Inverse forecasting:a new approach for predictive modelling

In the last two decades there have been substantial developments in the mathematical theory of inverse optimization problems, and their applications have expanded greatly. In parallel, time series analysis and forecasting have become increasingly important in various fields of research such as data mining, economics, business, engineering, medicine, politics, and many others. Despite the large uses of linear programming in forecasting models there is no a single application of inverse optimization reported in the forecasting literature when the time series data is available. Thus the goal of this paper is to introduce inverse optimization into forecasting field, and to provide a streamlined approach to time series analysis and forecasting using inverse linear programming. An application has been used to demonstrate the use of inverse forecasting developed in this study. © 2007 Elsevier Ltd. All rights reserved.

Productivity analysis and measurement

The state of the art in productivity measurement and analysis shows a gap between simple methods having little relevance in practice and sophisticated mathematical theory which is unwieldy for strategic and tactical planning purposes, -particularly at company level. An extension is made in this thesis to the method of productivity measurement and analysis based on the concept of added value, appropriate to those companies in which the materials, bought-in parts and services change substantially and a number of plants and inter-related units are involved in providing components for final assembly. Reviews and comparisons of productivity measurement dealing with alternative indices and their problems have been made and appropriate solutions put forward to productivity analysis in general and the added value method in particular. Based on this concept and method, three kinds of computerised models two of them deterministic, called sensitivity analysis and deterministic appraisal, and the third one, stochastic, called risk simulation, have been developed to cope with the planning of productivity and productivity growth with reference to the changes in their component variables, ranging from a single value 'to• a class interval of values of a productivity distribution. The models are designed to be flexible and can be adjusted according to the available computer capacity expected accuracy and 'presentation of the output. The stochastic model is based on the assumption of statistical independence between individual variables and the existence of normality in their probability distributions. The component variables have been forecasted using polynomials of degree four. This model is tested by comparisons of its behaviour with that of mathematical model using real historical data from British Leyland, and the results were satisfactory within acceptable levels of accuracy. Modifications to the model and its statistical treatment have been made as required. The results of applying these measurements and planning models to the British motor vehicle manufacturing companies are presented and discussed.

Application of thermal neutron radiography for the mass transport of moisture through freezing soil

This thesis reports on the development of a technique to evaluate hydraulic conductivities in a soil (Snowcal) subject to freezing conditions. The technique draws on three distinctly different disciplines, Nuclear Physics, Soil Physics and Remote Sensing to provide a non-destructive and reliable evaluation of hydraulic conductivity throughout a freezing test. Thermal neutron radiography is used to provide information on local water/ice contents at anytime throughout the test. The experimental test rig is designed so that the soil matrix can be radiated by a neutron beam, from a nuclear reactor, to obtain radiographs. The radiographs can then be interpreted, following a process of remote sensing image enhancement, to yield information on relative water/ice contents. Interpretation of the radiographs is accommodated using image analysis equipment capable of distinguishing between 256 shades of grey. Remote sensing image enhancing techniques are then employed to develop false colour images which show the movement of water and development of ice lenses in the soil. Instrumentation is incorporated in the soil in the form of psychrometer/thermocouples, to record water potential, electrical resistance probes to enable ice and water to be differentiated on the radiographs and thermocouples to record the temperature gradient. Water content determinations are made from the enhanced images and plotted against potential measurements to provide the moisture characteristic for the soil. With relevant mathematical theory pore water distributions are obtained and combined with water content data to give hydraulic conductivities. The values for hydraulic conductivity in the saturated soil and at the frozen fringe are compared with established values for silts and silty-sands. The values are in general agreement and, with refinement, this non-destructive technique could afford useful information on a whole range of soils. The technique is of value over other methods because ice lenses are actually seen forming in the soil, supporting the accepted theories of frost action. There are economic and experimental restraints to the work which are associated with the use of a nuclear facility, however, the technique is versatile and has been applied to the study of moisture transfer in porous building materials and could be further developed into other research areas.

Dissipative nonlinear structures in fiber optics

Optical fiber materials exhibit a nonlinear response to strong electric fields, such as those of optical signals confined within the small fiber core. Fiber nonlinearity is an essential component in the design of the next generation of advanced optical communication systems, but its use is often avoided by engineers because of its intractability. The application of nonlinear technologies in fiber optics offers new opportunities for the design of photonic systems and devices. In this chapter, we make an overview of recent progress in mathematical theory and practical applications of temporal dissipative solitons and self-similar nonlinear structures in optical fiber systems. The design of all-optical high-speed signal processing devices, based on nonlinear dissipative structures, is discussed.

Dissipative nonlinear structures in fiber optics

Optical fiber materials exhibit a nonlinear response to strong electric fields, such as those of optical signals confined within the small fiber core. Fiber nonlinearity is an essential component in the design of the next generation of advanced optical communication systems, but its use is often avoided by engineers because of its intractability. The application of nonlinear technologies in fiber optics offers new opportunities for the design of photonic systems and devices. In this chapter, we make an overview of recent progress in mathematical theory and practical applications of temporal dissipative solitons and self-similar nonlinear structures in optical fiber systems. The design of all-optical high-speed signal processing devices, based on nonlinear dissipative structures, is discussed.

Advanced mean field methods:theory and practice

A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Because exact computations are infeasible in such cases and Monte Carlo sampling techniques may reach their limits, there is a need for methods that allow for efficient approximate computations. One of the simplest approximations is based on the mean field method, which has a long history in statistical physics. The method is widely used, particularly in the growing field of graphical models. Researchers from disciplines such as statistical physics, computer science, and mathematical statistics are studying ways to improve this and related methods and are exploring novel application areas. Leading approaches include the variational approach, which goes beyond factorizable distributions to achieve systematic improvements; the TAP (Thouless-Anderson-Palmer) approach, which incorporates correlations by including effective reaction terms in the mean field theory; and the more general methods of graphical models. Bringing together ideas and techniques from these diverse disciplines, this book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling.

