Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems - with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry

This thesis presents a novel class of algorithms for the solution of scattering and eigenvalue problems on general two-dimensional domains under a variety of boundary conditions, including non-smooth domains and certain "Zaremba" boundary conditions - for which Dirichlet and Neumann conditions are specified on various portions of the domain boundary. The theoretical basis of the methods for the Zaremba problems on smooth domains concern detailed information, which is put forth for the first time in this thesis, about the singularity structure of solutions of the Laplace operator under boundary conditions of Zaremba type. The new methods, which are based on use of Green functions and integral equations, incorporate a number of algorithmic innovations, including a fast and robust eigenvalue-search algorithm, use of the Fourier Continuation method for regularization of all smooth-domain Zaremba singularities, and newly derived quadrature rules which give rise to high-order convergence even around singular points for the Zaremba problem. The resulting algorithms enjoy high-order convergence, and they can tackle a variety of elliptic problems under general boundary conditions, including, for example, eigenvalue problems, scattering problems, and, in particular, eigenfunction expansion for time-domain problems in non-separable physical domains with mixed boundary conditions.

Value roadmapping: A structured approach for early stage technology investment decisions

Deciding to invest in early stage technologies is one of the most important tasks of technology management and arguably also the most uncertain. It assumes a particular significance in the rise of technology companies in emerging economies, which have to make appropriate investment decisions. Technology managers already have a wide range of methods and tools at their disposal, but these are mostly focussed on quantitative measures such as discounted cash flow and real options techniques. However, in the early stages of technology development there seems to be a lot of dissatisfaction with these techniques as there appears to be a lack of accuracy with respect to the underlying assumptions that these models require. In order to complement these models this paper will discuss an alternative approach that we call value road-mapping. By adapting roadmapping techniques the potential value streams of early stages technologies can be plotted and hence a clearer consensus based picture of the future potential of new technologies emerges. Roadmapping is a workshop-based process bringing together multifunctional perspectives, and supporting communication in particular between technical and commercial groups. The study is work in progress and is based on a growing number of cases. (c) 2006 PICMET.

Designing tools that enhance communication and understanding between multiple stakeholders: the case of mobile payment value networks

The pervasive use of mobile technologies has provided new opportunities for organisations to achieve competitive advantage by using a value network of partners to create value for multiple users. The delivery of a mobile payment (m-payment) system is an example of a value network as it requires the collaboration of multiple partners from diverse industries, each bringing their own expertise, motivations and expectations. Consequently, managing partnerships has been identified as a core competence required by organisations to form viable partnerships in an m-payment value network and an important factor in determining the sustainability of an m-payment business model. However, there is evidence that organisations lack this competence which has been witnessed in the m-payment domain where it has been attributed as an influencing factor in a number of failed m-payment initiatives since 2000. In response to this organisational deficiency, this research project leverages the use of design thinking and visualisation tools to enhance communication and understanding between managers who are responsible for managing partnerships within the m-payment domain. By adopting a design science research approach, which is a problem solving paradigm, the research builds and evaluates a visualisation tool in the form of a Partnership Management Canvas. In doing so, this study demonstrates that when organisations encourage their managers to adopt design thinking, as a way to balance their analytical thinking and intuitive thinking, communication and understanding between the partners increases. This can lead to a shared understanding and a shared commitment between the partners. In addition, the research identifies a number of key business model design issues that need to be considered by researchers and practitioners when designing an m-payment business model. As an applied research project, the study makes valuable contributions to the knowledge base and to the practice of management.

Design Optimization and Security For Communication Networks

In this work we introduce a new mathematical tool for optimization of routes, topology design, and energy efficiency in wireless sensor networks. We introduce a vector field formulation that models communication in the network, and routing is performed in the direction of this vector field at every location of the network. The magnitude of the vector field at every location represents the density of amount of data that is being transited through that location. We define the total communication cost in the network as the integral of a quadratic form of the vector field over the network area. With the above formulation, we introduce a mathematical machinery based on partial differential equations very similar to the Maxwell's equations in electrostatic theory. We show that in order to minimize the cost, the routes should be found based on the solution of these partial differential equations. In our formulation, the sensors are sources of information, and they are similar to the positive charges in electrostatics, the destinations are sinks of information and they are similar to negative charges, and the network is similar to a non-homogeneous dielectric media with variable dielectric constant (or permittivity coefficient). In one of the applications of our mathematical model based on the vector fields, we offer a scheme for energy efficient routing. Our routing scheme is based on changing the permittivity coefficient to a higher value in the places of the network where nodes have high residual energy, and setting it to a low value in the places of the network where the nodes do not have much energy left. Our simulations show that our method gives a significant increase in the network life compared to the shortest path and weighted shortest path schemes. Our initial focus is on the case where there is only one destination in the network, and later we extend our approach to the case where there are multiple destinations in the network. In the case of having multiple destinations, we need to partition the network into several areas known as regions of attraction of the destinations. Each destination is responsible for collecting all messages being generated in its region of attraction. The complexity of the optimization problem in this case is how to define regions of attraction for the destinations and how much communication load to assign to each destination to optimize the performance of the network. We use our vector field model to solve the optimization problem for this case. We define a vector field, which is conservative, and hence it can be written as the gradient of a scalar field (also known as a potential field). Then we show that in the optimal assignment of the communication load of the network to the destinations, the value of that potential field should be equal at the locations of all the destinations. Another application of our vector field model is to find the optimal locations of the destinations in the network. We show that the vector field gives the gradient of the cost function with respect to the locations of the destinations. Based on this fact, we suggest an algorithm to be applied during the design phase of a network to relocate the destinations for reducing the communication cost function. The performance of our proposed schemes is confirmed by several examples and simulation experiments. In another part of this work we focus on the notions of responsiveness and conformance of TCP traffic in communication networks. We introduce the notion of responsiveness for TCP aggregates and define it as the degree to which a TCP aggregate reduces its sending rate to the network as a response to packet drops. We define metrics that describe the responsiveness of TCP aggregates, and suggest two methods for determining the values of these quantities. The first method is based on a test in which we drop a few packets from the aggregate intentionally and measure the resulting rate decrease of that aggregate. This kind of test is not robust to multiple simultaneous tests performed at different routers. We make the test robust to multiple simultaneous tests by using ideas from the CDMA approach to multiple access channels in communication theory. Based on this approach, we introduce tests of responsiveness for aggregates, and call it CDMA based Aggregate Perturbation Method (CAPM). We use CAPM to perform congestion control. A distinguishing feature of our congestion control scheme is that it maintains a degree of fairness among different aggregates. In the next step we modify CAPM to offer methods for estimating the proportion of an aggregate of TCP traffic that does not conform to protocol specifications, and hence may belong to a DDoS attack. Our methods work by intentionally perturbing the aggregate by dropping a very small number of packets from it and observing the response of the aggregate. We offer two methods for conformance testing. In the first method, we apply the perturbation tests to SYN packets being sent at the start of the TCP 3-way handshake, and we use the fact that the rate of ACK packets being exchanged in the handshake should follow the rate of perturbations. In the second method, we apply the perturbation tests to the TCP data packets and use the fact that the rate of retransmitted data packets should follow the rate of perturbations. In both methods, we use signature based perturbations, which means packet drops are performed with a rate given by a function of time. We use analogy of our problem with multiple access communication to find signatures. Specifically, we assign orthogonal CDMA based signatures to different routers in a distributed implementation of our methods. As a result of orthogonality, the performance does not degrade because of cross interference made by simultaneously testing routers. We have shown efficacy of our methods through mathematical analysis and extensive simulation experiments.

