The Douglas-Peucker algorithm for line simplification: Re-evaluation through visualization

The primary aim of this paper is to illustrate the value of visualization in cartography and to indicate that tools for the generation and manipulation of realistic images are of limited value within this application. This paper demonstrates the value of visualization within one problem in cartography, namely the generalisation of lines. It reports on the evaluation of the Douglas-Peucker algorithm for line simplification. Visualization of the simplification process and of the results suggest that the mathematical measures of performance proposed by some other researchers are inappropriate, misleading and questionable

Microscopic modelling of the flow properties of polymers

The understanding of the flow behaviour of polymeric liquids is of great interest from a practical as well as a theoretical point of view. An important part of the research in this field consists of the development of suitable models, describing the rheological properties of the materials. Depending upon its purpose, such a model may be based upon empirical knowledge of the macroscopic flow behaviour or on information about the microstructure of the materials. Moreover, for a given system, different types of modelling may be possible. In order to provide an overview of the various approaches in this area the basic principles of some important models are discussed: continuum, bead-rod-spring, transient network, reptation and configuration tensor models. Emphasis has been put on a consistent treatment of the fundamentals of the various models and their interrelationship, rather than considering any of them in much detail

Non-homogeneous polygonal Markov fields in the plane: graphical representations and geometry of higher order correlations

We consider polygonal Markov fields originally introduced by Arak and Surgailis (1989). Our attention is focused on fields with nodes of order two, which can be regarded as continuum ensembles of non-intersecting contours in the plane, sharing a number of features with the two-dimensional Ising model. We introduce non-homogeneous version of polygonal fields in anisotropic enviroment. For these fields we provide a class of new graphical constructions and random dynamics. These include a generalised dynamic representation, generalised and defective disagreement loop dynamics as well as a generalised contour birth and death dynamics. Next, we use these constructions as tools to obtain new exact results on the geometry of higher order correlations of polygonal Markov fields in their consistent regime.Comment: 54 page

An example-based approach to translating sign language

Users of sign languages are often forced to use a language in which they have reduced competence simply because documentation in their preferred format is not available. While some research exists on translating between natural and sign languages, we present here what we believe to be the first attempt to tackle this problem using an example-based (EBMT) approach. Having obtained a set of English–Dutch Sign Language examples, we employ an approach to EBMT using the ‘Marker Hypothesis’ (Green, 1979), analogous to the successful system of (Way & Gough, 2003), (Gough & Way, 2004a) and (Gough & Way, 2004b). In a set of experiments, we show that encouragingly good translation quality may be obtained using such an approach

Vanishing largest Lyapunov exponent and Tsallis entropy

We present a geometric argument that explains why some systems having vanishing largest Lyapunov exponent have underlying dynamics aspects of which can be effectively described by the Tsallis entropy. We rely on a comparison of the generalised additivity of the Tsallis entropy versus the ordinary additivity of the BGS entropy. We translate this comparison in metric terms by using an effective hyperbolic metric on the configuration/phase space for the Tsallis entropy versus the Euclidean one in the case of the BGS entropy. Solving the Jacobi equation for such hyperbolic metrics effectively sets the largest Lyapunov exponent computed with respect to the corresponding Euclidean metric to zero. This conclusion is in agreement with all currently known results about systems that have a simple asymptotic behaviour and are described by the Tsallis entropy.Comment: 15 pages, No figures. LaTex2e. Some overlap with arXiv:1104.4869 Additional references and clarifications in this version. To be published in QScience Connec

Dual generators of the fundamental group and the moduli space of flat connections

We define the dual of a set of generators of the fundamental group of an oriented two-surface $S_{g,n}$ of genus $g$ with $n$ punctures and the associated surface $S_{g,n}\setminus D$ with a disc $D$ removed. This dual is another set of generators related to the original generators via an involution and has the properties of a dual graph. In particular, it provides an algebraic prescription for determining the intersection points of a curve representing a general element of the fundamental group $\pi_1(S_{g,n}\setminus D)$ with the representatives of the generators and the order in which these intersection points occur on the generators.We apply this dual to the moduli space of flat connections on $S_{g,n}$ and show that when expressed in terms both, the holonomies along a set of generators and their duals, the Poisson structure on the moduli space takes a particularly simple form. Using this description of the Poisson structure, we derive explicit expressions for the Poisson brackets of general Wilson loop observables associated to closed, embedded curves on the surface and determine the associated flows on phase space. We demonstrate that the observables constructed from the pairing in the Chern-Simons action generate of infinitesimal Dehn twists and show that the mapping class group acts by Poisson isomorphisms.Comment: 54 pages, 13 .eps figure

On mean-convex Alexandrov embedded surfaces in the 3-sphere

We consider mean-convex Alexandrov embedded surfaces in the round unit 3-sphere, and show under which conditions it is possible to continuously deform these preserving mean-convex Alexandrov embeddedness.Comment: arXiv admin note: substantial text overlap with arXiv:1309.427