Dense spectrum of resonances and spin-1/2 particle capture in a near-black-hole metric

We show that a spin-1/2 particle in the gravitational field of a massive body of radius R which slightly exceeds the Schwarzschild radius rs, possesses a dense spectrum of narrow resonances. Their lifetimes and density tend to infinity in the limit R → rs. We determine the cross section of the particle capture into these resonances and show that it is equal to the spin-1/2 absorption cross section for a Schwarzschild black hole. Thus black-hole properties may emerge in a non-singular static metric prior to the formation of a black hole.

Factors influencing success of clinical genome sequencing across a broad spectrum of disorders

To assess factors influencing the success of whole-genome sequencing for mainstream clinical diagnosis, we sequenced 217 individuals from 156 independent cases or families across a broad spectrum of disorders in whom previous screening had identified no pathogenic variants. We quantified the number of candidate variants identified using different strategies for variant calling, filtering, annotation and prioritization. We found that jointly calling variants across samples, filtering against both local and external databases, deploying multiple annotation tools and using familial transmission above biological plausibility contributed to accuracy. Overall, we identified disease-causing variants in 21% of cases, with the proportion increasing to 34% (23/68) for mendelian disorders and 57% (8/14) in family trios. We also discovered 32 potentially clinically actionable variants in 18 genes unrelated to the referral disorder, although only 4 were ultimately considered reportable. Our results demonstrate the value of genome sequencing for routine clinical diagnosis but also highlight many outstanding challenges.

Care Leavers’ Experiences of Transition and Turning Points: Findings from a Biographical Narrative Study

This paper reports on the findings of a PhD research project that set out to explore how young people leaving out of home care experienced and made sense of their transition to adulthood. Using the Biographical Narrative Interpretative Method, in-depth accounts were collected and analysed for eight care leavers. The data suggest that in addition to care leavers living their lives as a series of biographical events, their ‘care career’, they also experience changes in the way they make sense of their lives which form a ‘subjective pathway’. Influenced by the literature on resilience, the research had anticipated that ‘turning point’ events would play a significant role in the young people’s subjective pathways. But the findings show a more gradual, phased shifting of subjectivity. It is suggested that legislation, policy, services and care practices need to facilitate this more drawn out ‘subjective pathway’. Attachment, resilience and humanistic social psychology are proposed as useful theoretical underpinnings for that work

The spectrum of paediatric cardiac disease presenting to an outpatient clinic in Malawi

BACKGROUND: As progress is made towards attaining Millennium Development Goal 4, further reductions in paediatric mortality will only be achieved by concentrating on the burden of non-communicable or neglected diseases. The literature relating to paediatric cardiac disease in sub-Saharan Africa is sparse. There are no published descriptions of paediatric cardiac disease from Malawi, making it impossible to estimate the contribution it makes to childhood morbidity and mortality.

FINDINGS: In 2008, a paediatric cardiac clinic with echocardiogram scanning was established in Blantyre, southern Malawi. Between January 2009 and February 2011, the age and cardiac diagnosis of every child with an abnormal echocardiogram was recorded in a database. Of 250 children, 139 (55.6%) had congenital heart disease, and 111 (44.4%) acquired heart disease. Ventricular septal defect (VSD) (24%), Tetralogy of Fallot (10%) and patent ductus arteriousus (7.2%) were the commonest forms of congenital heart disease. Rheumatic heart disease (RHD) (22.4%) and dilated cardiomyopathy (13.6%) were the commonest acquired diseases. The mean age of presentation was 3 years 2 months for VSD and 11 years 6 months for RHD.

CONCLUSIONS: In this cohort of children from one centre in Malawi, acquired heart disease - in particular rheumatic heart disease was almost as common as congenital heart disease. Most presented late. It is likely that untreated cardiac disease causes a large number of childhood deaths in Malawi. In addition to renewing secondary preventative efforts against rheumatic heart disease, adequate and accessible cardiothoracic surgical services should be established at a regional level.

The Rossiter-McLaughlin effect reloaded: Probing the 3D spin-orbit geometry, differential stellar rotation, and the spatially-resolved stellar spectrum of star-planet systems

