Production system model of children's development of number concepts

The purpose of the present research study was to produce a global, cumulative model of number concept development for children between the ages of two and eight years old. The theoretical and methodological orientation of this study was greatly influenced by Richard Young's production system analysis of seriation by young children (Young, 1971, 1976) and by Newell's (1973) seminal paper, ‘You can't play twenty questions with nature and win’. The methodology used in this investigation thus was as follows. A series of complex number tasks encompassing many aspects of the concept of number were developed. Five children aged between three and seven years then were videotaped while performing some of these complex number tasks. From a detailed protocol analysis of the video-recordings, computer simulation models written in the production system language PSS3 (Ohlsson, 1979) were produced. Specific production system models were produced for each of following aspects of the children's number knowledge: (i) sharing of discrete quantities; (ii) comparison of shares; and (iii) conservation/addition/subtraction of number. These domain-specific models were based on the converging experimental evidence obtained from each of the children’s responses to variants of the complex number tasks. Each child thus received a different set of problems which were chosen systematically in order to clarify particular features of the child's abilities. After a production system model for each child had been produced within a domain, these models were compared and contrasted. From this analysis, developmental trends within the domain were identified and discussed. The research and educational implications of these developmental trends then were discussed. In the concluding parts of this study, the children's domain-specific production system models were cumulated into global, comprehensive models which accurately represented their behaviour in a variety of number tasks. These comprehensive models were compared and contrasted and general developmental trends in young children's number knowledge were identified and discussed.

Hypothesis generation for management intelligence

Investigation of the role of hypothesis formation in complex (business) problem solving has resulted in a new approach to hypothesis generation. A prototypical hypothesis generation paradigm for management intelligence has been developed, reflecting a widespread need to support management in such areas as fraud detection and intelligent decision analysis. This dissertation presents this new paradigm and its application to goal directed problem solving methodologies, including case based reasoning. The hypothesis generation model, which is supported by a dynamic hypothesis space, consists of three components, namely, Anomaly Detection, Abductive Reasoning, and Conflict Resolution models. Anomaly detection activates the hypothesis generation model by scanning anomalous data and relations in its working environment. The respective heuristics are activated by initial indications of anomalous behaviour based on evidence from historical patterns, linkages with other cases, inconsistencies, etc. Abductive reasoning, as implemented in this paradigm, is based on joining conceptual graphs, and provides an inference process that can incorporate a new observation into a world model by determining what assumptions should be added to the world, so that it can explain new observations. Abductive inference is a weak mechanism for generating explanation and hypothesis. Although a practical conclusion cannot be guaranteed, the cues provided by the inference are very beneficial. Conflict resolution is crucial for the evaluation of explanations, especially those generated by a weak (abduction) mechanism.The measurements developed in this research for explanation and hypothesis provide an indirect way of estimating the ‘quality’ of an explanation for given evidence. Such methods are realistic for complex domains such as fraud detection, where the prevailing hypothesis may not always be relevant to the new evidence. In order to survive in rapidly changing environments, it is necessary to bridge the gap that exists between the system’s view of the world and reality.Our research has demonstrated the value of Case-Based Interaction, which utilises an hypothesis structure for the representation of relevant planning and strategic knowledge. Under, the guidance of case based interaction, users are active agents empowered by system knowledge, and the system acquires its auxiliary information/knowledge from this external source. Case studies using the new paradigm and drawn from the insurance industry have attracted wide interest. A prototypical system of fraud detection for motor vehicle insurance based on an hypothesis guided problem solving mechanism is now under commercial development. The initial feedback from claims managers is promising.

Fuzzy concepts and formal methods

It has been recognised that formal methods are useful as a modelling tool in requirements engineering. Specification languages such as Z permit the precise and unambiguous modelling of system properties and behaviour. However some system problems, particularly those drawn from the information systems problem domain, may be difficult to model in crisp or precise terms. It may also be desirable that formal modelling should commence as early as possible, even when our understanding of parts of the problem domain is only approximate. This thesis suggests fuzzy set theory as a possible representation scheme for this imprecision or approximation. A fuzzy logic toolkit that defines the operators, measures and modifiers necessary for the manipulation of fuzzy sets and relations is developed. The toolkit contains a detailed set of laws that demonstrate the properties of the definitions when applied to partial set membership. It also provides a set of laws that establishes an isomorphism between the toolkit notation and that of conventional Z when applied to boolean sets and relations. The thesis also illustrates how the fuzzy logic toolkit can be applied in the problem domains of interest. Several examples are presented and discussed including the representation of imprecise concepts as fuzzy sets and relations, system requirements as a series of linguistically quantified propositions, the modelling of conflict and agreement in terms of fuzzy sets and the partial specification of a fuzzy expert system. The thesis concludes with a consideration of potential areas for future research arising from the work presented here.

