Generalized dilatation operator method for non-relativistic holography

We present a general algorithm for constructing the holographic dictionary for Lifshitz and hyperscaling violating Lifshitz backgrounds for any value of the dynamical exponent $z$ and any value of the hyperscaling violation parameter $\theta$ 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

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