Achieving completeness: from constructive set theory to large cardinals

This thesis is an exploration of several completeness phenomena, both in the constructive and the classical settings. After some introductory chapters in the first part of the thesis where we outline the background used later on, the constructive part contains a categorical formulation of several constructive completeness theorems available in the literature, but presented here in an unified framework. We develop them within a constructive reverse mathematical viewpoint, highlighting the metatheory used in each case and the strength of the corresponding completeness theorems. The classical part of the thesis focuses on infinitary intuitionistic propositional and predicate logic. We consider a propositional axiomatic system with a special distributivity rule that is enough to prove a completeness theorem, and we introduce weakly compact cardinals as the adequate metatheoretical assumption for this development. Finally, we return to the categorical formulation focusing this time on infinitary first-order intuitionistic logic. We propose a first-order system with a special rule, transfinite transitivity, that embodies both distributivity as well as a form of dependent choice, and study the extent to which completeness theorems can be established. We prove completeness using a weakly compact cardinal, and, like in the constructive part, we study disjunction-free fragments as well. The assumption of weak compactness is shown to be essential for the completeness theorems to hold.

Antecedents and outcomes of union loyalty:a constructive replication and an extension

Primary data obtained from unionized employees in Singapore were used to examine P. A. Bamberger, A. N. Kluger, and R. Suchard's (1999) integrative model of the antecedents and outcomes of union commitment. Structural equation modeling results revealed support for their integrative model. Specifically, the results revealed the influence of job satisfaction on union loyalty to be indirect through organizational commitment. However, the union-related antecedents (union socialization and union instrumentality) were both directly and indirectly related to union loyalty through pro-union attitudes. In addition, union loyalty was related to the individually and organizationally directed union citizenship behavior dimensions. Limitations of the study and implications of the findings are discussed.

Genetic characterization of clinical isolates of Clostridium difficile using an optimized RAPD protocol and PCR ribotyping reveals strain diversity between two tertiary referral Trusts in the West Midlands, UK

Epidemiological investigations of Clostridium difficile often focus on differences between separate geographical areas. In this investigation, two populations of C. difficile recovered from separate tertiary referral Trusts within the West Midlands, UK, were characterized using both PCR ribotyping and an optimized RAPD (random amplification of polymorphic DNA) protocol. The PCR ribotyping and RAPD methodologies identified differences between the two C. difficile populations, in both the prevalence and the diversity of types identified. The use of PCR ribotyping in conjunction with RAPD further categorized different types within defined PCR ribotypes, identifying different types within the same PCR ribotype and therefore providing a greater discriminatory power than either of the methods when used alone. The differences observed in this study between the two Trusts in the distribution of both RAPD 'type' and PCR ribotype demonstrate the diversity that is present amongst isolates of C. difficile within a relatively small geographical area and warrants a need for further investigation into the local epidemiology of C. difficile.

Automatic refinement of constructive solid geometry models

Geometric information relating to most engineering products is available in the form of orthographic drawings or 2D data files. For many recent computer based applications, such as Computer Integrated Manufacturing (CIM), these data are required in the form of a sophisticated model based on Constructive Solid Geometry (CSG) concepts. A recent novel technique in this area transfers 2D engineering drawings directly into a 3D solid model called `the first approximation'. In many cases, however, this does not represent the real object. In this thesis, a new method is proposed and developed to enhance this model. This method uses the notion of expanding an object in terms of other solid objects, which are either primitive or first approximation models. To achieve this goal, in addition to the prepared subroutine to calculate the first approximation model of input data, two other wireframe models are found for extraction of sub-objects. One is the wireframe representation on input, and the other is the wireframe of the first approximation model. A new fast method is developed for the latter special case wireframe, which is named the `first approximation wireframe model'. This method avoids the use of a solid modeller. Detailed descriptions of algorithms and implementation procedures are given. In these techniques utilisation of dashed line information is also considered in improving the model. Different practical examples are given to illustrate the functioning of the program. Finally, a recursive method is employed to automatically modify the output model towards the real object. Some suggestions for further work are made to increase the domain of objects covered, and provide a commercially usable package. It is concluded that the current method promises the production of accurate models for a large class of objects.