When a planet transits its host star, it blocks regions of the stellar surface from view; this causes a distortion of the spectral lines and a change in the line-of-sight (LOS) velocities, known as the Rossiter-McLaughlin (RM) effect. Since the LOS velocities depend, in part, on the stellar rotation, the RM waveform is sensitive to the star-planet alignment (which provides information on the system’s dynamical history). We present a new RM modelling technique that directly measures the spatially-resolved stellar spectrum behind the planet. This is done by scaling the continuum flux of the (HARPS) spectra by the transit light curve, and then subtracting the infrom the out-of-transit spectra to isolate the starlight behind the planet. This technique does not assume any shape for the intrinsic local profiles. In it, we also allow for differential stellar rotation and centre-to-limb variations in the convective blueshift. We apply this technique to HD 189733 and compare to 3D magnetohydrodynamic (MHD) simulations. We reject rigid body rotation with high confidence (>99% probability), which allows us to determine the occulted stellar latitudes and measure the stellar inclination. In turn, we determine both the sky-projected (λ ≈ −0.4 ± 0.2◦) and true 3D obliquity (ψ ≈ 7+12 −4 ◦ ). We also find good agreement with the MHD simulations, with no significant centre-to-limb variations detectable in the local profiles. Hence, this technique provides a new powerful tool that can probe stellar photospheres, differential rotation, determine 3D obliquities, and remove sky-projection biases in planet migration theories. This technique can be implemented with existing instrumentation, but will become even more powerful with the next generation of high-precision radial velocity spectrographs.

Decay spectrum and decay subspace of normal operators

Let A be a self-adjoint operator on a Hilbert space. It is well known that A admits a unique decomposition into a direct sum of three self-adjoint operators A(p), A(ac) and A(sc) such that there exists an orthonormal basis of eigenvectors for the operator A(p) the operator A(ac) has purely absolutely continuous spectrum and the operator A(sc) has purely singular continuous spectrum. We show the existence of a natural further decomposition of the singular continuous component A c into a direct sum of two self-adjoint operators A(sc)(D) and A(sc)(ND). The corresponding subspaces and spectra are called decaying and purely non-decaying singular subspaces and spectra. Similar decompositions are also shown for unitary operators and for general normal operators.

A study of velocity fields in the transition region of ε Eri (K2 V)

Analyses of the widths and shifts of optically thin emission lines in the ultraviolet spectrum of the active dwarf e Eri (K2 V) are presented. The spectra were obtained using the Space Telescope Imaging Spectrograph on the Hubble Space Telescope and the Far Ultraviolet Spectroscopic Explorer. The linewidths are used to find the non-thermal energy density and its variation with temperature from the chromosphere to the upper transition region. The energy fluxes that could be carried by Alfvén and acoustic waves are investigated, to test their possible roles in coronal heating. Acoustic waves do not appear to be a viable means of coronal heating. There is, in principle, ample flux in Alfvén waves, but detailed calculations of wave propagation are required before definite conclusions can be drawn concerning their viability. The high sensitivity and spectral resolution of the above instruments have allowed two-component Gaussian fits to be made to the profiles of the stronger transition region lines. The broad and narrow components that result share some similarities with those observed in the Sun, but in e Eri the broad component is redshifted relative to the narrow component and contributes more to the total line flux. The possible origins of the two components and the energy fluxes implied are discussed. On balance our results support the conclusion of Wood, Linsky & Ayres, that the narrow component is related to Alfvén waves reaching to the corona, but the origin of the broad component is not clear.

Analyticity of smooth eigenfunctions and spectral analysis of the Gauss map

We provide a sufficient condition of analyticity of infinitely differentiable eigenfunctions of operators of the form Uf(x) = integral a(x, y) f(b( x, y)) mu(dy) acting on functions f: [u, v] --> C ( evolution operators of one-dimensional dynamical systems and Markov processes have this form). We estimate from below the region of analyticity of the eigenfunctions and apply these results for studying the spectral properties of the Frobenius-Perron operator of the continuous fraction Gauss map. We prove that any infinitely differentiable eigenfunction f of this Frobenius-Perron operator, corresponding to a non-zero eigenvalue admits a (unique) analytic extension to the set C\(-infinity, 1]. Analyzing the spectrum of the Frobenius Perron operator in spaces of smooth functions, we extend significantly the domain of validity of the Mayer and Ropstorff asymptotic formula for the decay of correlations of the Gauss map.

Structure of spectra of linear operators in Banach spaces

Descriptive characterizations of the point, the continuous, and the residual spectra of operators in Banach spaces are put forward. In particular, necessary and sufficient conditions for three disjoint subsets of the complex plane to be the point spectrum, the continuous spectrum, and the residual spectrum of a linear continuous operator in a separable Banach space are obtained.

Compactness properties of operator multipliers

We continue the study of multidimensional operator multipliers initiated in~cite{jtt}. We introduce the notion of the symbol of an operator multiplier. We characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers. We give sufficient conditions for the sets of compact and completely compact multipliers to coincide and characterise the cases where an operator multiplier in the minimal tensor product of two C*-algebras is automatically compact. We give a description of multilinear modular completely compact completely bounded maps defined on the direct product of finitely many copies of the C*-algebra of compact operators in terms of tensor products, generalising results of Saar