Optimal control of a class of discrete–continuous non-linear systems — decomposition and hierarchical structure

A technique is derived for solving a non-linear optimal control problem by iterating on a sequence of simplified problems in linear quadratic form. The technique is designed to achieve the correct solution of the original non-linear optimal control problem in spite of these simplifications. A mixed approach with a discrete performance index and continuous state variable system description is used as the basis of the design, and it is shown how the global problem can be decomposed into local sub-system problems and a co-ordinator within a hierarchical framework. An analysis of the optimality and convergence properties of the algorithm is presented and the effectiveness of the technique is demonstrated using a simulation example with a non-separable performance index.

The conditional performance of UK property funds

The evaluation of investment fund performance has been one of the main developments of modern portfolio theory. Most studies employ the technique developed by Jensen (1968) that compares a particular fund's returns to a benchmark portfolio of equal risk. However, the standard measures of fund manager performance are known to suffer from a number of problems in practice. In particular previous studies implicitly assume that the risk level of the portfolio is stationary through the evaluation period. That is unconditional measures of performance do not account for the fact that risk and expected returns may vary with the state of the economy. Therefore many of the problems encountered in previous performance studies reflect the inability of traditional measures to handle the dynamic behaviour of returns. As a consequence Ferson and Schadt (1996) suggest an approach to performance evaluation called conditional performance evaluation which is designed to address this problem. This paper utilises such a conditional measure of performance on a sample of 27 UK property funds, over the period 1987-1998. The results of which suggest that once the time varying nature of the funds beta is corrected for, by the addition of the market indicators, the average fund performance show an improvement over that of the traditional methods of analysis.

Military competition and the emergence of nationalism: putting the logic of political survival into historical context

This essay aims to make a contribution to the conversation between IR and nationalism literatures by considering a particular question: What is the relationship between interstate military competition and the emergence of nationalism as a potent force in world politics? The conventional wisdom among international security scholars, especially neorealists, holds that nationalism can be more or less treated like a “technology” that allowed states to extract significant resources as well as manpower from their respective populations. This paper underlines some of the problems involved with this perspective and pushes forward an interpretation that is based on the logic of political survival. I argue that nationalism’s emergence as a powerful force in world politics followed from the “mutation” and absorption of the universalistic/cosmopolitan republican ideas that gained temporary primacy in Europe during the eighteenth century into particularistic nationalist ideologies. This transformation, in turn, can be best explained by the French Revolution’s dramatic impacts on rulers’ political survival calculi vis-à-vis both interstate and domestic political challenges. The analysis offered in this essay contributes to our understanding of the relationship between IR and nationalism while also highlighting the potential value of the political survival framework for exploring macrohistorical puzzles.

Importance of resolution and model configuration when downscaling extreme precipitation

Dynamical downscaling is frequently used to investigate the dynamical variables of extra-tropical cyclones, for example, precipitation, using very high-resolution models nested within coarser resolution models to understand the processes that lead to intense precipitation. It is also used in climate change studies, using long timeseries to investigate trends in precipitation, or to look at the small-scale dynamical processes for specific case studies. This study investigates some of the problems associated with dynamical downscaling and looks at the optimum configuration to obtain the distribution and intensity of a precipitation field to match observations. This study uses the Met Office Unified Model run in limited area mode with grid spacings of 12, 4 and 1.5 km, driven by boundary conditions provided by the ECMWF Operational Analysis to produce high-resolution simulations for the Summer of 2007 UK flooding events. The numerical weather prediction model is initiated at varying times before the peak precipitation is observed to test the importance of the initialisation and boundary conditions, and how long the simulation can be run for. The results are compared to raingauge data as verification and show that the model intensities are most similar to observations when the model is initialised 12 hours before the peak precipitation is observed. It was also shown that using non-gridded datasets makes verification more difficult, with the density of observations also affecting the intensities observed. It is concluded that the simulations are able to produce realistic precipitation intensities when driven by the coarser resolution data.

Efficiency of evolutionary algorithms in water network pipe sizing

The pipe sizing of water networks via evolutionary algorithms is of great interest because it allows the selection of alternative economical solutions that meet a set of design requirements. However, available evolutionary methods are numerous, and methodologies to compare the performance of these methods beyond obtaining a minimal solution for a given problem are currently lacking. A methodology to compare algorithms based on an efficiency rate (E) is presented here and applied to the pipe-sizing problem of four medium-sized benchmark networks (Hanoi, New York Tunnel, GoYang and R-9 Joao Pessoa). E numerically determines the performance of a given algorithm while also considering the quality of the obtained solution and the required computational effort. From the wide range of available evolutionary algorithms, four algorithms were selected to implement the methodology: a PseudoGenetic Algorithm (PGA), Particle Swarm Optimization (PSO), a Harmony Search and a modified Shuffled Frog Leaping Algorithm (SFLA). After more than 500,000 simulations, a statistical analysis was performed based on the specific parameters each algorithm requires to operate, and finally, E was analyzed for each network and algorithm. The efficiency measure indicated that PGA is the most efficient algorithm for problems of greater complexity and that HS is the most efficient algorithm for less complex problems. However, the main contribution of this work is that the proposed efficiency ratio provides a neutral strategy to compare optimization algorithms and may be useful in the future to select the most appropriate algorithm for different types of optimization problems.

