23,737 research outputs found

    Analysis of equivalence mapping for terminology services

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    This paper assesses the range of equivalence or mapping types required to facilitate interoperability in the context of a distributed terminology server. A detailed set of mapping types were examined, with a view to determining their validity for characterizing relationships between mappings from selected terminologies (AAT, LCSH, MeSH, and UNESCO) to the Dewey Decimal Classification (DDC) scheme. It was hypothesized that the detailed set of 19 match types proposed by Chaplan in 1995 is unnecessary in this context and that they could be reduced to a less detailed conceptually-based set. Results from an extensive mapping exercise support the main hypothesis and a generic suite of match types are proposed, although doubt remains over the current adequacy of the developing Simple Knowledge Organization System (SKOS) Core Mapping Vocabulary Specification (MVS) for inter-terminology mapping

    Definable equivalence relations and zeta functions of groups

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    We prove that the theory of the pp-adics Qp{\mathbb Q}_p admits elimination of imaginaries provided we add a sort for GLn(Qp)/GLn(Zp){\rm GL}_n({\mathbb Q}_p)/{\rm GL}_n({\mathbb Z}_p) for each nn. We also prove that the elimination of imaginaries is uniform in pp. Using pp-adic and motivic integration, we deduce the uniform rationality of certain formal zeta functions arising from definable equivalence relations. This also yields analogous results for definable equivalence relations over local fields of positive characteristic. The appendix contains an alternative proof, using cell decomposition, of the rationality (for fixed pp) of these formal zeta functions that extends to the subanalytic context. As an application, we prove rationality and uniformity results for zeta functions obtained by counting twist isomorphism classes of irreducible representations of finitely generated nilpotent groups; these are analogous to similar results of Grunewald, Segal and Smith and of du Sautoy and Grunewald for subgroup zeta functions of finitely generated nilpotent groups.Comment: 89 pages. Various corrections and changes. To appear in J. Eur. Math. So

    On the Exact Evaluation of Certain Instances of the Potts Partition Function by Quantum Computers

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    We present an efficient quantum algorithm for the exact evaluation of either the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function Z for a family of graphs related to irreducible cyclic codes. This problem is related to the evaluation of the Jones and Tutte polynomials. We consider the connection between the weight enumerator polynomial from coding theory and Z and exploit the fact that there exists a quantum algorithm for efficiently estimating Gauss sums in order to obtain the weight enumerator for a certain class of linear codes. In this way we demonstrate that for a certain class of sparse graphs, which we call Irreducible Cyclic Cocycle Code (ICCC_\epsilon) graphs, quantum computers provide a polynomial speed up in the difference between the number of edges and vertices of the graph, and an exponential speed up in q, over the best classical algorithms known to date
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