Sharp Sobolev inequality involving a critical nonlinearity on a boundary

We consider the solvability of the Neumann problem for the equation -Delta u + lambda u = 0, partial derivative u/partial derivative v = Q(x)vertical bar u vertical bar(q-2)u on partial derivative Omega, where Q is a positive and continuous coefficient on partial derivative Omega, lambda is a parameter and q = 2(N - 1)/(N - 2) is a critical Sobolev exponent for the trace embedding of H-1(Omega) into L-q(partial derivative Omega). We investigate the joint effect of the mean curvature of partial derivative Omega and the shape of the graph of Q on the existence of solutions. As a by product we establish a sharp Sobolev inequality for the trace embedding. In Section 6 we establish the existence of solutions when a parameter lambda interferes with the spectrum of -Delta with the Neumann boundary conditions. We apply a min-max principle based on the topological linking.

3D statistical shape models to embed spatial relationship information

This paper presents the creation of 3D statistical shape models of the knee bones and their use to embed information into a segmentation system for MRIs of the knee. We propose utilising the strong spatial relationship between the cartilages and the bones in the knee by embedding this information into the created models. This information can then be used to automate the initialisation of segmentation algorithms for the cartilages. The approach used to automatically generate the 3D statistical shape models of the bones is based on the point distribution model optimisation framework of Davies. Our implementation of this scheme uses a parameterized surface extraction algorithm, which is used as the basis for the optimisation scheme that automatically creates the 3D statistical shape models. The current approach is illustrated by generating 3D statistical shape models of the patella, tibia and femoral bones from a segmented database of the knee. The use of these models to embed spatial relationship information to aid in the automation of segmentation algorithms for the cartilages is then illustrated.

A partial-correctness semantics for modelling assembler programs

Previous work on formally modelling and analysing program compilation has shown the need for a simple and expressive semantics for assembler level programs. Assembler programs contain unstructured jumps and previous formalisms have modelled these by using continuations, or by embedding the program in an explicit emulator. We propose a simpler approach, which uses techniques from compiler theory in a formal setting. This approach is based on an interpretation of programs as collections of program paths, each of which has a weakest liberal precondition semantics. We then demonstrate, by example, how we can use this formalism to justify the compilation of block-structured high-level language programs into assembler.

What nominal phrases are all about: the atypical case of indefinite pronouns with a determiner

This paper presents novel data that challenge the traditional categorial understanding of the nominal phrase. The established use of an indefinite pronoun with a determiner in French (ce quelqu'un, du n'importe quoi, un je ne sais quoi) contravenes assumptions both about pronouns, which should not be embedded, and nominal phrases, which should be headed by a noun. Analysed here for the first time, the embedding of a pronoun under a determiner is shown to find its justification in the semantic import of the construction. The anaphoric role guaranteeing referential continuity is promoted by a strong determiner; weak determiners typically contribute to constructing a designative use of the pronoun when a more precise characterisation cannot or will not be provided. How this construction would be analysed in the Minimalist Programme is presented to suggest that the phrase satisfies semantic requirements, which resolves the paradoxes of its traditional definition

DVMS 1.5: A user manual (the data visualization and modeling system)

The data available during the drug discovery process is vast in amount and diverse in nature. To gain useful information from such data, an effective visualisation tool is required. To provide better visualisation facilities to the domain experts (screening scientist, biologist, chemist, etc.),we developed a software which is based on recently developed principled visualisation algorithms such as Generative Topographic Mapping (GTM) and Hierarchical Generative Topographic Mapping (HGTM). The software also supports conventional visualisation techniques such as Principal Component Analysis, NeuroScale, PhiVis, and Locally Linear Embedding (LLE). The software also provides global and local regression facilities . It supports regression algorithms such as Multilayer Perceptron (MLP), Radial Basis Functions network (RBF), Generalised Linear Models (GLM), Mixture of Experts (MoE), and newly developed Guided Mixture of Experts (GME). This user manual gives an overview of the purpose of the software tool, highlights some of the issues to be taken care while creating a new model, and provides information about how to install & use the tool. The user manual does not require the readers to have familiarity with the algorithms it implements. Basic computing skills are enough to operate the software.

Independent component analysis for domain independent watermarking

A new principled domain independent watermarking framework is presented. The new approach is based on embedding the message in statistically independent sources of the covertext to mimimise covertext distortion, maximise the information embedding rate and improve the method's robustness against various attacks. Experiments comparing the performance of the new approach, on several standard attacks show the current proposed approach to be competitive with other state of the art domain-specific methods.

