Resource allocation analysis of the stochastic diffusion search

The Stochastic Diffusion Search (SDS) was developed as a solution to the best-fit search problem. Thus, as a special case it is capable of solving the transform invariant pattern recognition problem. SDS is efficient and, although inherently probabilistic, produces very reliable solutions in widely ranging search conditions. However, to date a systematic formal investigation of its properties has not been carried out. This thesis addresses this problem. The thesis reports results pertaining to the global convergence of SDS as well as characterising its time complexity. However, the main emphasis of the work, reports on the resource allocation aspect of the Stochastic Diffusion Search operations. The thesis introduces a novel model of the algorithm, generalising an Ehrenfest Urn Model from statistical physics. This approach makes it possible to obtain a thorough characterisation of the response of the algorithm in terms of the parameters describing the search conditions in case of a unique best-fit pattern in the search space. This model is further generalised in order to account for different search conditions: two solutions in the search space and search for a unique solution in a noisy search space. Also an approximate solution in the case of two alternative solutions is proposed and compared with predictions of the extended Ehrenfest Urn model. The analysis performed enabled a quantitative characterisation of the Stochastic Diffusion Search in terms of exploration and exploitation of the search space. It appeared that SDS is biased towards the latter mode of operation. This novel perspective on the Stochastic Diffusion Search lead to an investigation of extensions of the standard SDS, which would strike a different balance between these two modes of search space processing. Thus, two novel algorithms were derived from the standard Stochastic Diffusion Search, ‘context-free’ and ‘context-sensitive’ SDS, and their properties were analysed with respect to resource allocation. It appeared that they shared some of the desired features of their predecessor but also possessed some properties not present in the classic SDS. The theory developed in the thesis was illustrated throughout with carefully chosen simulations of a best-fit search for a string pattern, a simple but representative domain, enabling careful control of search conditions.

Convergence analysis of stochastic diffusion search

In this paper we present a connectionist searching technique - the Stochastic Diffusion Search (SDS), capable of rapidly locating a specified pattern in a noisy search space. In operation SDS finds the position of the pre-specified pattern or if it does not exist - its best instantiation in the search space. This is achieved via parallel exploration of the whole search space by an ensemble of agents searching in a competitive cooperative manner. We prove mathematically the convergence of stochastic diffusion search. SDS converges to a statistical equilibrium when it locates the best instantiation of the object in the search space. Experiments presented in this paper indicate the high robustness of SDS and show good scalability with problem size. The convergence characteristic of SDS makes it a fully adaptive algorithm and suggests applications in dynamically changing environments.

Validation of short tandem repeat analysis for the investigation of cases of disputed paternity

This study details validation of two separate multiplex STR systems for use in paternity investigations. These are the Second Generation Multiplex (SGM) developed by the UK Forensic Science Service and the PowerPlex 1 multiplex commercially available from Promega Inc. (Madison, WI, USA). These multiplexes contain 12 different STR systems (two are duplicated in the two systems). Population databases from Caucasian, Asian and Afro-Caribbean populations have been compiled for all loci. In all but two of the 36 STR/ethnic group combinations, no evidence was obtained to indicate inconsistency with Hardy-Weinberg (HW) proportions. Empirical and theoretical approaches have been taken to validate these systems for paternity testing. Samples from 121 cases of disputed paternity were analysed using established Single Locus Probe (SLP) tests currently in use, and also using the two multiplex STR systems. Results of all three test systems were compared and no non-conformities in the conclusions were observed, although four examples of apparent germ line mutations in the STR systems were identified. The data was analysed to give information on expected paternity indices and exclusion rates for these STR systems. The 12 systems combined comprise a highly discriminating test suitable for paternity testing. 99.96% of non-fathers are excluded from paternity on two or more STR systems. Where no exclusion is found, Paternity Index (PI) values of > 10,000 are expected in > 96% of cases.

Analysis of disputed single-parent/child and sibling relationships using 16 STR loci

This study describes the validation of short tandem repeat (STR) systems for the resolution of cases of disputed parentage where only a single parent is available for testing or where the claimed relationship of both parents is in doubt and also cases where sibship must be tested. Three separate multiplex systems the Second Generation Multiplex, Powerplex 1.2 and FFFL have been employed, giving a total of 16 STR loci. Both empirical and theoretical approaches to the validation have been adopted. Appropriate equations have been derived to calculate likelihood ratios for different relationships, incorporating a correction for subpopulation effects. An F(ST) point estimate of 1% has been applied throughout. Empirically, 101 cases of alleged father, alleged mother and child where analysed using six SLP systems and also using the three multiplex STR systems. Of the 202 relationships tested, 197 were independently resolved by both systems, providing either clear evidence of non-parentage or strong support for the relationship.

