From continuum mechanics to general relativity

Using ideas from continuum mechanics we construct a theory of gravity. We show that this theory is equivalent to Einstein's theory of general relativity; it is also a much faster way of reaching general relativity than the conventional route. Our approach is simple and natural: we form a very general model and then apply two physical assumptions supported by experimental evidence. This easily reduces our construction to a model equivalent to general relativity. Finally, we suggest a simple way of modifying our theory to investigate non-standard space-time symmetries.Comment: 7 pages, this essay received a honorable mention in the 2014 essay competition of the Gravity Research Foundatio

Rotational elasticity

We consider an infinite 3-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis which gives a field of orthonormal bases called the coframe. As the dynamical variables (unknowns) of our theory we choose the coframe and a density. We write down the general dynamic variational functional for our rotational theory of elasticity, assuming our material to be physically linear but the kinematic model geometrically nonlinear. Allowing geometric nonlinearity is natural when dealing with rotations because rotations in dimension 3 are inherently nonlinear (rotations about different axes do not commute) and because there is no reason to exclude from our study large rotations such as full turns. The main result of the paper is an explicit construction of a class of time-dependent solutions which we call plane wave solutions; these are travelling waves of rotations. The existence of such explicit closed form solutions is a nontrivial fact given that our system of Euler-Lagrange equations is highly nonlinear. In the last section we consider a special case of our rotational theory of elasticity which in the stationary setting (harmonic time dependence and arbitrary dependence on spatial coordinates) turns out to be equivalent to a pair of massless Dirac equations

Interventions to Deliver Vaccination to, and Improve Vaccination Rates in, People who are Homeless

Background: In comparison to the general population, people who are homeless have poorer health and health-related outcomes, including for vaccine-preventable diseases. Vaccination is safe, effective and cost-effective, and many vaccination guidelines specifically recommend vaccination in people who are homeless. This systematic review will identify interventions which are effective in delivering vaccination to, and/or at improving vaccination rates in, people who are homeless. Methods/Design: This systematic review is presented according to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. Searches will be undertaken on eight electronic databases, using combinations of search terms and subject headings or index terms. Citation chaining will also be undertaken. Literature will be screened for relevance against inclusion/exclusion criteria firstly by title/abstract and secondly by full text. The selected studies will be assessed for quality using an evidence-based tool appropriate to their methods. Data relevant to the topic will be extracted and examined using meta-analysis and narrative synthesis. Discussion: This systematic review will address an important gap in the literature about vaccination in people who are homeless. The review’s findings are particularly relevant considering the current coronavirus disease (COVID-19) pandemic, which is likely to be managed through vaccination

Spectral theoretic characterization of the massless Dirac action

We consider an elliptic self-adjoint first order differential operator L acting on pairs (2-columns) of complex-valued half-densities over a connected compact 3-dimensional manifold without boundary. The principal symbol of the operator L is assumed to be trace-free and the subprincipal symbol is assumed to be zero. Given a positive scalar weight function, we study the weighted eigenvalue problem for the operator L. The corresponding counting function (number of eigenvalues between zero and a positive lambda) is known to admit, under appropriate assumptions on periodic trajectories, a two-term asymptotic expansion as lambda tends to plus infinity and we have recently derived an explicit formula for the second asymptotic coefficient. The purpose of this paper is to establish the geometric meaning of the second asymptotic coefficient. To this end, we identify the geometric objects encoded within our eigenvalue problem - metric, nonvanishing spinor field and topological charge - and express our asymptotic coefficients in terms of these geometric objects. We prove that the second asymptotic coefficient of the counting function has the geometric meaning of the massless Dirac action

Spectral asymmetry of the massless Dirac operator on a 3-torus

Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant

Influenza Vaccination Rates, and Barriers to Influenza Vaccination, in People who are Homeless

Background: Influenza is a highly infectious virus which is endemic in most high-income countries. People experiencing homelessness are at an increased risk of contracting influenza, and often have poorer outcomes associated with hospitalisation and mortality. Annual influenza vaccination is recommended for all adults, and highly recommended for ‘at-risk’ groups, including people who are homeless. Despite this, the vaccination uptake within the homeless community is low. This systematic review will identify influenza vaccination rates, and barriers to influenza vaccination, in people who are homeless.   Methods: This review will consider primary studies about influenza vaccination in people who are homeless. Searches will be undertaken on five electronic databases and managed in EndNote X9. The literature will be screened by title/abstract, then by full-text, and citation chaining will be completed. Data about the influenza vaccination rates and barriers will be extracted. Each task, primarily the screening and extraction of data, will be completed by one researcher, and checked by at least one other.     Discussion: This review will identify influenza vaccination rates, and barriers to influenza vaccination, in people experiencing homelessness. This will inform vaccination delivery and funding, and may contribute to reducing the health disparities in this at-risk, hard-to-reach population.&nbsp

Clinical features of the pathogenic m.5540G>A mitochondrial transfer RNA tryptophan gene mutation

AbstractMitochondrial DNA disease is one of the most common groups of inherited neuromuscular disorders and frequently associated with marked phenotypic and genotypic heterogeneity. We describe an adult patient who initially presented with childhood-onset ataxia without a family history and an unremarkable diagnostic muscle biopsy. Subsequent multi-system manifestations included basal ganglia calcification, proteinuria, cataract and retinitis pigmentosa, prompting a repeat muscle biopsy that showed features consistent with mitochondrial myopathy 13 years later. She had a stroke with restricted diffusion change in the basal ganglia and internal capsule at age 44 years. Molecular genetic testing identified a previously-reported pathogenic, heteroplasmic mutation in the mitochondrial-encoded transfer RNA tryptophan (MT-TW) gene which based on family studies was likely to have arisen de novo in our patient. Interestingly, we documented an increase in the mutant mtDNA heteroplasmy level in her second biopsy (72% compared to 56%), reflecting the progression of clinical disease

Elemental Abundances in the Ejecta of Old Classical Novae from Late-Epoch Spitzer Spectra

We present Spitzer Space Telescope mid-infrared IRS spectra, supplemented by ground-based optical observations, of the classical novae V1974 Cyg, V382 Vel, and V1494 Aql more than 11, 8, and 4 years after outburst respectively. The spectra are dominated by forbidden emission from neon and oxygen, though in some cases, there are weak signatures of magnesium, sulfur, and argon. We investigate the geometry and distribution of the late time ejecta by examination of the emission line profiles. Using nebular analysis in the low density regime, we estimate lower limits on the abundances in these novae. In V1974 Cyg and V382 Vel, our observations confirm the abundance estimates presented by other authors and support the claims that these eruptions occurred on ONe white dwarfs. We report the first detection of neon emission in V1494 Aql and show that the system most likely contains a CO white dwarf.Comment: 22 pages, 12 figure