Canonical heights on the jacobians of curves of genus 2 and the infinite descent

We give an algorithm to compute the canonical height on a Jacobian of a curve of genus 2. The computations involve only working with the Kummer surface and so lengthy computations with divisors in the Jacobian are avoided. We use this height algorithm to give an algorithm to perform the infinite descent stage of computing the Mordell-Weil group. This last stage is performed by a lattice enlarging procedure

Experiences of post-qualifying study in social work

This article is based on a research project to explore the experiences of past and current candidates for post-qualifying awards in social work in England. Also included in the study are the Leads of the post-qualifying consortia in England. The study used questionnaire survey and nominal group techniques to gather data, which were coded and categorised into themes. The main findings relate to the perceived purposes of post-qualifying study, motivations for undertaking post-qualifying study, the factors that sustain and hinder study, the advice that those who have or who are experiencing post-qualifying study would give to those about to start and future plans and hopes in this area.Post-qualifying study is generally valued, especially in relation to the opportunities it provides for professional development. The support of a mentor who has direct experience of the candidate's programme is highly prized, as are clear and consistent guidance from the programme and meaningful study time and workload relief from employers. There are also frustrations for some candidates who do not feel that their post-qualifying study has stretched them beyond qualifying standards or who experience the teaching as divorced from the realities of daily practice. The appetite for a wider choice of post-qualifying modules suggests that providers of post-qualifying study will need to collaborate within and across regions in order to achieve a critical mass of candidates for more specialist or focused learning. The study suggests a need for further research to understand the impact of post-qualifying study on candidates' social work practice.The article concludes with two checklists of questions, one for individual candidates and another for agencies and programmes. These questions arise from the findings in the research

A model for the anisotropic response of fibrous soft tissues using six discrete fibre bundles

The development of accurate constitutive models of fibrous soft-tissues is a challenging problem. Many consider the tissue to be a collection of fibres with a continuous distribution function representing their orientations. A novel discrete fibre model is presented consisting of six weighted fibre bundles. Each bundle is oriented such that they pass through opposing vertices of a regular icosahedron. A novel aspect of the model is the use of simple analytical distribution functions to simulate the undulated collagen fibres. This approach yields a closed form analytical expression for the strain energy function for the collagen fibre bundle that avoids the sometimes costly numerical integration of some statistical distribution functions. The elastin fibres are characterized by a neo-Hookean strain energy function. The model accurately simulates the biaxial stretching of rabbit-skin (error-of-fit 8.7%), the uniaxial stretching of pig-skin (error-of-fit 7.6%), equibiaxial loading of aortic valve cusp (error-of-fit 0.8%), and the simple shear of rat septal myocardium (error-of-fit 9.1%). The proposed model compares favourably with previously published soft-tissue models and alternative methods of representing undulated collagen fibres. The stiffness of collagen fibres predicted by the model ranges from 8.0 MPa to 0.93 GPa. The stiffness of elastin fibres ranges from 2.5 kPa to 154.4 kPa. The anisotropy of model resulting from the representation of the fibre field with a discrete number of fibres is also explored

Search Tree Pruning for Progressive Neural Architecture Search

Our neural architecture search algorithm progressively searches a tree of neural network architectures. Child nodes are created by inserting new layers determined by a transition graph into a parent network up to a maximum depth and pruned when performance is worse than its parent. This increases efficiency but makes the algorithm greedy. Simpler networks are successfully found before more complex ones that can achieve benchmark performance similar to other top-performing networks

Professional boundaries: research report

In 2008 the General Social Care Council (GSCC) published Raising standards: Social work conduct in England 2003-2008. This constituted the GSCC’s first report covering the work undertaken to uphold standards and protect people who use social care services. The GSCC’s analysis revealed that a considerable proportion of conduct cases, some 40%, involved allegations of 'inappropriate relations'. In the light of this finding, and the release by the Council for Healthcare Regulatory Excellence (CHRE) of sexual boundaries guidance for healthcare workers at the beginning of this year (Halter et al, 2009), the GSCC committed itself to exploring the possibility of producing professional boundaries guidance for social workers. To begin this exploration, the GSCC commissioned a study in early 2009.This is the report of that study. There were two main purposes. First, to establish what professional boundaries1 guidance currently exists for social workers, or for sections of the workforce that includes social workers in the United Kingdom, and the content of any such guidance. Secondly, to identify and discuss a number of other examples of professional boundaries guidance to act as points of reference for the GSCC’s project. The aim was to identify and discuss examples relevant to the GSCC’s project

Connections of activated hopping processes with the breakdown of the Stokes-Einstein relation and with aspects of dynamical heterogeneities

We develop a new extended version of the mode-coupling theory (MCT) for glass transition, which incorporates activated hopping processes via the dynamical theory originally formulated to describe diffusion-jump processes in crystals. The dynamical-theory approach adapted here to glass-forming liquids treats hopping as arising from vibrational fluctuations in quasi-arrested state where particles are trapped inside their cages, and the hopping rate is formulated in terms of the Debye-Waller factors characterizing the structure of the quasi-arrested state. The resulting expression for the hopping rate takes an activated form, and the barrier height for the hopping is ``self-generated'' in the sense that it is present only in those states where the dynamics exhibits a well defined plateau. It is discussed how such a hopping rate can be incorporated into MCT so that the sharp nonergodic transition predicted by the idealized version of the theory is replaced by a rapid but smooth crossover. We then show that the developed theory accounts for the breakdown of the Stokes-Einstein relation observed in a variety of fragile glass formers. It is also demonstrated that characteristic features of dynamical heterogeneities revealed by recent computer simulations are reproduced by the theory. More specifically, a substantial increase of the non-Gaussian parameter, double-peak structure in the probability distribution of particle displacements, and the presence of a growing dynamic length scale are predicted by the extended MCT developed here, which the idealized version of the theory failed to reproduce. These results of the theory are demonstrated for a model of the Lennard-Jones system, and are compared with related computer-simulation results and experimental data.Comment: 13 pages, 5 figure