Computer generation and quantitative morphometric analysis of virtual neurons

An important goal in computational neuroanatomy is the complete and accurate simulation of neuronal morphology. We are developing computational tools to model three-dimensional dendritic structures based on sets of stochastic rules. This paper reports an extensive, quantitative anatomical characterization of simulated motoneurons and Purkinje cells. We used several local and global algorithms implemented in the L-Neuron and ArborVitae programs to generate sets of virtual neurons. Parameters statistics for all algorithms were measured from experimental data, thus providing a compact and consistent description of these morphological classes. We compared the emergent anatomical features of each group of virtual neurons with those of the experimental database in order to gain insights on the plausibility of the model assumptions, potential improvements to the algorithms, and non-trivial relations among morphological parameters. Algorithms mainly based on local constraints (e.g., branch diameter) were successful in reproducing many morphological properties of both motoneurons and Purkinje cells (e.g. total length, asymmetry, number of bifurcations). The addition of global constraints (e.g., trophic factors) improved the angle-dependent emergent characteristics (average Euclidean distance from the soma to the dendritic terminations, dendritic spread). Virtual neurons systematically displayed greater anatomical variability than real cells, suggesting the need for additional constraints in the models. For several emergent anatomical properties, a specific algorithm reproduced the experimental statistics better than the others did. However, relative performances were often reversed for different anatomical properties and/or morphological classes. Thus, combining the strengths of alternative generative models could lead to comprehensive algorithms for the complete and accurate simulation of dendritic morphology.

Blind equalization of nonminimum phase channels: higher order cumulant based algorithm

Higher order cumulant analysis is applied to the blind equalization of linear time-invariant (LTI) nonminimum-phase channels. The channel model is moving-average based. To identify the moving average parameters of channels, a higher-order cumulant fitting approach is adopted in which a novel relay algorithm is proposed to obtain the global solution. In addition, the technique incorporates model order determination. The transmitted data are considered as independently identically distributed random variables over some discrete finite set (e.g., set {±1, ±3}). A transformation scheme is suggested so that third-order cumulant analysis can be applied to this type of data. Simulation examples verify the feasibility and potential of the algorithm. Performance is compared with that of the noncumulant-based Sato scheme in terms of the steady state MSE and convergence rate.

An LMS style variable tap-length algorithm for structure adaptation

Searching for the optimum tap-length that best balances the complexity and steady-state performance of an adaptive filter has attracted attention recently. Among existing algorithms that can be found in the literature, two of which, namely the segmented filter (SF) and gradient descent (GD) algorithms, are of particular interest as they can search for the optimum tap-length quickly. In this paper, at first, we carefully compare the SF and GD algorithms and show that the two algorithms are equivalent in performance under some constraints, but each has advantages/disadvantages relative to the other. Then, we propose an improved variable tap-length algorithm using the concept of the pseudo fractional tap-length (FT). Updating the tap-length with instantaneous errors in a style similar to that used in the stochastic gradient [or least mean squares (LMS)] algorithm, the proposed FT algorithm not only retains the advantages from both the SF and the GD algorithms but also has significantly less complexity than existing algorithms. Both performance analysis and numerical simulations are given to verify the new proposed algorithm.

Modelling and control of Hammerstein system using B-spline approximation and the inverse of De Boor algorithm

In this article a simple and effective controller design is introduced for the Hammerstein systems that are identified based on observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a B-spline neural network. The controller is composed by computing the inverse of the B-spline approximated nonlinear static function, and a linear pole assignment controller. The contribution of this article is the inverse of De Boor algorithm that computes the inverse efficiently. Mathematical analysis is provided to prove the convergence of the proposed algorithm. Numerical examples are utilised to demonstrate the efficacy of the proposed approach.

The underlying return generating factors for REIT returns: an application of independent component analysis

Multi-factor approaches to analysis of real estate returns have, since the pioneering work of Chan, Hendershott and Sanders (1990), emphasised a macro-variables approach in preference to the latent factor approach that formed the original basis of the arbitrage pricing theory. With increasing use of high frequency data and trading strategies and with a growing emphasis on the risks of extreme events, the macro-variable procedure has some deficiencies. This paper explores a third way, with the use of an alternative to the standard principal components approach – independent components analysis (ICA). ICA seeks higher moment independence and maximises in relation to a chosen risk parameter. We apply an ICA based on kurtosis maximisation to weekly US REIT data using a kurtosis maximising algorithm. The results show that ICA is successful in capturing the kurtosis characteristics of REIT returns, offering possibilities for the development of risk management strategies that are sensitive to extreme events and tail distributions.

Tenant mix variety in regional shopping centres: some UK empirical analyses

The variety and quality of the tenant mix within a shopping centre is a key concern in shopping centre management. Tenant mix determines the extent of externalities between outlets in the centre, helps establish the image of the centre and, as a result, determines the attractiveness of the centre for consumers. This then translates into sales and rents. However, the management of tenant mix has largely been based on perceived “optimum” arrangements and industry rules of thumb. This paper attempts to model the impact of tenant mix on the rent paid by retailers in larger UK shopping centres and, hence, the returns made by shopping centre landlords. It extends work on shopping centre rent determination (see Working Paper 10/03) utilising a database of 148 regional shopping centres in the UK, with detailed data for over 1900 tenants. Econometric models test the relationship between rental levels and the levels of retail concentration and diversity, while controlling for a range of continuous and qualitative characteristics of each tenant, each retail product, and each shopping centre. Factor analysis is then used to extract the core retail and service categories from the tenant lists of the 148 shopping centres. The factor scores from these core retailer factors are then tested against rent payable. The results from the empirical analysis allow us to generate some clear analytical and empirical implications for optimal retail management.

