Three dimensional visualization of the World Wide Web

Although large-scale public hypermedia structures such as the World Wide Web are popularly referred to as "cyberspace", the extent to which they constitute a space in the everyday sense of the word is questionable. This paper reviews recent work in the area of three dimensional (3D) visualization of the Web that has attempted to depict it in the form of a recognizable space; in other words, as a navigable landscape that may be visibly populated by its users. Our review begins by introducing a range of visualizations that address different aspects of using the Web. These include visualizations of Web structure, especially of links, that act as 3D maps; browsing history; searches; evolution of the Web; and the presence and activities of multiple users. We then summarize the different techniques that are employed by these visualizations. We conclude with a discussion of key challenges for the future.

The Warwick-Edinburgh Mental Well-Being Scale

Background There is increasing international interest in the concept of mental well-being and its contribution to all aspects of human life. Demand for instruments to monitor mental well-being at a population level and evaluate mental health promotion initiatives is growing. This article describes the development and validation of a new scale, comprised only of positively worded items relating to different aspects of positive mental health: the Warwick-Edinburgh Mental Well-Being Scale (WEMWBS). Methods WEMWBS was developed by an expert panel drawing on current academic literature, qualitative research with focus groups, and psychometric testing of an existing scale. It was validated on a student and representative population sample. Content validity was assessed by reviewing the frequency of complete responses and the distribution of responses to each item. Confirmatory factor analysis was used to test the hypothesis that the scale measured a single construct. Internal consistency was assessed using Cronbach’s alpha. Criterion validity was explored in terms of correlations between WEMWBS and other scales and by testing whether the scale discriminated between population groups in line with pre-specified hypotheses. Test-retest reliability was assessed at one week using intra-class correlation coefficients. Susceptibility to bias was measured using the Balanced Inventory of Desired Responding. Results WEMWBS showed good content validity. Confirmatory factor analysis supported the single factor hypothesis. A Cronbach’s alpha score of 0.89 (student sample) and 0.91 (population sample) suggests some item redundancy in the scale. WEMWBS showed high correlations with other mental health and well-being scales and lower correlations with scales measuring overall health. Its distribution was near normal and the scale did not show ceiling effects in a population sample. It discriminated between population groups in a way that is largely consistent with the results of other population surveys. Test–retest reliability at one week was high (0.83). Social desirability bias was lower or similar to that of other comparable scales. Conclusions WEMWBS is a measure of mental well-being focusing entirely on positive aspects of mental health. As a short and psychometrically robust scale, with no ceiling effects in a population sample, it offers promise as a tool for monitoring mental well-being at a population level. Whilst WEMWBS should appeal to those evaluating mental health promotion initiatives, it is important that the scale’s sensitivity to change is established before it is recommended in this context.

Discrete breathers in a two-dimensional Fermi-Pasta-Ulam lattice

Using asymptotic methods, we investigate whether discrete breathers are supported by a two-dimensional Fermi-Pasta-Ulam lattice. A scalar (one-component) two-dimensional Fermi-Pasta-Ulam lattice is shown to model the charge stored within an electrical transmission lattice. A third-order multiple-scale analysis in the semi-discrete limit fails, since at this order, the lattice equations reduce to the (2+1)-dimensional cubic nonlinear Schrödinger (NLS) equation which does not support stable soliton solutions for the breather envelope. We therefore extend the analysis to higher order and find a generalised $(2+1)$-dimensional NLS equation which incorporates higher order dispersive and nonlinear terms as perturbations. We find an ellipticity criterion for the wave numbers of the carrier wave. Numerical simulations suggest that both stationary and moving breathers are supported by the system. Calculations of the energy show the expected threshold behaviour whereby the energy of breathers does {\em not} go to zero with the amplitude; we find that the energy threshold is maximised by stationary breathers, and becomes arbitrarily small as the boundary of the domain of ellipticity is approached.

Large-scale neural dynamics: simple and complex

We review the use of neural field models for modelling the brain at the large scales necessary for interpreting EEG, fMRI, MEG and optical imaging data. Albeit a framework that is limited to coarse-grained or mean-field activity, neural field models provide a framework for unifying data from different imaging modalities. Starting with a description of neural mass models we build to spatially extended cortical models of layered two-dimensional sheets with long range axonal connections mediating synaptic interactions. Reformulations of the fundamental non-local mathematical model in terms of more familiar local differential (brain wave) equations are described. Techniques for the analysis of such models, including how to determine the onset of spatio-temporal pattern forming instabilities, are reviewed. Extensions of the basic formalism to treat refractoriness, adaptive feedback and inhomogeneous connectivity are described along with open challenges for the development of multi-scale models that can integrate macroscopic models at large spatial scales with models at the microscopic scale.