Types of task, types of audience, types of actor: interactions between mere presence and personality type in a simple mathematical task

Research into social facilitation effects reveals three factors affecting response performance: types of task, types of audience and type of actor. This study attempts to establish a minimal baseline for task and audience type in order to examine difference between personality types in the actors. Results indicate that performance in both extraverts and introverts increases in the minimal conditions of the mere presence of another person whilst carrying out a simple mathematical task. These results are interpreted through an analysis of Zajonc's (1965) drive theory with Eysenck's (1967) personality theory indicating that through further investigation performance curves might be devised for introverts and extraverts performing under a variety of task and audience conditions.

Mathematical modelling and optimal multivariable control of chemical processes

This work reports the developnent of a mathenatical model and distributed, multi variable computer-control for a pilot plant double-effect climbing-film evaporator. A distributed-parameter model of the plant has been developed and the time-domain model transformed into the Laplace domain. The model has been further transformed into an integral domain conforming to an algebraic ring of polynomials, to eliminate the transcendental terms which arise in the Laplace domain due to the distributed nature of the plant model. This has made possible the application of linear control theories to a set of linear-partial differential equations. The models obtained have well tracked the experimental results of the plant. A distributed-computer network has been interfaced with the plant to implement digital controllers in a hierarchical structure. A modern rnultivariable Wiener-Hopf controller has been applled to the plant model. The application has revealed a limitation condition that the plant matrix should be positive-definite along the infinite frequency axis. A new multi variable control theory has emerged fram this study, which avoids the above limitation. The controller has the structure of the modern Wiener-Hopf controller, but with a unique feature enabling a designer to specify the closed-loop poles in advance and to shape the sensitivity matrix as required. In this way, the method treats directly the interaction problems found in the chemical processes with good tracking and regulation performances. Though the ability of the analytical design methods to determine once and for all whether a given set of specifications can be met is one of its chief advantages over the conventional trial-and-error design procedures. However, one disadvantage that offsets to some degree the enormous advantages is the relatively complicated algebra that must be employed in working out all but the simplest problem. Mathematical algorithms and computer software have been developed to treat some of the mathematical operations defined over the integral domain, such as matrix fraction description, spectral factorization, the Bezout identity, and the general manipulation of polynomial matrices. Hence, the design problems of Wiener-Hopf type of controllers and other similar algebraic design methods can be easily solved.

Mathematical and numerical modelling of dispersion-managed solitons, autosolitons and self-similar optical pulses

This thesis presents theoretical investigation of three topics concerned with nonlinear optical pulse propagation in optical fibres. The techniques used are mathematical analysis and numerical modelling. Firstly, dispersion-managed (DM) solitons in fibre lines employing a weak dispersion map are analysed by means of a perturbation approach. In the case of small dispersion map strengths the average pulse dynamics is described by a perturbation approach (NLS) equation. Applying a perturbation theory, based on the Inverse Scattering Transform method, an analytic expression for the envelope of the DM soliton is derived. This expression correctly predicts the power enhancement arising from the dispersion management.Secondly, autosoliton transmission in DM fibre systems with periodical in-line deployment of nonlinear optical loop mirrors (NOLMs) is investigated. The use of in-line NOLMs is addressed as a general technique for all-optical passive 2R regeneration of return-to-zero data in high speed transmission system with strong dispersion management. By system optimisation, the feasibility of ultra-long single-channel and wavelength-division multiplexed data transmission at bit-rates ³ 40 Gbit s-1 in standard fibre-based systems is demonstrated. The tolerance limits of the results are defined.Thirdly, solutions of the NLS equation with gain and normal dispersion, that describes optical pulse propagation in an amplifying medium, are examined. A self-similar parabolic solution in the energy-containing core of the pulse is matched through Painlevé functions to the linear low-amplitude tails. The analysis provides a full description of the features of high-power pulses generated in an amplifying medium.

A mean field theory of coded CDMA systems

We present a mean field theory of code-division multiple access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems.

The mathematical modelling of the environmental performance of buildings as an aid in the design process

This thesis is a theoretical study of the accuracy and usability of models that attempt to represent the environmental control system of buildings in order to improve environmental design. These models have evolved from crude representations of a building and its environment through to an accurate representation of the dynamic characteristics of the environmental stimuli on buildings. Each generation of models has had its own particular influence on built form. This thesis analyses the theory, structure and data of such models in terms of their accuracy of simulation and therefore their validity in influencing built form. The models are also analysed in terms of their compatability with the design process and hence their ability to aid designers. The conclusions are that such models are unlikely to improve environmental performance since: a the models can only be applied to a limited number of building types, b they can only be applied to a restricted number of the characteristics of a design, c they can only be employed after many major environmental decisions have been made, d the data used in models is inadequate and unrepresentative, e models do not account for occupant interaction in environmental control. It is argued that further improvements in the accuracy of simulation of environmental control will not significantly improve environmental design. This is based on the premise that strategic environmental decisions are made at the conceptual stages of design whereas models influence the detailed stages of design. It is hypothesised that if models are to improve environmental design it must be through the analysis of building typologies which provides a method of feedback between models and the conceptual stages of design. Field studies are presented to describe a method by which typologies can be analysed and a theoretical framework is described which provides a basis for further research into the implications of the morphology of buildings on environmental design.