372,075 research outputs found

    Generalized dilatation operator method for non-relativistic holography

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    We present a general algorithm for constructing the holographic dictionary for Lifshitz and hyperscaling violating Lifshitz backgrounds for any value of the dynamical exponent zz and any value of the hyperscaling violation parameter θ\theta compatible with the null energy condition. The objective of the algorithm is the construction of the general asymptotic solution of the radial Hamilton-Jacobi equation subject to the desired boundary conditions, from which the full dictionary can be subsequently derived. Contrary to the relativistic case, we find that a fully covariant construction of the asymptotic solution for running non-relativistic theories necessitates an expansion in the eigenfunctions of two commuting operators instead of one. This provides a covariant but non-relativistic grading of the expansion, according to the number of time derivatives.Comment: 6 pages; v2 references added, discussion of the algorithm and the holographic dictionary improve

    Grouping Synonyms by Definitions

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    We present a method for grouping the synonyms of a lemma according to its dictionary senses. The senses are defined by a large machine readable dictionary for French, the TLFi (Tr\'esor de la langue fran\c{c}aise informatis\'e) and the synonyms are given by 5 synonym dictionaries (also for French). To evaluate the proposed method, we manually constructed a gold standard where for each (word, definition) pair and given the set of synonyms defined for that word by the 5 synonym dictionaries, 4 lexicographers specified the set of synonyms they judge adequate. While inter-annotator agreement ranges on that task from 67% to at best 88% depending on the annotator pair and on the synonym dictionary being considered, the automatic procedure we propose scores a precision of 67% and a recall of 71%. The proposed method is compared with related work namely, word sense disambiguation, synonym lexicon acquisition and WordNet construction
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