Two-Stage Document Length Normalization for Information Retrieval

The standard approach for term frequency normalization is based only on the document length. However, it does not distinguish the verbosity from the scope, these being the two main factors determining the document length. Because the verbosity and scope have largely different effects on the increase in term frequency, the standard approach can easily suffer from insufficient or excessive penalization depending on the specific type of long document. To overcome these problems, this paper proposes two-stage normalization by performing verbosity and scope normalization separately, and by employing different penalization functions. In verbosity normalization, each document is pre-normalized by dividing the term frequency by the verbosity of the document. In scope normalization, an existing retrieval model is applied in a straightforward manner to the pre-normalized document, finally leading us to formulate our proposed verbosity normalized (VN) retrieval model. Experimental results carried out on standard TREC collections demonstrate that the VN model leads to marginal but statistically significant improvements over standard retrieval models.Comment: 40 pages (to appear in ACM TOIS

The equations of some dispersionless limit

This short article presents a table of new equations which can be regarded as the generalized equations of the dispersionless limit of several nonlinear equations. From the definition expressed in an algebraic formula, one can get an equation for any positive numbers p and q. The equations were calculated by using the computers and were examined by hand-calculation up to p=10. Relations with some dispersionless hierarchies are mentioned.Comment: AmSTeX, 6 pages, amsppt.st

On the Craw-Ishii conjecture

Craw and Ishii proved that for a finite abelian group G in SL_3(C) every (projective) relative minimal model of C^3/G is isomorphic to the fine moduli space of \theta-stable G-constellations for some GIT parameter \theta. In this article, we conjecture that the same is true for a finite group G in GL_3(C) if a relative minimal model Y of X=C^3/G is smooth. We prove this for some abelian groups.Comment: comments are welcom