Computational aspects of the numerical solution of SDEs

In the last 30 to 40 years, many researchers have combined to build the knowledge base of theory and solution techniques that can be applied to the case of differential equations which include the effects of noise. This class of ``noisy'' differential equations is now known as stochastic differential equations (SDEs). Markov diffusion processes are included within the field of SDEs through the drift and diffusion components of the Itô form of an SDE. When these drift and diffusion components are moderately smooth functions, then the processes' transition probability densities satisfy the Fokker-Planck-Kolmogorov (FPK) equation -- an ordinary partial differential equation (PDE). Thus there is a mathematical inter-relationship that allows solutions of SDEs to be determined from the solution of a noise free differential equation which has been extensively studied since the 1920s. The main numerical solution technique employed to solve the FPK equation is the classical Finite Element Method (FEM). The FEM is of particular importance to engineers when used to solve FPK systems that describe noisy oscillators. The FEM is a powerful tool but is limited in that it is cumbersome when applied to multidimensional systems and can lead to large and complex matrix systems with their inherent solution and storage problems. I show in this thesis that the stochastic Taylor series (TS) based time discretisation approach to the solution of SDEs is an efficient and accurate technique that provides transition and steady state solutions to the associated FPK equation. The TS approach to the solution of SDEs has certain advantages over the classical techniques. These advantages include their ability to effectively tackle stiff systems, their simplicity of derivation and their ease of implementation and re-use. Unlike the FEM approach, which is difficult to apply in even only two dimensions, the simplicity of the TS approach is independant of the dimension of the system under investigation. Their main disadvantage, that of requiring a large number of simulations and the associated CPU requirements, is countered by their underlying structure which makes them perfectly suited for use on the now prevalent parallel or distributed processing systems. In summary, l will compare the TS solution of SDEs to the solution of the associated FPK equations using the classical FEM technique. One, two and three dimensional FPK systems that describe noisy oscillators have been chosen for the analysis. As higher dimensional FPK systems are rarely mentioned in the literature, the TS approach will be extended to essentially infinite dimensional systems through the solution of stochastic PDEs. In making these comparisons, the advantages of modern computing tools such as computer algebra systems and simulation software, when used as an adjunct to the solution of SDEs or their associated FPK equations, are demonstrated.

Computational investigations on periodic trends in Group 14 chemistry

Describes the use of computer-aided molecular modelling to investigate trends in the chemistry of the Group 14 elements, namely carbon, silicon, germanium, tin and lead. The chemical behaviour of two classes of molecules containing Group 14 elements was related to trends in the fundamental properties of these elements.

Many-sample location and scale tests with quantile-function error distributions /by Azmeri Khan

This thesis, using a computer simulation, studies the effect of the normal distribution assumption on the power of several many-sample location and scale test procedures. It also suggests an almost robust parametric test, namely numerical likelihood ratio test (NLRT) for non-normal situations. The NLRT is found better than all of the tests considered. Some real life data sets were used as examples.

Prediction of ductile fracture in the cold forging of steel

The thesis describes the development of a model of the cold forging process that accurately predicts the initiation of ductile fracture. The effect of the deformation history of the material during multiple forming operations is considered. Both two- and three-dimensional numerical models of the forging process were combined with a ductile fracture criterion to predict the material ductility and damage distribution in the workpiece.

Testing and modelling to obtain material behaviour for crash simulations

The thesis focusses on improving the material behaviour models used in vehicle crash simulations by identifying the mechanical properties most important to crash events, reformulating the material models used in crash simulations, and developing new tests to obtain crash-relevant material.

Mixed transfer function neural networks for generalization and knowledge extraction

This thesis develops a novel framework of nonlinear modelling to adaptively fit the complexity of the model to the problem domain resulting in a better modelling capability and a straightforward knowledge acquisition. The developed framework also permits increased comprehensibility and user acceptability of modelling results.

Composite crashworthy structures

This study presents an innovative finite element delamination model which successfully reproduced the experimental failure behaviour observed in axial crush testing. Tests were conducted on tubes manufactured by a novel composite curing process, resulting in the ability to cure tubular profiles in 7 minutes - 95% quicker than traditional autoclave curing.

Haptically simulating soft tissue using spherical voxel and reactive agents

This thesis describes technology developed by the author enabling trainee surgeons to perform needle insertion procedures with force feedback (haptics) on a virtual patient. Addition of the sense of touch to medical simulation is arguably the most important step forward in the evolution of haptic technology to this day.

Input and output analysis of complex conveyor networks

Material transfer networks are at the heart of critical infrastructure in many modern service and manufacturing industries. This research identified key performance measures, while deriving generalised analysis methodologies, for simulation models. The technology was validated for international airports, and used to determine operational capacity constraints under varied demand conditions.

Realistic grasping of rigid virtual objects through event-based haptics

This research presents a novel haptic grasping interface and demonstrates its ability within multi-point event-based feedback. Through experimental methodology, the dynamics involved in grasp contact interactions are modelled based on first principles. The proposed approach demonstrates a method of realistically representing grasp contact with rigid virtual objects through multi-point interaction.

Prototyping real-time systems using Petri net and object-oriented models

The objective of the research for this thesis is to develop techniques in order to build an executable model of a real-time system. This model is to be used early in the development of the system not only to detect errors in the specification of the system but also to validate expectations of the developer as to the operation of the system. A graphical specification of a real-time system called the transformation schema was chosen to be used to build the model. Two executable models of a real-time system are described.