Boundary integral equations on unbounded rough surfaces: Fredholmness and the finite section method

We consider a class of boundary integral equations that arise in the study of strongly elliptic BVPs in unbounded domains of the form $D = \{(x, z)\in \mathbb{R}^{n+1} : x\in \mathbb{R}^n, z > f(x)\}$ where $f : \mathbb{R}^n \to\mathbb{R}$ is a sufficiently smooth bounded and continuous function. A number of specific problems of this type, for example acoustic scattering problems, problems involving elastic waves, and problems in potential theory, have been reformulated as second kind integral equations $u+Ku = v$ in the space $BC$ of bounded, continuous functions. Having recourse to the so-called limit operator method, we address two questions for the operator $A = I + K$ under consideration, with an emphasis on the function space setting $BC$. Firstly, under which conditions is $A$ a Fredholm operator, and, secondly, when is the finite section method applicable to $A$?

Literacy as a complex activity: deconstructing the simple view of reading

The Rose Review into the teaching of early reading recommended that the conceptual framework incorporated into the National Literacy Strategy Framework for Teaching – the Searchlights model of reading and its development – should be replaced by the Simple View of Reading. In this paper, we demonstrate how these two frameworks relate to each other, and show that nothing has been lost in this transformation from Searchlights to Simple View: on the contrary, much has been gained. That nothing has been lost is demonstrated by consideration of the underlying complexity inherent in each of the two dimensions delineated in the Simple View. That much has been gained is demonstrated by the increased understanding of each dimension that follows from careful scientific investigation of each. The better we understand what is involved in each dimension, the better placed we are to unravel and understand the essential, complex and continual interactions between each dimension which underlie skilled reading. This has clear implications for further improving the early teaching of reading.

The maturing discipline of robotics

The nature of the robotics discipline is changing. In turn the traditional engineering-based degree programmes that have promoted robotics as an application of engineering principles need to be supplemented with robot-centred degree programmes that reflect the diverse character of robotics, the diverse interests of students, and the diverse multi-disciplinary contributions to the robotics discipline. In this paper the nature of the change that robotics has undergone in recent years is described. An outline of the subject material of robotics, comprising robotics science and robotics engineering, is discussed The teaching of robotics degree programmes in the past has been hampered by the expense required to install and maintain a robotics teaching laboratory. Availability of online robot systems and numerous robot kits has changed this situation to some extent. However, the paper concludes that there is still a need for good educational toolkits for teaching robotics at a first degree level.

A simple method of calculating eigenvalues and resonances in domains with infinite regular ends

A new approach is presented for the solution of spectral problems on infinite domains with regular ends, which avoids the need to solve boundary-value problems for many trial values of the spectral parameter. We present numerical results both for eigenvalues and for resonances, comparing with results reported by Aslanyan, Parnovski and Vassiliev.

Curriculum theory, curriculum policy and the problem of ill-disciplined thinking

This paper examines the implications of policy fracture and arms length governance within the decision making processes currently shaping curriculum design within the English education system. In particular it argues that an unresolved ‘ideological fracture’ at government level has been passed down to school leaders whose response to the dilemma is distorted by the target-driven agenda of arms length agencies. Drawing upon the findings of a large scale on-line survey of history teaching in English secondary schools, this paper illustrates the problems that occur when policy making is divorced from curriculum theory, and in particular from any consideration of the nature of knowledge. Drawing on the social realist theory of knowledge elaborated by Young (2008), we argue that the rapid spread of alternative curricular arrangements, implemented in the absence of an understanding of curriculum theory, undermines the value of disciplined thinking to the detriment of many young people, particularly those in areas of social and economic deprivation.

English teachers in the digital age – a case study of policy and expert practice from England

This article is a case study of how English teachers in England have coped with the paradigm shift from print to digital literacy. It reviews a large scale national initiative that was intended to upskill all teachers, considers its weak impact and explores the author’s involvement in the evaluation of the project’s direct value to English teachers. It explores how this latter evaluation revealed how best practice in English using ICT was developing in a variable manner. It then reports on a recent small scale research project that investigated how very good teachers have adapted ICT successfully into their teaching. It focuses on how the English teachers studied in the project are developing a powerful new pedagogy situated in the life worlds of their students and suggests that this model may be of benefit to many teachers. The issues this article reports on have resonance in all English speaking countries. This article is also a personal story of the author’s close involvement with ICT and English over 20 years, and provides evidence for his conviction that digital technologies will eventually transform English teaching.

Enterprise pedagogy in music: an exploration of multiple pedagogies

This article investigates the nature of enterprise pedagogy in music. It presents the results of a research project that applied the practices of enterprise learning developed in the post-compulsory music curriculum in England to the teaching of the National Curriculum for music for 11-to-14-year-olds. In doing so, the article explores the nature of enterprise learning and the nature of pedagogy, in order to consider whether enterprise pedagogy offers an effective way to teach the National Curriculum. Enterprise pedagogy was found to have a positive effect on the motivation of students and on the potential to match learning to the needs of students of different abilities. Crucially, it was found that, to be effective, not only did the teacher’s practice need to be congruent with the beliefs and theories on which it rests, but that the students also needed to share in these underlying assumptions through their learning. The study has implications for the way in which teachers work multiple pedagogies in the process of developing their pedagogical identity.