A renormalisation group method. II. Approximation by local polynomials

This paper is the second in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. The method is set within a normed algebra $\mathcal{N}$ of functionals of the fields. In this paper, we develop a general method---localisation---to approximate an element of $\mathcal{N}$ by a local polynomial in the fields. From the point of view of the renormalisation group, the construction of the local polynomial corresponding to $F$ in $\mathcal{N}$ amounts to the extraction of the relevant and marginal parts of $F$. We prove estimates relating $F$ and its corresponding local polynomial, in terms of the $T_{\phi}$ semi-norm introduced in part I of the series.Comment: 30 page

Facilitating open plot structures in story driven video games using situation generation

Story driven video games are rising in popularity, along with the players desire to make meaningful choice within the plot and therefore become more involved and immersed within the experience. This paper investigates the problems which arise from implementing interactive narrative within video games and potential techniques to solve those problems. The main focus of the study was the situation generation technique, used to maintain the continuity within open, emergent plot structures, using behaviour trees as a means to implement and traverse plot sequences. The ISGEngine was developed during the course of this study in order to implement and evaluate the situation generation technique

An fMRI Compatible Touchscreen to Measure Hand Kinematics During a Complex Drawing Task

ACKNOWLEDGMENTS This study was funded by the Northwood Trust and the Aberdeen Biomedical Imaging Centre, University of Aberdeen. GDW is part of the SINASPE collaboration (Scottish Imaging Network - A Platform for Scientific Excellence www.SINAPSE.ac.uk). The authors thank Baljit Jagpal, Nichola Crouch, Beverly Maclennan and Katrina Klaasen for their help with running the experiment and Dawn Younie and Teresa Morris for their help with recruitment and scheduling. We also thank the participants for their generous participation.Peer reviewedPublisher PD

Overview of the Global Sanitation Problem

human development, water, sanitation

The strong interaction limit of continuous-time weakly self-avoiding walk

The strong interaction limit of the discrete-time weakly self-avoiding walk (or Domb--Joyce model) is trivially seen to be the usual strictly self-avoiding walk. For the continuous-time weakly self-avoiding walk, the situation is more delicate, and is clarified in this paper. The strong interaction limit in the continuous-time setting depends on how the fugacity is scaled, and in one extreme leads to the strictly self-avoiding walk, in another to simple random walk. These two extremes are interpolated by a new model of a self-repelling walk that we call the "quick step" model. We study the limit both for walks taking a fixed number of steps, and for the two-point function