Colour image segmentation by the vector-valued Allen-Cahn phase-field model: a multigrid solution

We propose a new method for the numerical solution of a PDE-driven model for colour image segmentation and give numerical examples of the results. The method combines the vector-valued Allen-Cahn phase field equation with initial data fitting terms. This method is known to be closely related to the Mumford-Shah problem and the level set segmentation by Chan and Vese. Our numerical solution is performed using a multigrid splitting of a finite element space, thereby producing an efficient and robust method for the segmentation of large images.Comment: 17 pages, 9 figure

Ethnicity and Impressions of Personality Using the Five-Factor Model: Stereotyping or Cultural Sensitivity?

The current research investigates whether communities use ethnicity as a cue when forming personality impressions of others. Past research has shown that dress, smiling, hairstyle, and even facial symmetry of targets produce systematic differences in personality impressions across the domains of the Five Factor model of personality. We investigated whether the stated or apparent ethnicity of groups and individuals also produce stereotypic impressions of personality. This study compared impressions across members and non-members of the target groups and examined cue utility i.e. whether impressions of the groups agreed with aggregated self-impressions by group members. In all, the results clearly suggest that people utilize ethnicity as a cue when forming impressions of the personalities of groups and individuals, and although those impressions are exaggerated consistent with stereotype theory, they confer some utility in interpersonal perceptions across cultures. Stereotypes are a strategy used to interpret the complex social environment in the absence of more specific information. When that information is available, perceptions of others become more refined and accurate. Keywords: stereotyping, ethnicity, Five Factor model, Native Americans, cultural sensitivity, personalit

Adaptive time-stepping for incompressible flow. Part II: Navier-Stokes equations

We outline a new class of robust and efficient methods for solving the Navier- Stokes equations. We describe a general solution strategy that has two basic building blocks: an implicit time integrator using a stabilized trapezoid rule with an explicit Adams-Bashforth method for error control, and a robust Krylov subspace solver for the spatially discretized system. We present numerical experiments illustrating the potential of our approach. © 2010 Society for Industrial and Applied Mathematics

An efficient implementation of an implicit FEM scheme for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a modelling tool for processes with anomalous diffusion or spatial heterogeneity. However, the presence of a fractional differential operator causes memory (time fractional) or nonlocality (space fractional) issues, which impose a number of computational constraints. In this paper we develop efficient, scalable techniques for solving fractional-in-space reaction diffusion equations using the finite element method on both structured and unstructured grids, and robust techniques for computing the fractional power of a matrix times a vector. Our approach is show-cased by solving the fractional Fisher and fractional Allen-Cahn reaction-diffusion equations in two and three spatial dimensions, and analysing the speed of the travelling wave and size of the interface in terms of the fractional power of the underlying Laplacian operator

Classification of Perturbations for Membranes with Bending Rigidity

A complete classification of the renormalization-group flow is given for impurity-like marginal operators of membranes whose elastic stress scales like (\Delta r)^2 around the external critical dimension d_c=2. These operators are classified by characteristic functions on R^2 x R^2.Comment: latex, 3 .eps-file

Stabilized lowest order finite element approximation for linear three-field poroelasticity

A stabilized conforming mixed finite element method for the three-field (displacement, fluid flux and pressure) poroelasticity problem is developed and analyzed. We use the lowest possible approximation order, namely piecewise constant approximation for the pressure and piecewise linear continuous elements for the displacements and fluid flux. By applying a local pressure jump stabilization term to the mass conservation equation we ensure stability and avoid pressure oscillations. Importantly, the discretization leads to a symmetric linear system. For the fully discretized problem we prove existence and uniqueness, an energy estimate and an optimal a-priori error estimate, including an error estimate for the divergence of the fluid flux. Numerical experiments in 2D and 3D illustrate the convergence of the method, show the effectiveness of the method to overcome spurious pressure oscillations, and evaluate the added mass effect of the stabilization term.Comment: 25 page

Next Generation User Skills

The world is awash with statistics on the impact of the web on 21st century living, learning and working. They are accompanied by the pronouncements and predictions of experts from every camp, from those heralding a new brave new world of co-creation and choice, to warnings from the dark side in terms of ethics and educational standards, tempered by increasing recognition that ‘we’ may no longer be in control of such matters. Meanwhile, surveys report that around 80% of businesses have invested in IT and 60% have websites. Whilst the extent and value of adoption differs significantly across businesses and sectors, the foundations for new ways of working and doing business are broadly in place, with older and static businesses typifying the laggards. It would not be unsafe to project that, by 2013, even more people will be required to use ICT in the workplace and in their everyday lives, increasingly involving online communication and web-based applications. This represents a scenario to which those responsible for developing curricula and awards must respond – in the primary and secondary phases, vocational and applied learning, work based and adult community provision and higher education. To ensure the relevance of and to influence the ongoing enhancement of user ICT provision and the associated awards, Digital 2020 and the Scottish Qualifications Authority jointly commissioned Sero Consulting to develop a vision for ICT user skills in 2013 – ‘Next Generation User Skills’ – taking account of: • Skills that all employers will need, which they may not currently recognise. • Skills that people (especially young people) will already have, but which may not be accredited. • Essential skills for living and learning in a digital age. This paper is drawn from the resulting public report, ‘Next Generation User Skills – Working, Learning & Living Online in 2013’ (September 2008), which provides: • An overview of the current ICT user skills landscape. • A model representing digital activities and competencies that might constitute the ‘Next Generation User Skillscape’. • A mapping of that activity space onto tools and awards, with a gap analysis identifying weaknesses in provision. • An overview of the recommendations to the report sponsors

Heats and Animosities: What Rural New Yorkers Think about Local Taxes and Services

CaRDI Research & Policy Brief Issue

A preconditioner for the 3D Oseen equations

We describe a preconditioner for the linearised incompressible Navier-Stokes equations (the Oseen equations) which requires as components only a preconditioner/solver for each of a discrete Laplacian and a discrete advection-diffusion operator. With this preconditioner, convergence of an iterative method such as GMRES is independent of the mesh size and depends only mildly on the viscosity parameter (the inverse Reynolds number). Thus when the component preconditioner/solvers are effective on their respective subproblems (as one expects with an appropriate multigrid cycle for instance) a fast Oseen solver results