ICA based steganography

A domain independent ICA-based watermarking method is introduced and studied by numerical simulations. This approach can be used either on images, music or video to convey a hidden message. It relies on embedding the information in a set of statistically independent sources (the independent components) as the feature space. For the experiments the medium has arbritraly chosen to be digital images.

Quantisation effects and watermarking capacity

Digital watermarking aims at embedding information in digital data. The watermark is usually required to be imperceptible, unremovable and to have a high information content. Unfortunately, these three requirements are contradicting. For example, having a more robust watermark makes it either more perceptible or/and less informative. This paper investigates the relationship between the watermark information content and the induced distortion due to quantisation, such as lossy compression.

Structured codebooks for SCS watermarking

Digital watermarking aims at embedding information in digital data. The watermark is usually required to be imperceptible, unremovable and to have a high information content. Unfortunately, these three requirements are contradicting. For example, having a more robust watermark makes it either more perceptible or/and less informative. For Gaussian data and additive white Gaussian noise, an optimal but also impractical scheme has already be devised. Since then, many practical schemes have tried to approach the theoretical limits. This paper investigate improvements to current state-of-the-art embedding schemes.

Engaging tutors in using e-repositories for learning and teaching

Universities which set up online repositories for the management of learning and teaching resources commonly find that uptake is poor. Tutors are often reluctant to upload their materials to e-repositories, even though the same tutors are happy to upload resources to the virtual learning environment (e.g. Blackboard, Moodle, Sakai) and happy to upload their research papers to the university’s research publications repository. The paper reviews this phenomenon and suggests constructive ways in which tutors can be encouraged to engage with an e-repository. The authors have recently completed a major project “Developing Repositories at Worcester” which is part of a group of similar projects in the UK. The paper includes the feedback and the lessons learned from these projects, based on the publications and reports they have produced. They cover ways of embedding repository use into institutional working practice, and give examples of different types of repository designed to meet the needs of those using different kinds of learning and teaching resources. As well as this specific experience, the authors summarise some of the main findings from UK publications, in particular the December 2008 report of Joint Information Systems Committee: Good intentions: improving the evidence base in support of sharing learning materials and Online Innovation in Higher Education, Ron Cooke’s report to a UK government initiative on the future of Higher Education. The issues covered include the development of Web 2.0 style repositories rather than conventionally structured ones, the use of tags rather than metadata, the open resources initiative, the best use for conventional repositories, links to virtual learning environments, and the processes for the management and support of repositories within universities. In summary the paper presents an optimistic, constructive view of how to embed the use of e-repositories into the working practices of university tutors. Equally, the authors are aware of the considerable difficulties in making progress and are realistic about what can be achieved. The paper uses evidence and experience drawn from those working in this field to suggest a strategic vision in which the management of e-learning resources is productive, efficient and meets the needs of both tutors and their students.

Advanced UV inscribed fibre grating structures and applications in optical sensing and laser systems

This thesis presents detailed investigation of UV inscribed fibre grating based devices and novel developments in the applications of such devices in optical sensing and fibre laser systems. The major contribution of this PhD programme includes the systematic study on fabrication, spectral characteristics and applications of different types of UV written in-fibre gratings such as Type I and IA Fibre Bragg Gratings (FBGs), Chirped Fibre Bragg Gratings (CFBGs) and Tilted Fibre Gratings (TFGs) with small, large and 45º tilted structures inscribed in normal silica fibre. Three fabrication techniques including holographic, phase-mask and blank beam exposure scanning, which were employed to fabricate a range of gratings in standard single mode fibre, are fully discussed. The thesis reports the creation of smart structures with self-sensing capability by embedding FBG-array sensors in Al matrix composite. In another part of this study, we have demonstrated the particular significant improvements made in sensitising standard FBGs to the chemical surrounding medium by inducing microstructure to the grating by femtosecond (fs) patterning assisted chemical etching technique. Also, a major work is presented for the investigation on the structures, inscription methods and spectral Polarisation Dependent Loss (PDL) and thermal characteristics of different angle TFGs. Finally, a very novel application in realising stable single polarisation and multiwavelength switchable Erbium Doped Fibre Lasers (EDFLs) using intracavity polarisation selective filters based on TFG devices with tilted structures at small, large and exact 45° angles forms another important contribution of this thesis.

