Piecewise Conserved Quantities

We review the treatment of conservation laws in spacetimes that are glued together in various ways, thus adding a boundary term to the usual conservation laws. Several examples of such spacetimes will be described, including the joining of Schwarzschild spacetimes of different masses, and the possibility of joining regions of different signatures. The opportunity will also be taken to explore some of the less obvious properties of Lorentzian vector calculus.Comment: To appear in Gravity and the Quantum, Springer 2017 (http://www.springer.com/in/book/9783319516998

Failure of Standard Conservation Laws at a Classical Change of Signature

The Divergence Theorem as usually stated cannot be applied across a change of signature unless it is re-expressed to allow for a finite source term on the signature change surface. Consequently all conservation laws must also be `modified', and therefore insistence on conservation of matter across such a surface cannot be physically justified. The Darmois junction conditions normally ensure conservation of matter via Israel's identities for the jump in the energy-momentum density, but not when the signature changes. Modified identities are derived for this jump when a signature change occurs, and the resulting surface effects in the conservation laws are calculated. In general, physical vector fields experience a jump in at least one component, and a source term may therefore appear in the corresponding conservation law. Thus current is also not conserved. These surface effects are a consequence of the change in the character of physical law. The only way to recover standard conservation laws is to impose restrictions that no realistic cosmological model can satisfy.Comment: 15pp, figures available on request from Charles Hellaby at [email protected]

A Multistage Incidence Estimation Model for Diseases with Differential Mortality

According to theWorld Health Organization, surgically removable cataract remains the leading cause of blindness worldwide. In sub-Saharan Africa, cataract surgical rate targets should ideally be set based on cataract incidence (the number of new cataracts developed each year). Unfortunately, the longitudinal studies necessary to measure incidence have not yet been feasible in these areas. Our research instead proposes a method for estimating incidence based on available cataract prevalence data. We extend a method proposed by Podgor and Leske (1986) to estimate age-specific incidence from age-specific prevalence in single diseases with differential mortality. A two-stage disease extension is created in order to differentiate between unilateral cataract and bilateral cataract. The new model, along with a numerical simulation method to generate confidence intervals, is implemented in the statistical programming language R. The model is then applied to Rapid Assessment of Avoidable Blindness survey data from parts of Eritrea, The Gambia, Kenya (two regions), Mali, Rwanda and Tanzania. Our results suggest significant geographic variations in cataract incidence, a hypothesis to be further investigated as the RAAB survey expands and improves. We also show how the model can be further extended to model any n-stage progressive disease with differential mortality. to model any n-stage progressive disease with differential mortality

BOUNDARY CONDITIONS FOR THE SCALAR FIELD IN THE PRESENCE OF SIGNATURE CHANGE

We show that, contrary to recent criticism, our previous work yields a reasonable class of solutions for the massless scalar field in the presence of signature change.Comment: 11 pages, Plain Tex, no figure

Tensor distributions on signature-changing space-times

Irregularities in the metric tensor of a signature-changing space-time suggest that field equations on such space-times might be regarded as distributional. We review the formalism of tensor distributions on differentiable manifolds, and examine to what extent rigorous meaning can be given to field equations in the presence of signature-change, in particular those involving covariant derivatives. We find that, for both continuous and discontinuous signature-change, covariant differentiation can be defined on a class of tensor distributions wide enough to be physically interesting.Comment: 9 pages, LaTeX 2.0

The Construction of Spinor Fields on Manifolds with Smooth Degenerate Metrics

We examine some of the subtleties inherent in formulating a theory of spinors on a manifold with a smooth degenerate metric. We concentrate on the case where the metric is singular on a hypersurface that partitions the manifold into Lorentzian and Euclidean domains. We introduce the notion of a complex spinor fibration to make precise the meaning of continuity of a spinor field and give an expression for the components of a local spinor connection that is valid in the absence of a frame of local orthonormal vectors. These considerations enable one to construct a Dirac equation for the discussion of the behavior of spinors in the vicinity of the metric degeneracy. We conclude that the theory contains more freedom than the spacetime Dirac theory and we discuss some of the implications of this for the continuity of conserved currents.Comment: 24 pages, LaTeX (RevTeX 3.0, no figures), To appear in J. Math. Phy

Undetermined and accidental mortality rates as possible sources of underreported suicides: population-based study comparing Islamic countries and traditionally religious Western countries.

BACKGROUND: Four Western countries (Greece, Ireland, Italy and Portugal) with strong Orthodox and Catholic traditions have been associated with the underreporting of death by suicide, and underreported suicides are sometimes found among deaths recorded as 'undetermined' or 'accidental'. AIMS: This population-based study tests whether there are any significant difference in patterns of suicides, undetermined deaths and accidental deaths between these four Western countries and 21 predominately Islamic countries. METHOD: World Health Organization age-standardised death rates per million population were used to compare suicide rates with combined undetermined death and accidental death (UnD+AccD) rates, from which odds ratios were calculated. Substantial odds ratios (OR > 2.0) were taken as indicative of likely underreporting of suicides. The Islamic countries come from four different historico-cultural regions, described as: less-traditional Islamic countries; former USSR countries; Gulf Arab states; and Middle Eastern and North African countries. χ2-tests were used to determine any significant differences between the Western comparator countries and the Islamic regions. RESULTS: For the Western comparator countries, the average suicide rate was 66 per million population, the average undetermined death rate 56 per million and the average accidental death rate 58 per million, yielding a suicide:UnD+AccD odds ratio (OR) of 1.73. The average values for the other three groups were as follows. Less-traditional Islamic countries: suicide rate, 31 per million; UnD+AccD rate, 101 per million; suicide:UnD+AccD OR = 3.3. Former USSR countries: suicide rate, 61 per million; UnD+AccD rate, 221 per million; suicide:UnD+AccD OR = 3.6. Gulf Arab states: suicide rate, 10 per million; UnD+AccD rate, 76 per million; suicide:UnD+AccD OR = 8.6. Middle Eastern and North African countries: suicide rate, 6 per million; UnD+AccD rate, 151 per million; suicide:UnD+AccD OR = 25.2. The patterns of these mortalities in the Islamic countries was significantly different from Western comparator countries. CONCLUSIONS: The results indicate underreporting of suicides in Islamic countries. This might inadvertently lead to reduced access to mental health preventive services in both Western and Islamic countries

Actions for signature change

This is a contribution on the controversy about junction conditions for classical signature change. The central issue in this debate is whether the extrinsic curvature on slices near the hypersurface of signature change has to be continuous ({\it weak} signature change) or to vanish ({\it strong} signature change). Led by a Lagrangian point of view, we write down eight candidate action functionals $S_1$,\dots $S_8$ as possible generalizations of general relativity and investigate to what extent each of these defines a sensible variational problem, and which junction condition is implied. Four of the actions involve an integration over the total manifold. A particular subtlety arises from the precise definition of the Einstein-Hilbert Lagrangian density $|g|^{1/2} R[g]$. The other four actions are constructed as sums of integrals over singe-signature domains. The result is that {\it both} types of junction conditions occur in different models, i.e. are based on different first principles, none of which can be claimed to represent the ''correct'' one, unless physical predictions are taken into account. From a point of view of naturality dictated by the variational formalism, {\it weak} signature change is slightly favoured over {\it strong} one, because it requires less {\it \`a priori} restrictions for the class of off-shell metrics. In addition, a proposal for the use of the Lagrangian framework in cosmology is made.Comment: 36 pages, LaTeX, no figures; some corrections have been made, several Comments and further references are included and a note has been added