Large scale heterogeneous networks, the Davis-Wielandt shell, and graph separation

We consider a large scale network of interconnected heterogeneous dynamical components. Scalable stability conditions are derived that involve the input/output properties of individual subsystems and the interconnection matrix. The analysis is based on the Davis-Wielandt shell, a higher dimensional version of the numerical range with important convexity properties. This can be used to allow heterogeneity in the agent dynamics while relaxing normality and symmetry assumptions on the interconnection matrix. The results include small gain and passivity approaches as special cases, with the three dimensional shell shown to be inherently connected with corresponding graph separation arguments. © 2012 Society for Industrial and Applied Mathematics.

Trust-Level Risk Evaluation and Risk Control Guidance in the NHS East of England

In recent years, the healthcare sector has adopted the use of operational risk assessment tools to help understand the systems issues that lead to patient safety incidents. But although these problem-focused tools have improved the ability of healthcare organizations to identify hazards, they have not translated into measurable improvements in patient safety. One possible reason for this is a lack of support for the solution-focused process of risk control. This article describes a content analysis of the risk management strategies, policies, and procedures at all acute (i.e., hospital), mental health, and ambulance trusts (health service organizations) in the East of England area of the British National Health Service. The primary goal was to determine what organizational-level guidance exists to support risk control practice. A secondary goal was to examine the risk evaluation guidance provided by these trusts. With regard to risk control, we found an almost complete lack of useful guidance to promote good practice. With regard to risk evaluation, the trusts relied exclusively on risk matrices. A number of weaknesses were found in the use of this tool, especially related to the guidance for scoring an event's likelihood. We make a number of recommendations to address these concerns. The guidance assessed provides insufficient support for risk control and risk evaluation. This may present a significant barrier to the success of risk management approaches in improving patient safety. © 2013 Society for Risk Analysis.