Boundary conditions associated with the Painlev\'e III' and V evaluations of some random matrix averages

In a previous work a random matrix average for the Laguerre unitary ensemble, generalising the generating function for the probability that an interval $(0,s)$ at the hard edge contains $k$ eigenvalues, was evaluated in terms of a Painlev\'e V transcendent in $\sigma$-form. However the boundary conditions for the corresponding differential equation were not specified for the full parameter space. Here this task is accomplished in general, and the obtained functional form is compared against the most general small $s$ behaviour of the Painlev\'e V equation in $\sigma$-form known from the work of Jimbo. An analogous study is carried out for the the hard edge scaling limit of the random matrix average, which we have previously evaluated in terms of a Painlev\'e \IIId transcendent in $\sigma$-form. An application of the latter result is given to the rapid evaluation of a Hankel determinant appearing in a recent work of Conrey, Rubinstein and Snaith relating to the derivative of the Riemann zeta function

Using remote substituents to control solution structure and anion binding in lanthanide complexes.

A study of the anion-binding properties of three structurally related lanthanide complexes, which all contain chemically identical anion-binding motifs, has revealed dramatic differences in their anion affinity. These arise as a consequence of changes in the substitution pattern on the periphery of the molecule, at a substantial distance from the binding pocket. Herein, we explore these remote substituent effects and explain the observed behaviour through discussion of the way in which remote substituents can influence and control the global structure of a molecule through their demands upon conformational space. Peripheral modifications to a binuclear lanthanide motif derived from α,α′-bis(DO3 Ayl)-m-xylene are shown to result in dramatic changes to the binding constant for isophthalate. In this system, the parent compound displays considerable conformational flexibility, yet can be assumed to bind to isophthalate through a well-defined conformer. Addition of steric bulk remote from the binding site restricts conformational mobility, giving rise to an increase in binding constant on entropic grounds as long as the ideal binding conformation is not excluded from the available range of conformers

Included outside: Evidence synthesis for engaging under-represented groups in nature

Natural England Commissioned Report NECR42

The lowest eigenvalue of Jacobi random matrix ensembles and Painlev\'e VI

We present two complementary methods, each applicable in a different range, to evaluate the distribution of the lowest eigenvalue of random matrices in a Jacobi ensemble. The first method solves an associated Painleve VI nonlinear differential equation numerically, with suitable initial conditions that we determine. The second method proceeds via constructing the power-series expansion of the Painleve VI function. Our results are applied in a forthcoming paper in which we model the distribution of the first zero above the central point of elliptic curve L-function families of finite conductor and of conjecturally orthogonal symmetry.Comment: 30 pages, 2 figure

Improving wrist imaging through a multicentre educational intervention: The challenge of orthogonal projections

YesIn relation to wrist imaging, the accepted requirement is two orthogonal projections obtained at 90°, each with the wrist in neutral position. However, the literature and anecdotal experience suggests that this principle is not universally applied. Method: This multiphase study was undertaken across eight different hospitals sites. Compliance with standard UK technique was confirmed if there was a change in ulna orientation between the dorsi-palmar (DP) and lateral wrist projections. A baseline evaluation for three days was randomly identified from the preceding three months. An educational intervention was implemented using a poster to demonstrate standard positioning. To measure the impact of the intervention, further evaluation took place at two weeks (early) and three months (late). Results: Across the study phases, only a minority of radiographs demonstrated compliance with the standard technique, with an identical anatomical appearance of the distal ulna across the projections. Initial compliance was 16.8% (n = 40/238), and this improved to 47.8% (n = 77/161) post-intervention, but declined to 32.8% (n = 41/125) within three months. The presence of pathology appeared to influence practice, with a greater proportion of those with an abnormal radiographic examination demonstrating a change in ulna appearances in the baseline cohort (

Random polynomials, random matrices, and LL-functions

We show that the Circular Orthogonal Ensemble of random matrices arises naturally from a family of random polynomials. This sheds light on the appearance of random matrix statistics in the zeros of the Riemann zeta-function.Comment: Added background material. Final version. To appear in Nonlinearit

