2,212 research outputs found
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
Developments in Random Matrix Theory
In this preface to the Journal of Physics A, Special Edition on Random Matrix
Theory, we give a review of the main historical developments of random matrix
theory. A short summary of the papers that appear in this special edition is
also given.Comment: 22 pages, Late
Steric engineering of metal-halide perovskites with tunable optical band gaps
Owing to their high energy-conversion efficiency and inexpensive fabrication
routes, solar cells based on metal-organic halide perovskites have rapidly
gained prominence as a disruptive technology. An attractive feature of
perovskite absorbers is the possibility of tailoring their properties by
changing the elemental composition through the chemical precursors. In this
context, rational in silico design represents a powerful tool for mapping the
vast materials landscape and accelerating discovery. Here we show that the
optical band gap of metal-halide perovskites, a key design parameter for solar
cells, strongly correlates with a simple structural feature, the largest
metal-halide-metal bond angle. Using this descriptor we suggest continuous
tunability of the optical gap from the mid-infrared to the visible. Precise
band gap engineering is achieved by controlling the bond angles through the
steric size of the molecular cation. Based on these design principles we
predict novel low-gap perovskites for optimum photovoltaic efficiency, and we
demonstrate the concept of band gap modulation by synthesising and
characterising novel mixed-cation perovskites.Comment: This manuscript was submitted for publication on March 6th, 2014.
Many of the results presented in this manuscript were presented at the
International Conference on Solution processed Semiconductor Solar Cells,
held in Oxford, UK, on 10-12 September 2014. The manuscript is 37 pages long
and contains 8 figure
Discretisation for odd quadratic twists
The discretisation problem for even quadratic twists is almost understood,
with the main question now being how the arithmetic Delaunay heuristic
interacts with the analytic random matrix theory prediction. The situation for
odd quadratic twists is much more mysterious, as the height of a point enters
the picture, which does not necessarily take integral values (as does the order
of the Shafarevich-Tate group). We discuss a couple of models and present data
on this question.Comment: To appear in the Proceedings of the INI Workshop on Random Matrix
Theory and Elliptic Curve
Random Matrix Theory and the Fourier Coefficients of Half-Integral Weight Forms
Conjectured links between the distribution of values taken by the
characteristic polynomials of random orthogonal matrices and that for certain
families of L-functions at the centre of the critical strip are used to
motivate a series of conjectures concerning the value-distribution of the
Fourier coefficients of half-integral weight modular forms related to these
L-functions. Our conjectures may be viewed as being analogous to the Sato-Tate
conjecture for integral weight modular forms. Numerical evidence is presented
in support of them.Comment: 28 pages, 8 figure
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
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
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