Rearranging trees for robust consensus

In this paper, we use the H2 norm associated with a communication graph to characterize the robustness of consensus to noise. In particular, we restrict our attention to trees and by systematic attention to the effect of local changes in topology, we derive a partial ordering for undirected trees according to the H2 norm. Our approach for undirected trees provides a constructive method for deriving an ordering for directed trees. Further, our approach suggests a decentralized manner in which trees can be rearranged in order to improve their robustness.Comment: Submitted to CDC 201

Starling flock networks manage uncertainty in consensus at low cost

Flocks of starlings exhibit a remarkable ability to maintain cohesion as a group in highly uncertain environments and with limited, noisy information. Recent work demonstrated that individual starlings within large flocks respond to a fixed number of nearest neighbors, but until now it was not understood why this number is seven. We analyze robustness to uncertainty of consensus in empirical data from multiple starling flocks and show that the flock interaction networks with six or seven neighbors optimize the trade-off between group cohesion and individual effort. We can distinguish these numbers of neighbors from fewer or greater numbers using our systems-theoretic approach to measuring robustness of interaction networks as a function of the network structure, i.e., who is sensing whom. The metric quantifies the disagreement within the network due to disturbances and noise during consensus behavior and can be evaluated over a parameterized family of hypothesized sensing strategies (here the parameter is number of neighbors). We use this approach to further show that for the range of flocks studied the optimal number of neighbors does not depend on the number of birds within a flock; rather, it depends on the shape, notably the thickness, of the flock. The results suggest that robustness to uncertainty may have been a factor in the evolution of flocking for starlings. More generally, our results elucidate the role of the interaction network on uncertainty management in collective behavior, and motivate the application of our approach to other biological networks.Comment: 19 pages, 3 figures, 9 supporting figure

Gambling addiction in primary care: a survey of general practitioners in Solihull

We set out to study GPs’ understanding of gambling addiction, their experiences of, and confidence in, managing these patients in primary care, their perceived role and feasibility, their views on funding gambling treatment services, etc. To this end, we carried out a postal questionnaire survey of all GPs (N=136) in Solihull, England. Ninety eight (98) of the 136 (72%) GPs returned completed questionnaires. Three-quarters of GPs had seen gambling addicts in their practice but none had ever received any training in the management of gambling addiction. The large majority of GPs acknowledged that gambling addiction was an important public health problem with significant potential adverse impacts. 90.8% of GPs expressed lack of confidence in managing these patients but most were keen to do more to help, and receive training. Although they saw this disorder being within their remit, they highlighted that potential resource implications ought to be addressed if gambling addicts are to be successfully managed in primary care. Much more needs to be done to improve the identification and treatment of gambling addicts in primary care settings. Most GPs saw the care of these patients as within their remit, were willing to get involved and were receptive to more training. We hope our findings will inform the development and implementation of any future training program for GPs.Keywords: Gambling addiction; Primary care; General practitioners; Managemen

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