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.

On the basis of the collective field method, we analyze the Calogero-Sutherland model (CSM) and the Selberg-Aomoto integral, which defines, in particular case, the partition function of the matrix models. Vertex operator realizations for some of the eigenstates (the Jack polynomials) of the CSM Hamiltonian are obtained. We derive Virasoro constraint for the generalized matrix models and indicate relations with the CSM operators. Similar results are presented for the q-deformed case (the Macdonald operator and polynomials), which gives the generating functional of infinitely many conserved charges in the CSM. * JSPS fellow

We present two derivations of the multiple D2 action from the multiple M2brane model proposed by Bagger-Lambert and Gustavsson. The first one is to start from Lie 3-algebra associated with given (arbitrary) Lie algebra. The Lie 3-algebra metric is not positive definite but the zero-norm generators merely correspond to Lagrange multipliers. Following the work of Mukhi and Papageorgakis, we derive D2-brane action from the model by giving a variable a vacuum expectation value. The second derivation is based on the correspondence between M2 and M5. We compactify one dimension and wind M5-brane along this direction. This leads to a noncommutative D4 action. Multiple D2 action is then obtained by suitably choosing the non-commutative parameter on the two-torus. It also implies a natural interpretation to the extra generator in Lie 3-algebra, namely the winding of M5 world volume around S 1 which defines the reduction of M theory to II A superstring.

Using the collective field method, we find a relation between the Jack symmetric polynomials, which describe the excited states of the Calogero-Sutherland model, and the singular vectors of the W N algebra. Based on this relation, we obtain their integral representations. We also give a direct algebraic method which leads to the same result, and integral representations of the skew-Jack polynomials.hep-th/9503043

Social networks play important roles in the Semantic Web: knowledge management, information retrieval, ubiquitous computing, and so on. We propose a social network extraction system called POLY-PHONET, which employs several advanced techniques to extract relations of persons, detect groups of persons, and obtain keywords for a person. Search engines, especially Google, are used to measure co-occurrence of information and obtain Web documents.Several studies have used search engines to extract social networks from the Web, but our research advances the following points: First, we reduce the related methods into simple pseudocodes using Google so that we can build up integrated systems. Second, we develop several new algorithms for social networking mining such as those to classify relations into categories, to make extraction scalable, and to obtain and utilize person-to-word relations. Third, every module is implemented in POLYPHONET, which has been used at four academic conferences, each with more than 500 participants. We overview that system. Finally, a novel architecture called Super Social Network Mining is proposed; it utilizes simple modules using Google and is characterized by scalability and Relate-Identify processes: Identification of each entity and extraction of relations are repeated to obtain a more precise social network.