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 Generalizations of Affine Symmetry Vectors

A definition is suggested for affine symmetry tensors, which generalize the notion of affine vectors in the same way that (conformal) Killing tensors generalize (conformal) Killing vectors. An identity for these tensors is proved, which gives the second derivative of the tensor in terms of the curvature tensor, generalizing a well-known identity for affine vectors. Additionally, the definition leads to a good definition of homothetic tensors. The inclusion relations between these types of tensors are exhibited. The relationship between affine symmetry tensors and solutions to the equation of geodesic deviation is clarified, again extending known results about Killing tensors.Comment: 11 page

Parametric Manifolds I: Extrinsic Approach

A parametric manifold can be viewed as the manifold of orbits of a (regular) foliation of a manifold by means of a family of curves. If the foliation is hypersurface orthogonal, the parametric manifold is equivalent to the 1-parameter family of hypersurfaces orthogonal to the curves, each of which inherits a metric and connection from the original manifold via orthogonal projections; this is the well-known Gauss-Codazzi formalism. We generalize this formalism to the case where the foliation is not hypersurface orthogonal. Crucial to this generalization is the notion of deficiency, which measures the failure of the orthogonal tangent spaces to be surface-forming, and which behaves very much like torsion. Some applications to initial value problems in general relativity will be briefly discussed.Comment: Plain TeX, 21 pages, no figure

Initial Long-Term Scenarios for COVID-19’s Impact on Aviation and Implications for Climate Policy

The COVID-19 pandemic had a dramatic impact on aviation in 2020, and the industry’s future is uncertain. In this paper, we consider scenarios for recovery and ongoing demand, and discuss the implications of these scenarios for aviation emissions-related policy, including the Carbon Offsetting and Reduction Scheme for International Aviation (CORSIA) and the EU Emissions Trading Scheme (ETS). Using the Aviation Integrated Model (AIM2015), a global aviation systems model, we project how long-term demand, fleet, and emissions projections might change. Depending on recovery scenario, we project cumulative aviation fuel use to 2050 might be up to 9% below that in scenarios not including the pandemic. The majority of this difference arises from reductions in relative global income levels. Around 40% of modeled scenarios project no offset requirement in either the CORSIA pilot or first phases; however, because of its more stringent emissions baseline (based on reductions from year 2004–2006 CO_{2}, The COVID-19 pandemic had a dramatic impact on aviation in 2020, and the industry’s future is uncertain. In this paper, we consider scenarios for recovery and ongoing demand, and discuss the implications of these scenarios for aviation emissions-related policy, including the Carbon Offsetting and Reduction Scheme for International Aviation (CORSIA) and the EU Emissions Trading Scheme (ETS). Using the Aviation Integrated Model (AIM2015), a global aviation systems model, we project how long-term demand, fleet, and emissions projections might change. Depending on recovery scenario, we project cumulative aviation fuel use to 2050 might be up to 9% below that in scenarios not including the pandemic. The majority of this difference arises from reductions in relative global income levels. Around 40% of modeled scenarios project no offset requirement in either the CORSIA pilot or first phases; however, because of its more stringent emissions baseline (based on reductions from year 2004–2006 CO_{2}), the EU ETS is likely to be less affected. However, if no new policies are applied and technology developments follow historical trends, year-2050 global net aviation CO_{2} is still likely to be well above industry goals, including the goal of carbon-neutral growth from 2019, even when the demand effects of the pandemic are accounted for

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]

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

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

Quaternionic Spin

We rewrite the standard 4-dimensional Dirac equation in terms of quaternionic 2-component spinors, leading to a formalism which treats both massive and massless particles on an equal footing. The resulting unified description has the correct particle spectrum to be a generation of leptons, with the correct number of spin/helicity states. Furthermore, precisely three such generations naturally combine into an octonionic description of the 10-dimensional massless Dirac equation, as discussed in previous work.Comment: LaTeX2e, 15 pages, 1 PS figure; to appear in Clifford '99 proceeding

Costs of mitigating CO2 emissions from passenger aircraft

In response to strong growth in air transportation CO2 emissions, governments and industry began to explore and implement mitigation measures and targets in the early 2000s. However, in the absence of rigorous analyses assessing the costs for mitigating CO2 emissions, these policies could be economically wasteful. Here we identify the cost-effectiveness of CO2 emission reductions from narrow-body aircraft, the workhorse of passenger air transportation. We find that in the US, a combination of fuel burn reduction strategies could reduce the 2012 level of life cycle CO2 emissions per passenger kilometre by around 2% per year to mid-century. These intensity reductions would occur at zero marginal costs for oil prices between US$50–100 per barrel. Even larger reductions are possible, but could impose extra costs and require the adoption of biomass-based synthetic fuels. The extent to which these intensity reductions will translate into absolute emissions reductions will depend on fleet growth