Generalized Julia Sets: An Extension of Cayley\u27s Problem

There are many iterative techniques to find a root or zero of a given function. For any iterative technique, it is often of interest to know which initial seeds lead to which roots. When the iterative technique used is Newton’s Method, this is known as Cayley’s Problem. In this thesis, I investigate two extensions of Cayley’s Problem. In particular, I study generalizations of Newton’s Method, in both C and R2, and the associated fractal structures that arise from using more sophisticated numerical approximation techniques

Do all countries follow the same growth process?

We estimate a finite mixture model in which countries are sorted into groups based on the similarity of the conditional distributions of their growth rates. We strongly reject the hypothesis that all countries follow a common growth process in favor of a model in which there are two classes of countries, each with its own distinct growth process. Group membership does not conform to the usual categories used to control for parameter heterogeneity such as region or income. However, we find strong evidence that one country characteristic that helps to sort countries into different regimes is the quality of institutions, specifically, the degree of law and order. Once institutional features of the economy are controlled for, we find no evidence that geographic characteristics play a role in determining the country groupings.finite mixture models; multiple equilibria; institutional quality

Liberal education and moral development: an integrated model of moral education

Two central questions are raised: at a college level, what should be our educational goals and methods in the realm of moral development? and, what curricular or instructional model is most logically consistent and ethically acceptable with the mission and philosophy of liberal education? The major purpose of this study is to answer these questions and develop one reasonable, clearly defined model of college-level moral education.;As a normative inquiry into the goals of moral education, this philosophical study rests on the assumption that statements of moral value can be rationally understood and taught and is guided by an awareness of the major findings in social scientific research on moral development and education and practical use of the conceptual analysis of educational terminology.;In order to answer the central questions, it is argued that the ideal of liberal education (its inherent logical and ethical criteria as well as a developed set of explicit curricular goals) can help determine legitimate curricular goals and methods that are focused on moral development. An extended definition of liberal education is developed through reference to widely accepted historical statements and examination of contemporary principles and goals.;Five contemporary models of undergraduate moral education are next identified and described in detail: values clarification, wholistic, humanities, normative ethics, and cognitive-developmental. The specific criteria for liberal education are then critically applied, evaluating the respective strengths and weaknesses of each model. It is argued that the normative ethics and cognitive-developmental models are most closely connected with the historical aims and contemporary goals of liberal education.;The study concludes with a detailed analysis of the two selected models. Reasons for their integration are developed, pedagogical methods and resources which emerge from their combination are outlined, and a summary of this approach to selecting and developing an acceptable model of college-level moral education is offered. In closing, it is stated that college students can legitimately be taught to reflect on morality, to be committed to the rational analysis and selection of moral values and lifestyles, and to act in accordance with their convictions

Early assessment of the UK innovation investment fund

The UK Innovation Investment Fund (UKIIF), announced by the UK Government in June 2009, is a venture capital fund of funds that aims to drive economic growth and create highly skilled jobs by investing in innovative businesses where there are significant growth opportunities. The UKIIF attempts to mark a step change in the UK venture capital (VC) market by establishing a substantial fund of funds that will replicate the best US funds by making investments at all business stages, with the market scale that can build companies with global reach. The underlying funds within the UKIIF fund of funds will invest in technology based businesses in strategically important sectors to the UK including digital technologies, life sciences1, clean technology2 and advanced manufacturing. This research provides an early assessment of the lessons learned in implementing and delivering the UKIIF ahead of the main evaluation and provides early indications of the extent to which it is addressing market failures in the UK VC market and contributing to business growth

Blood analogue for thrombogenicity assessment

The chief problem at present with artificial heart valves is their thrombogenicity, which requires the recipients to undergo dangerous anticoagulant therapy, which is not always successful. The present accepted method of testing valve thrombogenicity is implantation in experimental animals. This technique is unsatisfactory because of its high cost, the lack of control, the length of the experiments and because differences between the blood of various species render the results of dubious value. A more fundamental approach to the problem based on fluid mechanics'fails because of the complexity of the situation and because of the opposed effects of a given fluid mechanical phenomenon. The in vitro use of blood is not possible due to the need for a single pass system to avoid recirculating clots, necessitating some thirty gallons of blood for a run of only one hour. An analogue method using a fluid which does not have the disadvantages of the alternatives described above, therefore, seems worth exploring. Rennetized milk is a possible fluid for such a purpose and experiments were performed to ascertain whether it behaves in a manner analogous to blood in respect of its essential clotting properties. The first indications from the Lee-White inverted test tube test were very promising with milk behaving in a manner apparently identical to blood. Further experiments using the Stagnation Point Flow Chamber showed that there was a striking similarity in the microscopic appearance of the deposits forming at and around the stagnation point when a jet of milk/blood impinges normally onto a glass slide. A subsequent experiment, in which the fluids are pumped through a mesh, revealed that the sequence of clot growth as measured by the pressure variation upstream of the mesh is the same for both fluids. Finally, full scale tests of the clotting propensity of various heart valves were performed using an artificial heart system, which showed that the location and appearance of the clots forming on the valves with rennetized milk were similar to those found in humans and that the results were reproducible. It is, therefore, apparent that rennetized milk shows great potential as an analogue for the flow related clotting of blood and can be used for testing artificial heart valves provided care is taken in the choice of materials for construction

Comparative Dosimetric Analysis and Normal Tissue Complication Probability Modelling of Four-Dimensional Computed Tomography Planning Scans Within the UK NeoSCOPE Trial

Neoadjuvant chemoradiotherapy for resectable oesophageal cancer improves overall survival compared to surgery alone but is associated with increased toxicity. NeoSCOPE is a trial of two different nCRT regimens for resectable oesophageal and was the first multi-centre trial in the UK to incorporate 4D-CT into the radiotherapy planning. Using NeoSCOPE 4D-CT cases, we undertook a dosimetric comparison study of 3D-CT versus 4D-CT plans comparing target volume coverage and dose to organs at risk. We used established normal tissue complication probability (NTCP) models to evaluate the potential toxicity reduction of using 4D-CT plans in oesophageal cancer. Our work shows that incorporating 4D-CT into treatment planning may significantly reduce the toxicity burden from this treatment

Study of Determined Town and Village Green Applications: Final Report to Common Land Team, Defra

The purpose of the research, as set out in the Project Brief, was to ‘examine a sample of the sites which have been registered as town or village greens (TVGs) since January 2004 as well as a sample of those that have not been registered’. The common term for both successful and unsuccessful applications is that either outcome has been ‘determined’ by Commons Registration Authority (CRA), therefore the study was an investigation into determined town and village green (dTVG) applications. The project also set out to examine whether the sites were earmarked for development in local development plans or subject to planning applications. The full diversity of sites, both approved and rejected, was analysed