Neural network basis function center selection using cluster analysis

This paper deals with the selection of centres for radial basis function (RBF) networks. A novel mean-tracking clustering algorithm is described as a way in which centers can be chosen based on a batch of collected data. A direct comparison is made between the mean-tracking algorithm and k-means clustering and it is shown how mean-tracking clustering is significantly better in terms of achieving an RBF network which performs accurate function modelling.

Cluster analysis for multivariable process control

This paper describes the novel use of cluster analysis in the field of industrial process control. The severe multivariable process problems encountered in manufacturing have often led to machine shutdowns, where the need for corrective actions arises in order to resume operation. Production faults which are caused by processes running in less efficient regions may be prevented or diagnosed using a reasoning based on cluster analysis. Indeed the intemal complexity of a production machinery may be depicted in clusters of multidimensional data points which characterise the manufacturing process. The application of a Mean-Tracking cluster algorithm (developed in Reading) to field data acquired from a high-speed machinery will be discussed. The objective of such an application is to illustrate how machine behaviour can be studied, in particular how regions of erroneous and stable running behaviour can be identified.

Application of logistic regression for fault analysis in an industrial printing process

A statistical technique for fault analysis in industrial printing is reported. The method specifically deals with binary data, for which the results of the production process fall into two categories, rejected or accepted. The method is referred to as logistic regression, and is capable of predicting future fault occurrences by the analysis of current measurements from machine parts sensors. Individual analysis of each type of fault can determine which parts of the plant have a significant influence on the occurrence of such faults; it is also possible to infer which measurable process parameters have no significant influence on the generation of these faults. Information derived from the analysis can be helpful in the operator's interpretation of the current state of the plant. Appropriate actions may then be taken to prevent potential faults from occurring. The algorithm is being implemented as part of an applied self-learning expert system.

Kinetic energy analysis of the response of the Atlantic meridional overturning circulation to CO2-forced climate change

Atmosphere–ocean general circulation models (AOGCMs) predict a weakening of the Atlantic meridional overturning circulation (AMOC) in response to anthropogenic forcing of climate, but there is a large model uncertainty in the magnitude of the predicted change. The weakening of the AMOC is generally understood to be the result of increased buoyancy input to the north Atlantic in a warmer climate, leading to reduced convection and deep water formation. Consistent with this idea, model analyses have shown empirical relationships between the AMOC and the meridional density gradient, but this link is not direct because the large-scale ocean circulation is essentially geostrophic, making currents and pressure gradients orthogonal. Analysis of the budget of kinetic energy (KE) instead of momentum has the advantage of excluding the dominant geostrophic balance. Diagnosis of the KE balance of the HadCM3 AOGCM and its low-resolution version FAMOUS shows that KE is supplied to the ocean by the wind and dissipated by viscous forces in the global mean of the steady-state control climate, and the circulation does work against the pressure-gradient force, mainly in the Southern Ocean. In the Atlantic Ocean, however, the pressure-gradient force does work on the circulation, especially in the high-latitude regions of deep water formation. During CO2-forced climate change, we demonstrate a very good temporal correlation between the AMOC strength and the rate of KE generation by the pressure-gradient force in 50–70°N of the Atlantic Ocean in each of nine contemporary AOGCMs, supporting a buoyancy-driven interpretation of AMOC changes. To account for this, we describe a conceptual model, which offers an explanation of why AOGCMs with stronger overturning in the control climate tend to have a larger weakening under CO2 increase

Analysis of the intermediate housing market mechanism in the UK

Government policies have backed intermediate housing market mechanisms like shared equity, intermediate rented and shared ownership (SO) as potential routes for some households, who are otherwise squeezed between the social housing and the private market. The rhetoric deployed around such housing has regularly contained claims about its social progressiveness and role in facilitating socio-economic mobility, centring on a claim that SO schemes can encourage people to move from rented accommodation through a shared equity phase and into full owner-occupation. SO has been justified on the grounds of it being transitional state, rather than a permanent tenure. However SO buyers may be laden with economic cost-benefit structures that do not stack up evenly and as a consequence there may be little realistic prospect of ever reaching a preferred outcome. Such behaviours have received little empirical attention as yet despite, the SO model arguably offers a sub-optimal solution towards homeownership, or in terms of wider quality of life. Given the paucity of rigorous empirical work on this issue, this paper delineates the evidence so far and sets out a research agenda. Our analysis is based on a large dataset of new shared owners, observing an information base that spans the past decade. We then set out an agenda to further examine the behaviours of the SO occupants and to examine the implications for future public policy based on existing literature and our outline findings. This paper is particularly opportune at a time of economic uncertainty and an overriding ‘austerity’ drive in public funding in the UK, through which SO schemes have enjoyed support uninterruptedly thus far.