Digital Methods for Process Development in Manufacturing and Their Relevance to Value Driven Design

This paper examines the applicability of a digital manufacturing framework to the implementation of a Value Driven Design (VDD) approach for the development of a stiffened composite panel. It presents a means by which environmental considerations can be integrated with conventional product and process design drivers within a customized, digital environment. A composite forming process is used as an exemplar for the work which creates a collaborative environment for the integration of more traditional design drivers with parameters related to manufacturability as well as more sustainable processes and products. The environmental stakeholder is introduced to the VDD process through a customized product/process/resource (PPR) environment where application specific power consumption and material waste data has been measured and characterised in the process design interface. This allows the manufacturing planner to consider power consumption as a concurrent design driver and the inclusion of energy as a parameter in a VDD approach to the development of efficiently manufactured, sustainable transport systems.

Analysing partial ranks by using smoothed paired comparison methods:An investigation of value orientation in Europe

This paper introduces the paired comparison model as a suitable approach for the analysis of partially ranked data. For example, the Inglehart index, collected in international social surveys to examine shifts in post-materialistic values, generates such data on a set of attitude items. However, current analysis methods have failed to account for the complex shifts in individual item values, or to incorporate subject covariates. The paired comparison model is thus developed to allow for covariate subject effects at the individual level, and a reparameterization allows the inclusion of smooth non-linear effects of continuous covariates. The Inglehart index collected in the 1993 International Social Science Programme survey is analysed, and complex non-linear changes of item values with age, level of education and religion are identified. The model proposed provides a powerful tool for social scientists.

Informing pre-registration nurse education: a proposal outline on the value, methods and ethical considerations of involving children in doctoral research

As pre-registration nurse education programmes evolve within the United Kingdom, it is imperative to involve patient/client groups within the research process, as the outcome may invoke a change in the care delivery of the registered nurse (RN). This paper focuses upon children and how children might hypothetically contribute to informing a generic nursing programme in their capacity as a rights holder and expert in their own lives. Even though their contribution and value has been debated around their capacity as research advisor, research participant and co researcher, this paper explores how the child's view of their experience of hospital and of the good nurse could be best captured. Research is a powerful vehicle that can enable their voice to equally inform UK nurse educators and policy makers so that the child's health care needs are effectively met in hospital by RN's who complete a generic programme.

'Talk to me': a mixed methods study on preferred physician behaviours during end-of-life communication from the patient perspective

Background
Despite the recognized importance of end-of-life (EOL) communication between patients and physicians, the extent and quality of such communication is lacking.

Objective
We sought to understand patient perspectives on physician behaviours during EOL communication.

Design
In this mixed methods study, we conducted quantitative and qualitative strands and then merged data sets during a mixed methods analysis phase. In the quantitative strand, we used the quality of communication tool (QOC) to measure physician behaviours that predict global rating of satisfaction in EOL communication skills, while in the qualitative strand we conducted semi-structured interviews. During the mixed methods analysis, we compared and contrasted qualitative and quantitative data.

Setting and Participants
Seriously ill inpatients at three tertiary care hospitals in Canada.

Results
We found convergence between qualitative and quantitative strands: patients desire candid information from their physician and a sense of familiarity. The quantitative results (n = 132) suggest a paucity of certain EOL communication behaviours in this seriously ill population with a limited prognosis. The qualitative findings (n = 16) suggest that at times, physicians did not engage in EOL communication despite patient readiness, while sometimes this may represent an appropriate deferral after assessment of a patient's lack of readiness.

Conclusions
Avoidance of certain EOL topics may not always be a failure if it is a result of an assessment of lack of patient readiness. This has implications for future tool development: a measure could be built in to assess whether physician behaviours align with patient readiness.