. Consistent with previous work, the comparison group went onto report more schema typical misinformation than atypical misinformation. However, so too did the ASD group, suggesting that individuals with ASD do have understanding of the causal links between events, persons and actions, an important finding from both theoretical and applied perspectives