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

Exploring the effect of group polarisation on perceived invulnerability in general aviation pilots : a thesis presented in partial fulfilment of the requirements for the degree of Master of Aviation at Massey University

Although both perceived invulnerability and group polarisation are well known psychological phenomena, there has not been any research conducted to examine the effect of group polarisation on the level of perceived invulnerability amongst general aviation pilots. Two studies were conducted to measure the level of perceived invulnerability amongst general aviation pilots and to test whether the level of perceived invulnerability was affected due to group polarisation. The first study tested 34 pilots. Although the majority of the pilots exhibited perceived invulnerability, there was no evidence suggesting that low level group interaction induced group polarisation leading to an increase in individual's level of perceived invulnerability. The second study examined 78 pilots. Although the majority of the participants displayed perceived invulnerability, there was no evidence suggesting that high level group interaction resulted in group polarisation leading to an increase in individual's level of perceived invulnerability. There was no evidence that the two experimental manipulations (low group interaction and high group interaction) differed in effectiveness, as the effect size between studies I and II did not significantly differ. Although it is of some concern to general aviation safety that the majority of the pilots in both studies exhibited perceived invulnerability, the level of perceived invulnerability does not appear to be increased by a group polarisation effect. The latter finding is consistent with safe operations, having found no evidence that multi-crew operations lead to increased levels of perceived invulnerability. In addition to the implication of the current findings, limitations of the present study, possible areas for further research and recommendations are presented

Correlation Structures Corresponding to Forward Rates

In finance, there is a constant effort to model future prices of stocks, bonds, and commodities; the ability to predict future behaviour provides important information about the underlying structure of these securities. While it has become common to model a single stock using the Black-Scholes formulation, the modelling of bond prices requires one to simulate the change of interest rates as a function of their maturity, which requires one to model the movement of an entire yield curve. If one studies the spectral decomposition of the correlation matrix corresponding to the spot rates from this curve, then one finds that the top three components can explain nearly all of the data; in addition, this same structure is observed for any bond or commodity. In his 2000 paper, Ilias Lekkos [4] proposes that such results are an artefact due to the implicit correlation between spot rates, and that the analysis should instead be performed using forward rates. In this paper, we discuss the results obtained for the spectral structure of the correlation matrices of forward rates, and investigate a model for this associated structure. The paper is divided into four parts, covering forward rates background material, principal components analysis, yield curve modelling, and conclusions and research extensions