The Maximal Positively Invariant Set: Polynomial Setting

This note considers the maximal positively invariant set for polynomial discrete time dynamics subject to constraints specified by a basic semialgebraic set. The note utilizes a relatively direct, but apparently overlooked, fact stating that the related preimage map preserves basic semialgebraic structure. In fact, this property propagates to underlying set--dynamics induced by the associated restricted preimage map in general and to its maximal trajectory in particular. The finite time convergence of the corresponding maximal trajectory to the maximal positively invariant set is verified under reasonably mild conditions. The analysis is complemented with a discussion of computational aspects and a prototype implementation based on existing toolboxes for polynomial optimization

Euclidean distance between Haar orthogonal and gaussian matrices

In this work we study a version of the general question of how well a Haar distributed orthogonal matrix can be approximated by a random gaussian matrix. Here, we consider a gaussian random matrix $Y_n$ of order $n$ and apply to it the Gram-Schmidt orthonormalization procedure by columns to obtain a Haar distributed orthogonal matrix $U_n$. If $F_i^m$ denotes the vector formed by the first $m$-coordinates of the $i$th row of $Y_n-\sqrt{n}U_n$ and $\alpha=\frac{m}{n}$, our main result shows that the euclidean norm of $F_i^m$ converges exponentially fast to $\sqrt{ \left(2-\frac{4}{3} \frac{(1-(1 -\alpha)^{3/2})}{\alpha}\right)m}$, up to negligible terms. To show the extent of this result, we use it to study the convergence of the supremum norm $\epsilon_n(m)=\sup_{1\leq i \leq n, 1\leq j \leq m} |y_{i,j}- \sqrt{n}u_{i,j}|$ and we find a coupling that improves by a factor $\sqrt{2}$ the recently proved best known upper bound of $\epsilon_n(m)$. Applications of our results to Quantum Information Theory are also explained.Comment: v2: minor modifications to match journal version, 26 pages, 0 figures, J Theor Probab (2016

EVIDENCE-BASED IMPROVEMENT PROJECT PROSPECTUS IMPROVING MAMMOGRAPHY SCREENING SCHEDULING THROUGH COVID-19 VACCINE CLINICS UTILIZING AN ONLINE POPULATION MANAGEMENT SYSTEM—A TEAM APPROACH

Abstract Problem: The recent Covid-19 Pandemic led to delays in necessary cancer screening procedures, such as Breast Cancer Mammography Screening (BCS). Suboptimal mammography screening rates persisted at 11% compared to the regional goal of 30% of eligible women in a primary care setting. Context: Covid-19 Vaccination Clinics are part of a private HMO health plan that participates in quality accreditation and data benchmarking utilizing Healthcare Effectiveness Data and Information Set Measures (HEDIS). In this managed care health system, primary care clinics offer appointments and referrals for screening tests similar to mammography. Interventions: Change ideas such as standardized scheduling scripting, standard work process for clinic registration staff, and team education related to population health management were incorporated to foster a Quality Improvement (QI) culture to increase breast cancer screening scheduling for eligible women 40-74 years of age. Measures: The primary outcome measure addressed increasing breast cancer screening mammography scheduling, following organizational guidelines for the population of average risk eligible women aged 40-74. From a baseline of 11% to a target quarterly goal of 25% or more excellent by July 15, 2022. One process measure aimed for 90% of clinic staff to receive breast cancer screening scheduling training by June 8, 20222. Results: For two months, 90% of clinic staff (N=15) received 1 to 1 real-time hands-on training related to scripting, scheduling, and same-day mammography scheduling. Conclusion: Healthcare restrictions resulting from Covid-19 had unintended consequences that resulted in late cancer diagnoses and missed opportunities for life-saving cancer screening mammography. Clinical nurse leaders are encouraged to employ evidence-based practices in the microsystem setting

A Risk-Adjusted Model for Ovarian Cancer Care and Disparities in Access to High-Performing Hospitals.

ObjectiveTo validate the observed/expected ratio for adherence to ovarian cancer treatment guidelines as a risk-adjusted measure of hospital quality care, and to identify patient characteristics associated with disparities in access to high-performing hospitals.MethodsThis was a retrospective population-based study of stage I-IV invasive epithelial ovarian cancer reported to the California Cancer Registry between 1996 and 2014. A fit logistic regression model, which was risk-adjusted for patient and disease characteristics, was used to calculate the observed/expected ratio for each hospital, stratified by hospital annual case volume. A Cox proportional hazards model was used for survival analyses, and a multivariable logistic regression model was used to identify independent predictors of access to high-performing hospitals.ResultsThe study population included 30,051 patients who were treated at 426 hospitals: low observed/expected ratio (n=304) 23.5% of cases; intermediate observed/expected ratio (n=92) 57.8% of cases; and high observed/expected ratio (n=30) 18.7% of cases. Hospitals with high observed/expected ratios were significantly more likely to deliver guideline-adherent care (53.3%), compared with hospitals with intermediate (37.8%) and low (27.5%) observed/expected ratios (P<.001). Median disease-specific survival time ranged from 73.0 months for hospitals with high observed/expected ratios to 48.1 months for hospitals with low observed/expected ratios (P<.001). Treatment at a hospital with a high observed/expected ratio was an independent predictor of superior survival compared with hospitals with intermediate (hazard ratio [HR] 1.06, 95% CI 1.01-1.11, P<.05) and low (HR 1.10, 95% CI 1.04-1.16, P<.001) observed/expected ratios. Being of Hispanic ethnicity (odds ratio [OR] 0.85, 95% CI 0.78-0.93, P<.001, compared with white), having Medicare insurance (OR 0.74, 95% CI 0.68-0.81 P<.001, compared with managed care), having a Charlson Comorbidity Index score of 2 or greater (OR 0.91, 95% CI 0.83-0.99, P<.05), and being of lower socioeconomic status (lowest quintile OR 0.41, 95% CI 0.36-0.46, P<.001, compared with highest quintile) were independent negative predictors of access to a hospital with a high observed/expected ratio.ConclusionOvarian cancer care at a hospital with a high observed/expected ratio is an independent predictor of improved survival. Barriers to high-performing hospitals disproportionately affect patients according to sociodemographic characteristics. Triage of patients with suspected ovarian cancer according to a performance-based observed/expected ratio hospital classification is a potential mechanism for expanded access to expert care

Methods for Increasing Children\u27s Comprehension of Prosocial Values as Transmitted Through Television Programs

This study examined the effect of intervening commentary and generalization discussions upon the generalization of prosocial values as transmitted through a commercially broadcast prosocial television program. The subjects participating were 50 first graders and 50 third graders. They were randomly assigned to one of five treatment conditions (control, film only, film with commentary, film with generalization, and film with commentary and generalization). Contrary to predications, the intervening commentary used as a means of directing attention to the critical points in the story, did not have an effect upon the comprehension of the values implied in the program. It is suggested that explicitly explanatory comments coupled with value judgements may be effective in enhancing comprehension. Also contrary to predictions, the use of the general discussion concerning the value promoted in the program did not increase generalization of the value to a novel but similar situation. The effect of the prosocial program upon the first grade audience differed according to their level of comprehension. First graders with higher comprehension errors violated the rule significantly more than those with lower comprehension errors. Although the third graders as a whole had high levels of comprehension, the prosocial film appeared to have a suggestive effect, as those exposed to the prosocial film violated the rule significantly more than those exposed to the control film. It appears that in order for the prosocial values to be generalized it is important that the program be directed towards the demonstration of the prosocial behaviors themselves