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.

Loss as a universal concept: Review of the literature to identify common aspects of loss in diverse situations

It has long been recognized that loss and its associated grief are important elements of many adverse life events that affect the entire global population: death, disability, traumatic events, abuse., terminal and chronic illness, aging, addiction, unemployment, relationship breakdown, war, migration, and educational failure. While there is significant empirical evidence of the potential deleterious effects of specific situations of loss across the global community, systematic discussion concerning the common elements of loss that are associated with adverse life situations in general has been limited. This review of the theoretical and empirical literature concerning various losses and the recommendations for care of those affected by such losses identifies common aspects of situations of loss and common recommendations in the care of those confronted by such losses. These common themes of loss are described by simple summary statements that can be communicated to a broad audience, hence enhancing community education and, potentially, community-wide mental health promotion.

Riddling and invariance for discontinuous maps preserving Lebesgue measure

In this paper we use the mixture of topological and measure-theoretic dynamical approaches to consider riddling of invariant sets for some discontinuous maps of compact regions of the plane that preserve two-dimensional Lebesgue measure. We consider maps that are piecewise continuous and with invertible except on a closed zero measure set. We show that riddling is an invariant property that can be used to characterize invariant sets, and prove results that give a non-trivial decomposion of what we call partially riddled invariant sets into smaller invariant sets. For a particular example, a piecewise isometry that arises in signal processing (the overflow oscillation map), we present evidence that the closure of the set of trajectories that accumulate on the discontinuity is fully riddled. This supports a conjecture that there are typically an infinite number of periodic orbits for this system.

Lexicographic decomposition of chains and the concept of a planar chain

In an earlier paper [Journal of Mathematical Economics, 37 (2002) 17-38], we proved that if a preference relation on a commodity space is non-representable by a real-valued function then that chain is necessarily a long chain, a planar chain, an Aronszajn-like chain or a Souslin chain. In this paper, we study the class of planar chains, the simplest example of which is the Debreu chain (R-2, <(l)). (C) 2002 Elsevier Science B.V. All rights reserved.