The metaphorical understanding of power and authority

No abstract available

Foregrounding, burying and plot construction

No abstract available

Diachronic and synchronic thesauruses

No abstract available

"Civilization arranged in chronological strata": a digital approach to the English semantic space

No abstract available

Mapping metaphors of wealth and want: a digital approach

The AHRC-funded Mapping Metaphor with the Historical Thesaurus project aims to provide data on the extent and development of metaphor across the history of English. It uses the full database of the Historical Thesaurus of English, which extensively categorises and classifies the recorded vocabulary of the English language from Old English to the present day. By using this database to map semantic categories onto one another, and thus showing lexical overlap in different conceptual fields, we aim in the project to provide results which will demonstrate the widespread, systematic and far-reaching impact of metaphor on English.<p></p> This paper outlines the digital and linguistic methodologies used by the project, and presents a case study of the semantic categories of wealth and poverty, demonstrating the metaphorical links between these categories and the rest of the language. In addition, we discuss the nature of lexical overlap as we use it in the project, and discuss both the quantitative and diachronic dimensions of the data we are manipulating and their implications for projects of this type.<p></p&gt

Unknotting genus one knots

For any knot with genus one and unknotting number one, other than the figure-eight knot, we prove that there is exactly one way to unknot it by means of a crossing change. In the case of the figure-eight knot, we prove that there are precisely two unknotting crossing changes. The proof uses sutured manifold theory and an analysis of the arc complex of the once-punctured torus.Comment: 17 pages, 11 figures; v2 corrects an error in Section 4; v3 is the final version. To appear in Commentarii Mathematici Helvetic

Schemata

No abstract available

An upper bound on Reidemeister moves

We provide an explicit upper bound on the number of Reidemeister moves required to pass between two diagrams of the same link. This leads to a conceptually simple solution to the equivalence problem for links.Comment: 40 pages, 14 figures; v2: very minor change

Distribution of diameters for Erd\"os-R\'enyi random graphs

We study the distribution of diameters d of Erd\"os-R\'enyi random graphs with average connectivity c. The diameter d is the maximum among all shortest distances between pairs of nodes in a graph and an important quantity for all dynamic processes taking place on graphs. Here we study the distribution P(d) numerically for various values of c, in the non-percolating and the percolating regime. Using large-deviations techniques, we are able to reach small probabilities like 10^{-100} which allow us to obtain the distribution over basically the full range of the support, for graphs up to N=1000 nodes. For values c<1, our results are in good agreement with analytical results, proving the reliability of our numerical approach. For c>1 the distribution is more complex and no complete analytical results are available. For this parameter range, P(d) exhibits an inflection point, which we found to be related to a structural change of the graphs. For all values of c, we determined the finite-size rate function Phi(d/N) and were able to extrapolate numerically to N->infinity, indicating that the large deviation principle holds.Comment: 9 figure

Scheduling Parallel Jobs with Linear Speedup

We consider a scheduling problem where a set of jobs is distributed over parallel machines. The processing time of any job is dependent on the usage of a scarce renewable resource, e.g., personnel. An amount of k units of that resource can be allocated to the jobs at any time, and the more of that resource is allocated to a job, the smaller its processing time. The dependence of processing times on the amount of resources is linear for any job. The objective is to find a resource allocation and a schedule that minimizes the makespan. Utilizing an integer quadratic programming relaxation, we show how to obtain a (3+e)-approximation algorithm for that problem, for any e>0. This generalizes and improves previous results, respectively. Our approach relies on a fully polynomial time approximation scheme to solve the quadratic programming relaxation. This result is interesting in itself, because the underlying quadratic program is NP-hard to solve in general. We also briefly discuss variants of the problem and derive lower bounds.operations research and management science;