Mesenteric desmoid tumor developing on the site of an excised gastrointestinal stromal tumor

We present a case of a rare and unusual occurrence of a desmoid tumor at the site of a resected gastrointestinal stromal tumor and mimicking a recurrence, with a brief discussion of the management of desmoid tumors

Limitations of perturbative techniques in the analysis of rhythms and oscillations

Perturbation theory is an important tool in the analysis of oscillators and their response to external stimuli. It is predicated on the assumption that the perturbations in question are “sufficiently weak”, an assumption that is not always valid when perturbative methods are applied. In this paper, we identify a number of concrete dynamical scenarios in which a standard perturbative technique, based on the infinitesimal phase response curve (PRC), is shown to give different predictions than the full model. Shear-induced chaos, i.e., chaotic behavior that results from the amplification of small perturbations by underlying shear, is missed entirely by the PRC. We show also that the presence of “sticky” phase–space structures tend to cause perturbative techniques to overestimate the frequencies and regularity of the oscillations. The phenomena we describe can all be observed in a simple 2D neuron model, which we choose for illustration as the PRC is widely used in mathematical neuroscience

Phase-amplitude descriptions of neural oscillator models

Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now particularly well advanced, and has allowed for the development of a theory of weakly connected neural networks. However, the strong-attraction assumption may well not be the natural one for many neural oscillator models. For example, the popular conductance based Morris-Lecar model is known to respond to periodic pulsatile stimulation in a chaotic fashion that cannot be adequately described with a phase reduction. In this paper, we generalise the phase description that allows one to track the evolution of distance from the cycle as well as phase on cycle. We use a classical technique from the theory of ordinary differential equations that makes use of a moving coordinate system to analyse periodic orbits. The subsequent phase-amplitude description is shown to be very well suited to understanding the response of the oscillator to external stimuli (which are not necessarily weak). We consider a number of examples of neural oscillator models, ranging from planar through to high dimensional models, to illustrate the effectiveness of this approach in providing an improvement over the standard phase-reduction technique. As an explicit application of this phase-amplitude framework, we consider in some detail the response of a generic planar model where the strong-attraction assumption does not hold, and examine the response of the system to periodic pulsatile forcing. In addition, we explore how the presence of dynamical shear can lead to a chaotic response

Willingness-to-pay surveys - a streamlined approach: Guidance notes for small town water services

These guidance notes describe good practice for conducting robust 'willingness-to-pay' (WTP) surveys in small towns, using the Contingent Valuation Method (CVM), as part of a demand-responsive approach to the supply of services. The urban water sector in low- and middle-income countries requires good quality data to justify future investment proposals; develop a better understanding of user perceptions and preferences; support the selection of preferred service options; and to set out the scope for future tariff increases. CVM surveys are a reliable means of generating such valuable information. Key areas covered in this book include how to design and implement a WTP survey, as well as how to best use the survey information to inform project design and policy-making. Its aim is to encourage wider use of WTP surveys, particularly for small towns where it is inappropriate to merely assume which service options users prefer and are willing to pay for. This book has been developed as part of the DFID Knowledge and Research project R7852 Optimised Management of Watsan Services in Small Towns

Mathematical Biology Limitations of perturbative techniques in the analysis of rhythms and oscillations

Abstract Perturbation theory is an important tool in the analysis of oscillators and their response to external stimuli. It is predicated on the assumption that the perturbations in question are "sufficiently weak", an assumption that is not always valid when perturbative methods are applied. In this paper, we identify a number of concrete dynamical scenarios in which a standard perturbative technique, based on the infinitesimal phase response curve (PRC), is shown to give different predictions than the full model. Shear-induced chaos, i.e., chaotic behavior that results from the amplification of small perturbations by underlying shear, is missed entirely by the PRC. We show also that the presence of "sticky" phase-space structures tend to cause perturbative techniques to overestimate the frequencies and regularity of the oscillations. The phenomena we describe can all be observed in a simple 2D neuron model, which we choose for illustration as the PRC is widely used in mathematical neuroscience