A constructive learning algorithm based on back-propagation

There are been a resurgence of interest in the neural networks field in recent years, provoked in part by the discovery of the properties of multi-layer networks. This interest has in turn raised questions about the possibility of making neural network behaviour more adaptive by automating some of the processes involved. Prior to these particular questions, the process of determining the parameters and network architecture required to solve a given problem had been a time consuming activity. A number of researchers have attempted to address these issues by automating these processes, concentrating in particular on the dynamic selection of an appropriate network architecture.The work presented here specifically explores the area of automatic architecture selection; it focuses upon the design and implementation of a dynamic algorithm based on the Back-Propagation learning algorithm. The algorithm constructs a single hidden layer as the learning process proceeds using individual pattern error as the basis of unit insertion. This algorithm is applied to several problems of differing type and complexity and is found to produce near minimal architectures that are shown to have a high level of generalisation ability.

Selectivity and timing performance of UK investment trusts

This study examines the selectivity and timing performance of 218 UK investment trusts over the period July 1981 to June 2009. We estimate the Treynor and Mazuy (1966) and Henriksson and Merton (1981) models augmented with the size, value, and momentum factors, either under the OLS method adjusted with the Newey-West procedure or under the GARCH(1,1)-in-mean method following the specification of Glosten et al. (1993; hereafter GJR-GARCH-M). We find that the OLS method provides little evidence in favour of the selectivity and timing ability, consistent with previous studies. Interestingly, the GJR-GARCH-M method reverses this result, showing some relatively strong evidence on favourable selectivity ability, particularly for international funds, as well as favourable timing ability, particularly for domestic funds. We conclude that the GJR-GARCH-M method performs better in evaluating fund performance compared with the OLS method and the non-parametric approach, as it essentially accounts for the time-varying characteristics of factor loadings and hence obtains more reliable results, in particular, when the high frequency data, such as the daily returns, are used in the analysis. Our results are robust to various in-sample and out-of-sample tests and have valuable implications for practitioners in making their asset allocation decisions across different fund styles. © 2012 Elsevier B.V.

Co-owners and severance - determining beneficial entitlement after Stack

The article seeks to examine the effect of a severance of a joint beneficial title following the House of Lords' ruling in Stack v Dowden [2007] 2 AC 432. If, under Stack, the parties' beneficial interests fall to be treated as identical to their legal interests (in effect, giving rise to a joint tenancy both at law and in equity), how does the mechanism of severance of a joint beneficial tenancy actually operate so as to give rise to separate and unequal shares where the parties' common intention has changed by virtue of post-acquisition events? The question is examined by reference to an ambulatory and new constructive trust, as well as where the parties have entered into an express declaration of trust of their beneficial interests.

Constructive updating/downdating of oblique projectors:a generalization of the Gram-Schmidt process

A generalization of the Gram-Schmidt procedure is achieved by providing equations for updating and downdating oblique projectors. The work is motivated by the problem of adaptive signal representation outside the orthogonal basis setting. The proposed techniques are shown to be relevant to the problem of discriminating signals produced by different phenomena when the order of the signal model needs to be adjusted. © 2007 IOP Publishing Ltd.

Testamentary trusts and the rule against capricious purposes:an underlying rationale?

This paper examines the rule against capricious purpose trusts and examines its application in English law but more particularly drawing upon the experiences of other common law jurisdictions and seeks to create a rationale for the operation o the doctrine in the common law world.

Introduction to the Law of Trusts by Simon Gardner

Book review of Prof Gardiner's work on Trusts, thrid edition.

Interpreting "D.I.Y." documents:severance, release, trusts, certainty, vesting and undue influence

Comments on the Chancery Division decision in Wallbank v Price on whether a home-made ("DIY") document signed by a wife and purporting to revoke her rights as a beneficial joint tenant in the matrimonial home, which was acquired under the right-to-buy scheme, should be set aside for duress or undue influence. Details the court's analysis of the principles supporting a successful claim of undue influence, the nature of the DIY document, its meaning and its effect. Considers possible reasons for the parties' use of the document. Cases Wallbank v Price (2007) EWHC 3001 (Ch); (2008) 2 FLR 501 (Ch D (Birmingham)) : Royal Bank of Scotland Plc v Etridge (No.2) (2001) UKHL 44; (2002) 2 AC 773 (HL) : Paul v Constance (1977) 1 WLR 527 (CA (Civ Div)) Statutes Housing Act 1985

Overlapping of legal concepts:classifying the law of trusts

The purpose of this piece is to explain how the trust concept fits the overlapping analysis, presenting an example of why discrete categorisation is often unhelpful in understanding the operation of legal concepts.