Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities

In this paper we consider instabilities of localised solutions in planar neural field firing rate models of Wilson-Cowan or Amari type. Importantly we show that angular perturbations can destabilise spatially localised solutions. For a scalar model with Heaviside firing rate function we calculate symmetric one-bump and ring solutions explicitly and use an Evans function approach to predict the point of instability and the shapes of the dominant growing modes. Our predictions are shown to be in excellent agreement with direct numerical simulations. Moreover, beyond the instability our simulations demonstrate the emergence of multi-bump and labyrinthine patterns. With the addition of spike-frequency adaptation, numerical simulations of the resulting vector model show that it is possible for structures without rotational symmetry, and in particular multi-bumps, to undergo an instability to a rotating wave. We use a general argument, valid for smooth firing rate functions, to establish the conditions necessary to generate such a rotational instability. Numerical continuation of the rotating wave is used to quantify the emergent angular velocity as a bifurcation parameter is varied. Wave stability is found via the numerical evaluation of an associated eigenvalue problem.

National evaluation of NHS genetics service investments: emerging issues from the cancer genetics pilots

In seeking to fulfil the ambition of the 2003 genetics white paper, Our Inheritance, Our Future, to ‘mainstream’ genetic knowledge and practices, the Department of Health provided start-up funding for pilot services in various clinical areas, including seven cancer genetics projects. To help to understand the challenges encountered by such an attempt at reconfiguring the organization and delivery of services in this field, a programme-level evaluation of the genetics projects was commissioned to consider the organizational issues faced. Using a qualitative approach, this research has involved comparative case-study work in 11 of the pilot sites, including four of the seven cancer genetics pilots. In this paper, the researchers present early findings from their work, focusing in particular on the cancer genetics pilots. They consider some of the factors that have influenced how the pilots have sought to address pre-existing sector, organizational and professional boundaries to these new ways of working. The article examines the relationship between these factors and the extent to which pilots have succeeded in setting up boundary-spanning services, dealing with human-resource issues and creating sustainable, ‘mainstreamed’ provision which attracts ongoing funding in a volatile NHS commissioning environment where funding priorities do not always favour preventive, risk-assessment services.