On invariant 2x2 \beta-ensembles of random matrices

We introduce and solve exactly a family of invariant 2x2 random matrices, depending on one parameter \eta, and we show that rotational invariance and real Dyson index \beta are not incompatible properties. The probability density for the entries contains a weight function and a multiple trace-trace interaction term, which corresponds to the representation of the Vandermonde-squared coupling on the basis of power sums. As a result, the effective Dyson index \beta_{eff} of the ensemble can take any real value in an interval. Two weight functions (Gaussian and non-Gaussian) are explored in detail and the connections with \beta-ensembles of Dumitriu-Edelman and the so-called Poisson-Wigner crossover for the level spacing are respectively highlighted. A curious spectral twinning between ensembles of different symmetry classes is unveiled. The proposed technical tool more generically allows for designing actual matrix models which i) are rotationally invariant; ii) have a real Dyson index \beta_{eff}; iii) have a pre-assigned confining potential or alternatively level-spacing profile. The analytical results have been checked through numerical simulations with an excellent agreement. Eventually, we discuss possible generalizations and further directions of research.Comment: Minor modifications. Published versio

Asymptotics for products of characteristic polynomials in classical β\beta-Ensembles

We study the local properties of eigenvalues for the Hermite (Gaussian), Laguerre (Chiral) and Jacobi $\beta$-ensembles of $N\times N$ random matrices. More specifically, we calculate scaling limits of the expectation value of products of characteristic polynomials as $N\to\infty$. In the bulk of the spectrum of each $\beta$-ensemble, the same scaling limit is found to be $e^{p_{1}}{}_1F_{1}$ whose exact expansion in terms of Jack polynomials is well known. The scaling limit at the soft edge of the spectrum for the Hermite and Laguerre $\beta$-ensembles is shown to be a multivariate Airy function, which is defined as a generalized Kontsevich integral. As corollaries, when $\beta$ is even, scaling limits of the $k$-point correlation functions for the three ensembles are obtained. The asymptotics of the multivariate Airy function for large and small arguments is also given. All the asymptotic results rely on a generalization of Watson's lemma and the steepest descent method for integrals of Selberg type.Comment: [v3] 35 pages; this is a revised and enlarged version of the article with new references, simplified demonstations, and improved presentation. To be published in Constructive Approximation 37 (2013

A cluster randomised control trial to evaluate the effectiveness and cost-effectiveness of the Italian medicines use review (I-MUR) for asthma patients

Background The economic burden of asthma, which relates to the degree of control, is €5 billion annually in Italy. Pharmacists could help improve asthma control, reducing this burden. This study aimed to evaluate the effectiveness and cost-effectiveness of Medicines Use Reviews provided by community pharmacists in asthma. Methods This cluster randomised, multi-centre, controlled trial in adult patients with asthma was conducted in 15 of the 20 regions of Italy between September 2014 and July 2015. After stratification by region, community pharmacists were randomly allocated to group A (trained in and delivered the intervention at baseline) or B (training and delivery 3 months later), using computerised random number generation in blocks of 10. Each recruited up to five patients, with both groups followed for 9 months. The intervention consisted of a systematic, structured face-to-face consultation with a pharmacist, covering asthma symptoms, medicines used, attitude towards medicines and adherence, recording pharmacist-identified pharmaceutical care issues (PCIs). The primary outcome was asthma control, assessed using the Asthma-Control-Test (ACT) score (ACT ≥ 20 represents good control). Secondary outcomes were: number of active ingredients, adherence, cost-effectiveness compared with usual care. Although blinding was not possible for either pharmacists or patients, assessment of outcomes was conducted by researchers blind to group allocation. Results Numbers of pharmacists and patients enrolled were 283 (A = 136; B = 147) and 1263 (A = 600; B = 663), numbers completing were 201 (A = 97; B = 104) and 816 (A = 400; B = 416), respectively. Patients were similar in age and gender and 56.13% (458/816) had poor/partial asthma control. Pharmacists identified 1256 PCIs (mean 1.54/patient), mostly need for education, monitoring and potentially ineffective therapy. Median ACT score at baseline differed between groups (A = 19, B = 18; p < 0.01). Odds ratio for improved asthma control was 1.76 (95% CI 1.33–2.33) and number needed to treat 10 (95% CI 6–28). Number of active ingredients reduced by 7.9% post-intervention (p < 0.01). Adherence improved by 35.4% 3 months post-intervention and 40.0% at 6 months (p < 0.01). The probability of the intervention being more cost-effective than usual care was 100% at 9 months. Conclusions This community pharmacist-based intervention demonstrated both effectiveness and cost-effectiveness. It has since been implemented as the first community pharmacy cognitive service in Italy

A mixed methods pilot study with a cluster randomized control trial to evaluate the impact of a leadership intervention on guideline implementation in home care nursing

Abstract Background Foot ulcers are a significant problem for people with diabetes. Comprehensive assessments of risk factors associated with diabetic foot ulcer are recommended in clinical guidelines to decrease complications such as prolonged healing, gangrene and amputations, and to promote effective management. However, the translation of clinical guidelines into nursing practice remains fragmented and inconsistent, and a recent homecare chart audit showed less than half the recommended risk factors for diabetic foot ulcers were assessed, and peripheral neuropathy (the most significant predictor of complications) was not assessed at all. Strong leadership is consistently described as significant to successfully transfer guidelines into practice. Limited research exists however regarding which leadership behaviours facilitate and support implementation in nursing. The purpose of this pilot study is to evaluate the impact of a leadership intervention in community nursing on implementing recommendations from a clinical guideline on the nursing assessment and management of diabetic foot ulcers. Methods Two phase mixed methods design is proposed (ISRCTN 12345678). Phase I: Descriptive qualitative to understand barriers to implementing the guideline recommendations, and to inform the intervention. Phase II: Matched pair cluster randomized controlled trial (n = 4 centers) will evaluate differences in outcomes between two implementation strategies. Primary outcome: Nursing assessments of client risk factors, a composite score of 8 items based on Diabetes/Foot Ulcer guideline recommendations. Intervention: In addition to the organization's 'usual' implementation strategy, a 12 week leadership strategy will be offered to managerial and clinical leaders consisting of: a) printed materials, b) one day interactive workshop to develop a leadership action plan tailored to barriers to support implementation; c) three post-workshop teleconferences. Discussion This study will provide vital information on which leadership strategies are well received to facilitate and support guideline implementation. The anticipated outcomes will provide information to assist with effective management of foot ulcers for people with diabetes. By tracking clinical outcomes associated with guideline implementation, health care administrators will be better informed to influence organizational and policy decision-making to support evidence-based quality care. Findings will be useful to inform the design of future multi-centered trials on various clinical topics to enhance knowledge translation for positive outcomes. Trial Registration Current Control Trials ISRCTN0691089