We present a new keyword extraction algorithm that applies to a single document without using a corpus. Frequent terms are extracted first, then a set of co-occurrences between each term and the frequent terms, i.e., occurrences in the same sentences, is generated. Co-occurrence distribution shows importance of a term in the document as follows. If the probability distribution of co-occurrence between term a and the frequent terms is biased to a particular subset of frequent terms, then term a is likely to be a keyword. The degree of bias of a distribution is measured by the χ 2 -measure. Our algorithm shows comparable performance to tfidf without using a corpus.

Recently an action based on Lie 3-algebras was proposed to describe M2-branes. We study the case of infinite dimensional Lie 3-algebras based on the Nambu-Poisson structure of three dimensional manifolds. We show that the model contains self-dual 2-form gauge fields in 6 dimensions, and the result may be interpreted as the M5-brane world-volume action.

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Abstract:We investigate the Bagger-Lambert-Gustavsson model associated with the Nambu-Poisson algebra as a theory describing a single M5-brane. We argue that the model is a gauge theory associated with the volume-preserving diffeomorphism in the threedimensional internal space. We derive gauge transformations, actions, supersymmetry transformations, and equations of motions in terms of six-dimensional fields. The equations of motions are written in gauge-covariant form, and the equations for tensor fields have manifest self-dual structure. We demonstrate that the double dimensional reduction of the model reproduces the non-commutative U(1) gauge theory on a D4-brane with a small noncommutativity parameter. We establish relations between parameters in the BLG model and those in M-theory. This shows that the model describes an M5-brane in a large C-field background.