The board of directors, executives and risk knowledge management

Enterprise Risk Management (ERM) and Knowledge Management (KM) both encompass top-down and bottom-up approaches developing and embedding risk knowledge concepts and processes in strategy, policies, risk appetite definition, the decision-making process and business processes. The capacity to transfer risk knowledge affects all stakeholders and understanding of the risk knowledge about the enterprise's value is a key requirement in order to identify protection strategies for business sustainability. There are various factors that affect this capacity for transferring and understanding. Previous work has established that there is a difference between the influence of KM variables on Risk Control and on the perceived value of ERM. Communication among groups appears as a significant variable in improving Risk Control but only as a weak factor in improving the perceived value of ERM. However, the ERM mandate requires for its implementation a clear understanding, of risk management (RM) policies, actions and results, and the use of the integral view of RM as a governance and compliance program to support the value driven management of the organization. Furthermore, ERM implementation demands better capabilities for unification of the criteria of risk analysis, alignment of policies and protection guidelines across the organization. These capabilities can be affected by risk knowledge sharing between the RM group and the Board of Directors and other executives in the organization. This research presents an exploratory analysis of risk knowledge transfer variables used in risk management practice. A survey to risk management executives from 65 firms in various industries was undertaken and 108 answers were analyzed. Potential relationships among the variables are investigated using descriptive statistics and multivariate statistical models. The level of understanding of risk management policies and reports by the board is related to the quality of the flow of communication in the firm and perceived level of integration of the risk policy in the business processes.

Approximating differentiable relationships between delay embedded dynamical systems with radical basis functions

This thesis is about the study of relationships between experimental dynamical systems. The basic approach is to fit radial basis function maps between time delay embeddings of manifolds. We have shown that under certain conditions these maps are generically diffeomorphisms, and can be analysed to determine whether or not the manifolds in question are diffeomorphically related to each other. If not, a study of the distribution of errors may provide information about the lack of equivalence between the two. The method has applications wherever two or more sensors are used to measure a single system, or where a single sensor can respond on more than one time scale: their respective time series can be tested to determine whether or not they are coupled, and to what degree. One application which we have explored is the determination of a minimum embedding dimension for dynamical system reconstruction. In this special case the diffeomorphism in question is closely related to the predictor for the time series itself. Linear transformations of delay embedded manifolds can also be shown to have nonlinear inverses under the right conditions, and we have used radial basis functions to approximate these inverse maps in a variety of contexts. This method is particularly useful when the linear transformation corresponds to the delay embedding of a finite impulse response filtered time series. One application of fitting an inverse to this linear map is the detection of periodic orbits in chaotic attractors, using suitably tuned filters. This method has also been used to separate signals with known bandwidths from deterministic noise, by tuning a filter to stop the signal and then recovering the chaos with the nonlinear inverse. The method may have applications to the cancellation of noise generated by mechanical or electrical systems. In the course of this research a sophisticated piece of software has been developed. The program allows the construction of a hierarchy of delay embeddings from scalar and multi-valued time series. The embedded objects can be analysed graphically, and radial basis function maps can be fitted between them asynchronously, in parallel, on a multi-processor machine. In addition to a graphical user interface, the program can be driven by a batch mode command language, incorporating the concept of parallel and sequential instruction groups and enabling complex sequences of experiments to be performed in parallel in a resource-efficient manner.

On the stress analysis of cracked bodies by means of finite elements

The work described in this thesis deals with the development and application of a finite element program for the analysis of several cracked structures. In order to simplify the organisation of the material presented herein, the thesis has been subdivided into two Sections : In the first Section the development of a finite element program for the analysis of two-dimensional problems of plane stress or plane strain is described. The element used in this program is the six-mode isoparametric triangular element which permits the accurate modelling of curved boundary surfaces. Various cases of material aniftropy are included in the derivation of the element stiffness properties. A digital computer program is described and examples of its application are presented. In the second Section, on fracture problems, several cracked configurations are analysed by embedding into the finite element mesh a sub-region, containing the singularities and over which an analytic solution is used. The modifications necessary to augment a standard finite element program, such as that developed in Section I, are discussed and complete programs for each cracked configuration are presented. Several examples are included to demonstrate the accuracy and flexibility of the technique.

Digital image watermarking

In recent years, interest in digital watermarking has grown significantly. Indeed, the use of digital watermarking techniques is seen as a promising mean to protect intellectual property rights of digital data and to ensure the authentication of digital data. Thus, a significant research effort has been devoted to the study of practical watermarking systems, in particular for digital images. In this thesis, a practical and principled approach to the problem is adopted. Several aspects of practical watermarking schemes are investigated. First, a power constaint formulation of the problem is presented. Then, a new analysis of quantisation effects on the information rate of digital watermarking scheme is proposed and compared to other approaches suggested in the literature. Subsequently, a new information embedding technique, based on quantisation, is put forward and its performance evaluated. Finally, the influence of image data representation on the performance of practical scheme is studied along with a new representation based on independent component analysis.