9,722 research outputs found
"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>
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
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
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;
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