Quantum gray solitons in confining potentials

We define and study hole-like excitations (the Lieb II mode) in a weakly interacting Bose liquid subject to external confinement. These excitations are obtained by semiclassical quantization of gray solitons propagating on top of a Thomas-Fermi background. Radiation of phonons by an accelerated gray soliton leads to a finite life-time for the trapped Lieb II mode. It is shown that, for a large number of trapped atoms, most of the Lieb II levels can be experimentally resolved.Comment: 5 pages, 2 figure

Understanding the Performance-Limiting Factors of Cs₂AgBiBr₆ Double-Perovskite Solar Cells

Double perovskites have recently emerged as possible alternatives to lead-based halide perovskites for photovoltaic applications. In particular, Understanding the Performance-Limiting Factors of Cs₂AgBiBr₆ Double-Perovskite Solar Cells has been the subject of several studies because of its environmental stability, low toxicity, and its promising optoelectronic features. Despite these encouraging features, the performances of solar cells based on this double perovskite are still low, suggesting severe limitations that need to be addressed. In this work we combine experimental and theoretical studies to show that the short electron diffusion length is one of the major causes for the limited performance of Cs₂AgBiBr₆ solar cells. Using EQE measurements on semitransparent Cs₂AgBiBr₆ solar cells we estimate the electron diffusion length to be only 30 nm and corroborated this value by terahertz spectroscopy. By using photothermal deflection spectroscopy and surface photovoltage measurements we correlate the limited electron diffusion length with a high density of electron traps. Our findings highlight important faults affecting this double perovskite, showing the challenges to overcome and hinting to a possible path to improve the efficiency of Cs₂AgBiBr₆ solar cells

Non-pharmacological interventions to reduce the risk of diabetes in people with impaired glucose regulation : a systematic review and economic evaluation

Background The prevalence of type 2 diabetes mellitus (T2DM) is increasing in the UK and worldwide. Before the onset of T2DM, there are two conditions characterised by blood glucose levels that are above normal but below the threshold for diabetes. If screening for T2DM in introduced, many people with impaired glucose tolerance (IGT) will be found and it is necessary to consider how they should be treated. The number would depend on what screening test was used and what cut-offs were chosen. Objective To review the clinical effectiveness and cost-effectiveness of non-pharmacological interventions, including diet and physical activity, for the prevention of T2DM in people with intermediate hyperglycaemia. Data sources Electronic databases, MEDLINE (1996–2011), EMBASE (1980–2011) and all sections of The Cochrane Library, were searched for systematic reviews, randomised controlled trials (RCTs) and other relevant literature on the effectiveness of diet and/or physical activity in preventing, or delaying, progression to T2DM.The databases were also searched for studies on the cost-effectiveness of interventions. Review methods The review of clinical effectiveness was based mainly on RCTs, which were critically appraised. Subjects were people with intermediate hyperglycaemia, mainly with IGT. Interventions could be diet alone, physical activity alone, or the combination. For cost-effectiveness analysis, we updated the Sheffield economic model of T2DM. Modelling based on RCTs may not reflect what happens in routine care so we created a ‘real-life’ modelling scenario wherein people would try lifestyle change but switch to metformin after 1 year if they failed. Results Nine RCTs compared lifestyle interventions (predominantly dietary and physical activity advice, with regular reinforcement and frequent follow-up) with standard care. The primary outcome was progression to diabetes. In most trials, progression was reduced, by over half in some trials. The best effects were seen in participants who adhered best to the lifestyle changes; a scenario of a trial of lifestyle change but a switch to metformin after 1 year in those who did not adhere sufficiently appeared to be the most cost-effective option. Limitations Participants in the RCTs were volunteers and their results may have been better than in general populations. Even among the volunteers, many did not adhere. Some studies were not long enough to show whether the interventions reduced cardiovascular mortality as well as diabetes. The main problem is that we know what people should do to reduce progression, but not how to persuade most to do it. Conclusion In people with IGT, dietary change to ensure weight loss, coupled with physical activity, is clinically effective and cost-effective in reducing progression to diabetes

On the algebraic K-theory of the complex K-theory spectrum

Let p>3 be a prime, let ku be the connective complex K-theory spectrum, and let K(ku) be the algebraic K-theory spectrum of ku. We study the p-primary homotopy type of the spectrum K(ku) by computing its mod (p,v_1) homotopy groups. We show that up to a finite summand, these groups form a finitely generated free module over a polynomial algebra F_p[b], where b is a class of degree 2p+2 defined as a higher Bott element.Comment: Revised and expanded version, 42 pages