Analytical Study of the Julia Set of a Coupled Generalized Logistic Map

A coupled system of two generalized logistic maps is studied. In particular influence of the coupling to the behaviour of the Julia set in two dimensional complex space is analyzed both analytically and numerically. It is proved analytically that the Julia set disappears from the complex plane uniformly as a parameter interpolates from the chaotic phase to the integrable phase, if the coupling strength satisfies a certain condition.Comment: 30pages, 22figure

On the Hausdorff dimension of certain sets

Imperial Users onl

Hyperbolic geometry and the Hillam-Thron theorem

Every open ball within $\mathbb{R}\frac{N}{\infty}$ has an associated hyperbolic metric and Möbius transformations act as hyperbolic isometries from one ball to another. The Hillam–Thron Theorem is concerned with images of balls under Möbius transformation, yet existing proofs of the theorem do not make use of hyperbolic geometry. We exploit hyperbolic geometry in proving a generalisation of the Hillam–Thron Theorem and examine the precise configurations of points and balls that arise in that theorem

Talking with pictures: Exploring the possibilities of iconic communication

As multimedia computing becomes the order of the day, so there is a greater need to understand and to come to terms with the problems of visual presentation. This paper deals with iconic languages as a means of communicating ideas and concepts without words. Two example systems, developed respectively at the universities of Exeter and Brighton, are described. Both embody basic principles of the iconic communication which,, though not unique to learning technology, is forming an increasingly important part of user‐interfaces, including those in the area computer‐assisted learning

Implementation of Health-Justice Partnerships: Integrating welfare rights advice services with patient care

Background: Health-justice partnerships exist to support patients with social welfare legal issues, which occur among more deprived population groups and are significant causes and consequences of illness. Integrating welfare rights advice with patient care is a means towards important policy goals of both health and legal sectors, including improving access to justice, supporting health outcomes and addressing health inequalities. However, myriad approaches exist and there are clear challenges in delivering and sustaining these partnerships in practice. / Methods: This research investigates the question ‘How can health-justice partnerships be implemented successfully?’ The systematic scoping review examined existing evidence on the impacts and implementation of the partnerships. The comparative case study investigated service design and delivery in practice, drawing on a diverse sample of health-justice partnerships across England. The stakeholder engagement exercise explored professionals’ responses to the findings and their priorities to support implementation in future. / Results: 118 publications were included in the review. The strength of evidence for impacts of the partnerships varied across different topics. Evidence on implementation was of low quality but identified prominent factors affecting service delivery. Nine partnerships participated as case studies in the primary research, from various geographical regions and care settings. The extent of collaborative working between health and welfare rights teams was variable and influenced strongly by individual attitudes and capabilities. Close collaborative working contributed to more impactful partnerships. Some partnerships were currently operating, while others had closed. Decisions to discontinue had been influenced predominantly by resource constraints and strategic priorities. Stakeholders were concerned with how best to design partnerships and engage effectively with healthcare organisations, as well as how to evaluate partnerships and fund them sustainably. / Conclusion: This research provides new evidence to support the successful implementation of health-justice partnerships and identifies priorities for future research and policy work in the field

A finitely generated, locally indicable group with no faithful action by C^1 diffeomorphisms of the interval

According to Thurston's stability theorem, every group of C^1 diffeomorphisms of the closed interval is locally indicable (.e., every finitely generated subgroup factors through Z). We show that, even for finitely generated groups, the converse of this statement is not true. More precisely, we show that the semi-direct product between F_2 an Z^2, although locally indicable, does not embed into Diff_+^1 (]0,1[). (Here F_2 is any free subgroup of SL(2,Z), and its action on Z^2 is the projective one.) Moreover, we show that for every non-solvable subgroup G of SL(2,Z), the semi-direct product between G and Z^2 does not embed into Diff^1_+(S^1).Comment: 8 pages, no figur

Virtual reality in theatre education and design practice - new developments and applications

The global use of Information and Communication Technologies (ICTs) has already established new approaches to theatre education and research, shifting traditional methods of knowledge delivery towards a more visually enhanced experience, which is especially important for teaching scenography. In this paper, I examine the role of multimedia within the field of theatre studies, with particular focus on the theory and practice of theatre design and education. I discuss various IT applications that have transformed the way we experience, learn and co-create our cultural heritage. I explore a suite of rapidly developing communication and computer-visualization techniques that enable reciprocal exchange between students, theatre performances and artefacts. Eventually, I analyse novel technology-mediated teaching techniques that attempt to provide a new media platform for visually enhanced information transfer. My findings indicate that the recent developments in the personalization of knowledge delivery, and also in student-centred study and e-learning, necessitate the transformation of the learners from passive consumers of digital products to active and creative participants in the learning experience

Convex projective structures on Gromov--Thurston manifolds

We consider Gromov-Thurston examples of negatively curved n-manifolds which do not admit metrics of constant sectional curvature. We show that for each n some of the Gromov-Thurston manifolds admit strictly convex real-projective structures.Comment: 28 pages, 6 figure

The design of software to support creative practice

There is general acceptance of the need to include 'the user' in the process of design. The design of software for creative practice involves software designers treating product designers as 'users' and it is argued that neither party has a clear understanding of this relationship. It is also argued that software for creative practice is better seen as a language, rather than as a task-oriented product. As such it should establish a code and allow users to make interesting statements within that code. The 'Visual Assistant' is new applications software that has been developed over the past three years to support performance education. Fundamentally, it involves the manipulation of 2D images within a 3D space. A set of design objectives for the product are described. The design method used in development is also described. The process of evaluation is not clearly defined in relation to such applications and the general procedure whereby users' experience is fed into evolving design is discussed in the light of the experience at three teaching workshops