Note on Signature Change and Colombeau Theory

Recent work alludes to various `controversies' associated with signature change in general relativity. As we have argued previously, these are in fact disagreements about the (often unstated) assumptions underlying various possible approaches. The choice between approaches remains open.Comment: REVTex, 3 pages; to appear in GR

Comment on `Smooth and Discontinuous Signature Type Change in General Relativity'

Kossowski and Kriele derived boundary conditions on the metric at a surface of signature change. We point out that their derivation is based not only on certain smoothness assumptions but also on a postulated form of the Einstein field equations. Since there is no canonical form of the field equations at a change of signature, their conclusions are not inescapable. We show here that a weaker formulation is possible, in which less restrictive smoothness assumptions are made, and (a slightly different form of) the Einstein field equations are satisfied. In particular, in this formulation it is possible to have a bounded energy-momentum tensor at a change of signature without satisfying their condition that the extrinsic curvature vanish.Comment: Plain TeX, 6 pages; Comment on Kossowski and Kriele: Class. Quantum Grav. 10, 2363 (1993); Reply by Kriele: Gen. Rel. Grav. 28, 1409-1413 (1996

Gravity and Signature Change

The use of proper ``time'' to describe classical ``spacetimes'' which contain both Euclidean and Lorentzian regions permits the introduction of smooth (generalized) orthonormal frames. This remarkable fact permits one to describe both a variational treatment of Einstein's equations and distribution theory using straightforward generalizations of the standard treatments for constant signature.Comment: Plain TeX, 6 pages; to appear in GR

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

Octonions, E6, and Particle Physics

In 1934, Jordan et al. gave a necessary algebraic condition, the Jordan identity, for a sensible theory of quantum mechanics. All but one of the algebras that satisfy this condition can be described by Hermitian matrices over the complexes or quaternions. The remaining, exceptional Jordan algebra can be described by 3x3 Hermitian matrices over the octonions. We first review properties of the octonions and the exceptional Jordan algebra, including our previous work on the octonionic Jordan eigenvalue problem. We then examine a particular real, noncompact form of the Lie group E6, which preserves determinants in the exceptional Jordan algebra. Finally, we describe a possible symmetry-breaking scenario within E6: first choose one of the octonionic directions to be special, then choose one of the 2x2 submatrices inside the 3x3 matrices to be special. Making only these two choices, we are able to describe many properties of leptons in a natural way. We further speculate on the ways in which quarks might be similarly encoded.Comment: 13 pages; 6 figures; TonyFest plenary talk (York 2008

Barriers to HIV Testing in Côte d'Ivoire: The Role of Individual Characteristics and Testing Modalities

BACKGROUND: Expanding HIV testing requires a better understanding of barriers to its uptake. We investigated barriers to HIV testing in Côte d'Ivoire, taking into account test circumstances (client vs. provider-initiated). METHODS: We used data from the 2005 nationally representative Demographic and Health Survey conducted in Côte d'Ivoire. Socio-demographic characteristics, sexual behaviour and knowledge and attitudes toward HIV/AIDS associated with recent (<2 years) HIV testing were identified using gender-specific univariate and multivariate logistic regressions. Among women, differential effects of barriers to testing according to test circumstance (whether they have been offered for a prenatal test or not) were assessed through interaction tests. RESULTS: Recent HIV testing was reported by 6.1% of men and 9.5% of women (including 4.6% as part of antenatal care). Among men, having a low socioeconomic status, having a low HIV-related knowledge level and being employed [compared to those inactive: adjusted Odds Ratio (aOR) 0.46; 95% confidence interval (CI) 0.25-0.87] were associated with lower proportions of recent HIV testing. Among women without a prenatal HIV testing offer, living outside the capital (aOR 0.38; CI 0.19-0.77) and reporting a unique lifetime sexual partner constituted additional barriers to HIV testing. By contrast, among women recently offered to be tested in prenatal care, none of these variables was found to be associated with recent HIV testing. CONCLUSIONS: Various dimensions of individuals' characteristics constituted significant barriers to HIV testing in Côte d'Ivoire in 2005, with gender specificities. Such barriers are substantially reduced when testing was proposed in the framework of antenatal care. This suggests that provider-initiated testing strategies may help overcome individual barriers to HIV testing

Computer-Assisted Segmentation of Videocapsule Images Using Alpha-Divergence-Based Active Contour in the Framework of Intestinal Pathologies Detection

Visualization of the entire length of the gastrointestinal tract through natural orifices is a challenge for endoscopists. Videoendoscopy is currently the “gold standard” technique for diagnosis of different pathologies of the intestinal tract. Wireless Capsule Endoscopy (WCE) has been developed in the 1990's as an alternative to videoendoscopy to allow direct examination of the gastrointestinal tract without any need for sedation. Nevertheless, the systematic post-examination by the specialist of the 50,000 (for the small bowel) to 150,000 images (for the colon) of a complete acquisition using WCE remains time-consuming and challenging due to the poor quality of WCE images. In this article, a semiautomatic segmentation for analysis of WCE images is proposed. Based on active contour segmentation, the proposed method introduces alpha-divergences, a flexible statistical similarity measure that gives a real flexibility to different types of gastrointestinal pathologies. Results of segmentation using the proposed approach are shown on different types of real-case examinations, from (multi-) polyp(s) segmentation, to radiation enteritis delineation

A quantum cosmology and discontinuous signature changing classical solutions

We revisit the classical and quantum cosmology of a universe in which a self interacting scalar field is coupled to gravity with a flat FRW type metric undergoing continuous signature transition. We arrange for quantum cosmologically allowed discontinuity in the classical solutions at the signature changing hypersurface, provided these solutions be dual in some respects. This may be of some importance in the study of early universe within the signature changing scenarios.Comment: 11 pages, Latex, title and abstract changed, some cghanges in the text, to appear in GR

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

Quaternionic eigenvalue problem

We discuss the (right) eigenvalue equation for $\mathbb{H}$, $\mathbb{C}$ and $\mathbb{R}$ linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows to translate the quaternionic problem into an {\em equivalent} real or complex counterpart. Interesting applications are found in solving differential equations within quaternionic formulations of quantum mechanics.Comment: 13 pages, AMS-Te