An Urn Model for Cascading Failures on a Lattice

A cascading failure is a failure in a system of interconnected parts, in which the breakdown of one element can lead to the subsequent collapse of the others. The aim of this paper is to introduce a simple combinatorial model for the study of cascading failures. In particular, having in mind particle systems and Markov random fields, we take into consideration a network of interacting urns displaced over a lattice. Every urn is Pólya-like and its reinforcement matrix is not only a function of time (time contagion) but also of the behavior of the neighboring urns (spatial contagion), and of a random component, which can represent either simple fate or the impact of exogenous factors. In this way a non-trivial dependence structure among the urns is built, and it is used to study default avalanches over the lattice. Thanks to its flexibility and its interesting probabilistic properties, the given construction may be used to model different phenomena characterized by cascading failures such as power grids and financial networks.

No surgical innovation without evaluation: the IDEAL recommendations

Surgery and other invasive therapies are complex interventions, the assessment of which is challenged by factors that depend on operator, team, and setting, such as learning curves, quality variations, and perception of equipoise. We propose recommendations for the assessment of surgery based on a five-stage description of the surgical development process. We also encourage the widespread use of prospective databases and registries. Reports of new techniques should be registered as a professional duty, anonymously if necessary when outcomes are adverse. Case series studies should be replaced by prospective development studies for early technical modifications and by prospective research databases for later pre-trial evaluation. Protocols for these studies should be registered publicly. Statistical process control techniques can be useful in both early and late assessment. Randomised trials should be used whenever possible to investigate efficacy, but adequate pre-trial data are essential to allow power calculations, clarify the definition and indications of the intervention, and develop quality measures. Difficulties in doing randomised clinical trials should be addressed by measures to evaluate learning curves and alleviate equipoise problems. Alternative prospective designs, such as interrupted time series studies, should be used when randomised trials are not feasible. Established procedures should be monitored with prospective databases to analyse outcome variations and to identify late and rare events. Achievement of improved design, conduct, and reporting of surgical research will need concerted action by editors, funders of health care and research, regulatory bodies, and professional societies.