Asymmetric page split generalized index search trees for formal concept analysis

Formal Concept Analysis is an unsupervised machine learning technique that has successfully been applied to document organisation by considering documents as objects and keywords as attributes. The basic algorithms of Formal Concept Analysis then allow an intelligent information retrieval system to cluster documents according to keyword views. This paper investigates the scalability of this idea. In particular we present the results of applying spatial data structures to large datasets in formal concept analysis. Our experiments are motivated by the application of the Formal Concept Analysis idea of a virtual filesystem [11,17,15]. In particular the libferris [1] Semantic File System. This paper presents customizations to an RD-Tree Generalized Index Search Tree based index structure to better support the application of Formal Concept Analysis to large data sources.

An Economic Analysis of the Legal Concept of Trustees' Power of Investment

Authorised trustee status is a legal concept which has economic implications; one of the major implications is that it assists in the direction of investment funds into particular securities and areas of the economy. The concept of authorised trustee status, while attempting to achieve specific outcomes for the beneficiaries of trusts cannot be relied upon to secure these results. Economic analysis of the role of the trustee maintains that this role is one of portfolio manager; a role which is complex but which is explicable in terms of definable procedures and practices. The role of trustee as portfolio manager is one which requires greater financial knowledge than can be assumed is possessed by all trustees. The trustee as portfolio manager is required to maintain a review of decisions make under powers to invest trust assets. A solution to the problem of authorised trustee status is proposed. The solution takes two parts: the first is the adoption of the prudent person approach but with the codification of duties of the trustee and the explicit listing of the factors that a trustee should consider in using the investment powers. The second part of the proposed solution is to link the investment powers of trustees to the best practice features of securities advisers who are now licensed by a regulatory body, the Australian Securities and Investment Commission.

A direct composite resin stratification technique for restoration of the smile

Composite resins can be used to improve the esthetics of the smile at a low cost and with relatively high clinical performance, The aim of this article was to describe an approach to restore and enhance the esthetic appearance of the anterior dentition through vital tooth whitening and the direct layering of composite resin during predictable esthetic procedures, (Quintessence lot 2011;42205-211)

Matrix-product codes over Fq

Codes C-1,...,C-M of length it over F-q and an M x N matrix A over F-q define a matrix-product code C = [C-1 (...) C-M] (.) A consisting of all matrix products [c(1) (...) c(M)] (.) A. This generalizes the (u/u + v)-, (u + v + w/2u + v/u)-, (a + x/b + x/a + b + x)-, (u + v/u - v)- etc. constructions. We study matrix-product codes using Linear Algebra. This provides a basis for a unified analysis of /C/, d(C), the minimum Hamming distance of C, and C-perpendicular to. It also reveals an interesting connection with MDS codes. We determine /C/ when A is non-singular. To underbound d(C), we need A to be 'non-singular by columns (NSC)'. We investigate NSC matrices. We show that Generalized Reed-Muller codes are iterative NSC matrix-product codes, generalizing the construction of Reed-Muller codes, as are the ternary 'Main Sequence codes'. We obtain a simpler proof of the minimum Hamming distance of such families of codes. If A is square and NSC, C-perpendicular to can be described using C-1(perpendicular to),...,C-M(perpendicular to) and a transformation of A. This yields d(C-perpendicular to). Finally we show that an NSC matrix-product code is a generalized concatenated code.

On the direct product of two weak uniquely completable partial latin squares

In this note we show by counter-example that the direct product of two weak uniquely completable partial latin squares is not necessarily a uniquely completable partial latin square. This counter-example rejects a conjecture by Gower (see [3]) on the direct product of two uniquely completable partial latin squares.

Calculation of product state distributions from resonance decay via Lanczos subspace filter diagonalization: Application to HO2

Resonance phenomena associated with the unimolecular dissociation of HO2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation function-based filter diagonalization (ACFFD) method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of O-2 show strong fluctuations, indicating the dissociation of HO2 is essentially irregular. (C) 2001 American Institute of Physics.