Triple correlation of the Riemann zeros

We use the conjecture of Conrey, Farmer and Zirnbauer for averages of ratios of the Riemann zeta function to calculate all the lower order terms of the triple correlation function of the Riemann zeros. A previous approach was suggested in 1996 by Bogomolny and Keating taking inspiration from semi-classical methods. At that point they did not write out the answer explicitly, so we do that here, illustrating that by our method all the lower order terms down to the constant can be calculated rigourously if one assumes the ratios conjecture of Conrey, Farmer and Zirnbauer. Bogomolny and Keating returned to their previous results simultaneously with this current work, and have written out the full expression. The result presented in this paper agrees precisely with their formula, as well as with our numerical computations, which we include here. We also include an alternate proof of the triple correlation of eigenvalues from random U(N) matrices which follows a nearly identical method to that for the Riemann zeros, but is based on the theorem for averages of ratios of characteristic polynomials

Coupled Ocean Atmosphere Processes and European Climate (COAPEC): improved understanding of the coupled climate system

COAPEC (http://coapec.nerc.ac.uk/) is a five-year Directed Science Programme funded by the Natural Environment Research Council (NERC). COAPEC is providing advances in understanding the mechanisms by which the ocean and atmosphere interact, how these processes are represented in state-of-the-art numerical climate models and how they determine the predictability of the climate system over seasonal-decadal timescales. Processes studied include the generation and propagation of salinity and heat anomalies in the North Atlantic, the influence of the thermohaline circulation and the role of storm tracks on European Climate. The influence of remote processes, including ocean-atmosphere coupling in tropical Atlantic warm events and Southern Ocean circulation are also being investigated. As part of the programme, new coupled models are being developed, including: a coupled hybrid isopycnic coordinate model; fast models for multi-ensemble runs to investigate model parameters space, using both high performance machines and spare home PC resources; a QG model to investigate high resolution ocean processes in coupled systems and validated ice models for coupled modelling. Underpinning research into improving the observational datasets, such as the SOC flux climatology, and into the influence of sea-ice observations in General Circulation Models is also being carried out as part of the programme. To place these advances into a socially relevant context, COAPEC is also investigating the methods for using, and economic benefits of, climate forecasts at seasonal timescales for the UK health sector and the UK energy industry

A tribute to a patient safety pioneer – Mr Robert L. Law

Editoria

Signatures of radial migration in barred galaxies: Azimuthal variations in the metallicity distribution of old stars

By means of N-body simulations, we show that radial migration in galaxy disks, induced by bar and spiral arms, leads to significant azimuthal variations in the metallicity distribution of old stars at a given distance from the galaxy center. Metals do not show an axisymmetric distribution during phases of strong migration. Azimuthal variations are visible during the whole phase of strong bar phase, and tend to disappear as the effect of radial migration diminishes, together with a reduction in the bar strength. These results suggest that the presence of inhomogeneities in the metallicity distribution of old stars in a galaxy disk can be a probe of ongoing strong migration. Such signatures may be detected in the Milky Way by Gaia (and complementary spectroscopic data), as well as in external galaxies, by IFU surveys like CALIFA and ATLAS3D. Mixing - defined as the tendency toward a homogeneous, azimuthally symmetric, stellar distribution in the disk - and migration turns out to be two distinct processes, the effects of mixing starting to be visible when strong migration is over.Comment: 8 pages, 10 figures, accepted for publication on Astronomy and Astrophysic

Diagnostic radiographer advanced clinical practice in the United Kingdom – A national cross-sectional survey

Objectives: To survey the diagnostic radiography workforce in the United Kingdom (UK) at an organisational level to ascertain the scope of advanced practice and compliance with Health Education England standards for multiprofessional advanced clinical practice (ACP). Methods: 174 diagnostic imaging departments were invited to participate in a cross-sectional electronic survey focused upon advanced level practice and their educational and accreditation expectations (October–December 2019). Breast imaging, computed tomography, fluoroscopy, interventional radiology, lithotripsy, magnetic resonance imaging and projectional radiography were included. Results: A total of 97 responses were received, of which 79 were eligible for inclusion (45%). Respondents reported advanced-level practice roles across all imaging modalities, which included clinical reporting, procedural-based and combined roles. Radiograph and mammogram reporting were most prevalent (95 and 67% of Trusts), with fluoroscopy the most frequent procedure-only role (25%). Only 39% of trusts required adherence to the four pillars of ACP within job descriptions, and only 12% requiring a full Masters qualification. Conclusions: Diagnostic radiographer reporting and procedure-based roles in the NHS are varied and widespread. However, inconsistencies in fulfilment against the expected standards for advanced practice exist. Realignment of advanced-level roles to delineate enhanced and advanced clinical practice may ensure consistency between roles and professions. A requirement for accreditation as an advanced (clinical) practitioner with adherence to advanced practice requirements could therefore provide value to accreditation for both individual practitioners and Trusts. Advances in knowledge: Within the UK, diagnostic radiographer roles previously self-identified as advanced-level practice may be termed enhanced practice when not adhering to expected ACP standards

Embedding consultant radiographer roles within radiology departments: a framework for success

Introduction: Many organisations struggle to clearly differentiate the radiographer consultant role from advanced or specialist practice, with newly appointed consultant practitioners often ill-prepared for working at this level. This article discusses the design, implementation and validation of an outcomes framework for benchmarking competencies for trainee or new-in-post consultant radiographers. Methods: Five experienced radiographers from different clinical specialisms were seconded to a twelve month consultant trainee post, guided by a locally-devised outcomes framework. A longitudinal qualitative study explored, from the radiographers’ perspective, the impact of the outcomes framework on the transition to consultant practice and beyond. Data collection included semi-structured interviews (months 1, 6 and 12), validation via a focus group (month 18) and a group interview (5 years). Results: Early interactions with framework objectives were mechanistic, but as participants better understood the role more creative approaches emerged. Despite diverse clinical expertise, the framework facilitated parity between participants, promoting transparency and credibility which was important in how the consultant role was perceived. All participants achieved all framework outcomes and were subsequently appointed to substantive consultant radiographer positions. Conclusion: This outcomes framework facilitates experienced radiographers to successfully transition into consultant radiographers, enabling them to meet multiple non-clinical targets while continuing to work effectively within a changing clinical environment. It is the first validated benchmarking tool designed to support the transition to radiographer consultant practice. Adoption of the tool will provide a standardised measure of consultant radiographer outcomes that will promote inter-organisational transferability hitherto unseen in the U

Autocorrelation of Random Matrix Polynomials

We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in three equivalent forms: as a determinant sum (and hence in terms of symmetric polynomials), as a combinatorial sum, and as a multiple contour integral. These formulae are analogous to those previously obtained for the Gaussian ensembles of Random Matrix Theory, but in this case are identities for any size of matrix, rather than large-matrix asymptotic approximations. They also mirror exactly autocorrelation formulae conjectured to hold for L-functions in a companion paper. This then provides further evidence in support of the connection between Random Matrix Theory and the theory of L-functions

Correlations of eigenvalues and Riemann zeros

We present a new approach to obtaining the lower order terms for $n$-correlation of the zeros of the Riemann zeta function. Our approach is based on the `ratios conjecture' of Conrey, Farmer, and Zirnbauer. Assuming the ratios conjecture we prove a formula which explicitly gives all of the lower order terms in any order correlation. Our method works equally well for random matrix theory and gives a new expression, which is structurally the same as that for the zeta function, for the $n$-correlation of eigenvalues of matrices from U(N)