Tracking of non-stationary time-series using resource allocating RBF networks

In this paper, we discuss some practical implications for implementing adaptable network algorithms applied to non-stationary time series problems. Using electricity load data and training with the extended Kalman filter, we demonstrate that the dynamic model-order increment procedure of the resource allocating RBF network (RAN) is highly sensitive to the parameters of the novelty criterion. We investigate the use of system noise and forgetting factors for increasing the plasticity of the Kalman filter training algorithm, and discuss the consequences for on-line model order selection. We also find that a recently-proposed alternative novelty criterion, found to be more robust in stationary environments, does not fare so well in the non-stationary case due to the need for filter adaptability during training.

Recursive self-organizing map as a contractive iterative function system

Recently, there has been a considerable research activity in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. However, the representational capabilities and internal representations of the models are not well understood. We rigorously analyze a generalization of the Self-Organizing Map (SOM) for processing sequential data, Recursive SOM (RecSOM [1]), as a non-autonomous dynamical system consisting off a set of fixed input maps. We show that contractive fixed input maps are likely to produce Markovian organizations of receptive fields o the RecSOM map. We derive bounds on parameter $\beta$ (weighting the importance of importing past information when processing sequences) under which contractiveness of the fixed input maps is guaranteed.

A pragmatic Bayesian approach to wind field retrieval

The ERS-1 Satellite was launched in July 1991 by the European Space Agency into a polar orbit at about 800 km, carrying a C-band scatterometer. A scatterometer measures the amount of backscatter microwave radiation reflected by small ripples on the ocean surface induced by sea-surface winds, and so provides instantaneous snap-shots of wind flow over large areas of the ocean surface, known as wind fields. Inherent in the physics of the observation process is an ambiguity in wind direction; the scatterometer cannot distinguish if the wind is blowing toward or away from the sensor device. This ambiguity implies that there is a one-to-many mapping between scatterometer data and wind direction. Current operational methods for wind field retrieval are based on the retrieval of wind vectors from satellite scatterometer data, followed by a disambiguation and filtering process that is reliant on numerical weather prediction models. The wind vectors are retrieved by the local inversion of a forward model, mapping scatterometer observations to wind vectors, and minimising a cost function in scatterometer measurement space. This thesis applies a pragmatic Bayesian solution to the problem. The likelihood is a combination of conditional probability distributions for the local wind vectors given the scatterometer data. The prior distribution is a vector Gaussian process that provides the geophysical consistency for the wind field. The wind vectors are retrieved directly from the scatterometer data by using mixture density networks, a principled method to model multi-modal conditional probability density functions. The complexity of the mapping and the structure of the conditional probability density function are investigated. A hybrid mixture density network, that incorporates the knowledge that the conditional probability distribution of the observation process is predominantly bi-modal, is developed. The optimal model, which generalises across a swathe of scatterometer readings, is better on key performance measures than the current operational model. Wind field retrieval is approached from three perspectives. The first is a non-autonomous method that confirms the validity of the model by retrieving the correct wind field 99% of the time from a test set of 575 wind fields. The second technique takes the maximum a posteriori probability wind field retrieved from the posterior distribution as the prediction. For the third technique, Markov Chain Monte Carlo (MCMC) techniques were employed to estimate the mass associated with significant modes of the posterior distribution, and make predictions based on the mode with the greatest mass associated with it. General methods for sampling from multi-modal distributions were benchmarked against a specific MCMC transition kernel designed for this problem. It was shown that the general methods were unsuitable for this application due to computational expense. On a test set of 100 wind fields the MAP estimate correctly retrieved 72 wind fields, whilst the sampling method correctly retrieved 73 wind fields.

Practical methods of tracking of nonstationary time series applied to real-world data

In this paper, we discuss some practical implications for implementing adaptable network algorithms applied to non-stationary time series problems. Two real world data sets, containing electricity load demands and foreign exchange market prices, are used to test several different methods, ranging from linear models with fixed parameters, to non-linear models which adapt both parameters and model order on-line. Training with the extended Kalman filter, we demonstrate that the dynamic model-order increment procedure of the resource allocating RBF network (RAN) is highly sensitive to the parameters of the novelty criterion. We investigate the use of system noise for increasing the plasticity of the Kalman filter training algorithm, and discuss the consequences for on-line model order selection. The results of our experiments show that there are advantages to be gained in tracking real world non-stationary data through the use of more complex adaptive models.

An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium

Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170) proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems. However, in many applied problems, operators appear that do not satisfy these requirements, e.g. Helmholtz-type operators. Therefore, in this study, an alternating procedure for solving Cauchy problems for self-adjoint non-coercive elliptic operators of second order is presented. A convergence proof of this procedure is given.

Numerical solution of parabolic Cauchy problems in planar corner domains

An iterative method for the parabolic Cauchy problem in planar domains having a finite number of corners is implemented based on boundary integral equations. At each iteration, mixed well-posed problems are solved for the same parabolic operator. The presence of corner points renders singularities of the solutions to these mixed problems, and this is handled with the use of weight functions together with, in the numerical implementation, mesh grading near the corners. The mixed problems are reformulated in terms of boundary integrals obtained via discretization of the time-derivative to obtain an elliptic system of partial differential equations. To numerically solve these integral equations a Nyström method with super-algebraic convergence order is employed. Numerical results are presented showing the feasibility of the proposed approach. © 2014 IMACS.

Multi-threaded parallel simulation of non-local non-linear problems in ultrashort laser pulse propagation in the presence of plasma

We describe a parallel multi-threaded approach for high performance modelling of wide class of phenomena in ultrafast nonlinear optics. Specific implementation has been performed using the highly parallel capabilities of a programmable graphics processor. © 2011 SPIE.

The exact sample complexity of PAC-learning problems with unit VC dimension

The Vapnik-Chervonenkis (VC) dimension is a combinatorial measure of a certain class of machine learning problems, which may be used to obtain upper and lower bounds on the number of training examples needed to learn to prescribed levels of accuracy. Most of the known bounds apply to the Probably Approximately Correct (PAC) framework, which is the framework within which we work in this paper. For a learning problem with some known VC dimension, much is known about the order of growth of the sample-size requirement of the problem, as a function of the PAC parameters. The exact value of sample-size requirement is however less well-known, and depends heavily on the particular learning algorithm being used. This is a major obstacle to the practical application of the VC dimension. Hence it is important to know exactly how the sample-size requirement depends on VC dimension, and with that in mind, we describe a general algorithm for learning problems having VC dimension 1. Its sample-size requirement is minimal (as a function of the PAC parameters), and turns out to be the same for all non-trivial learning problems having VC dimension 1. While the method used cannot be naively generalised to higher VC dimension, it suggests that optimal algorithm-dependent bounds may improve substantially on current upper bounds.

Non-zero mean Gaussian process prior wind field models

This report outlines the derivation and application of a non-zero mean, polynomial-exponential covariance function based Gaussian process which forms the prior wind field model used in 'autonomous' disambiguation. It is principally used since the non-zero mean permits the computation of realistic local wind vector prior probabilities which are required when applying the scaled-likelihood trick, as the marginals of the full wind field prior. As the full prior is multi-variate normal, these marginals are very simple to compute.

Biocomposites of non-crosslinked natural and synthetic polymers

Biocomposite films comprising a non-crosslinked, natural polymer (collagen) and a synthetic polymer, poly(var epsilon-caprolactone) (PCL), have been produced by impregnation of lyophilised collagen mats with a solution of PCL in dichloromethane followed by solvent evaporation. This approach avoids the toxicity problems associated with chemical crosslinking. Distinct changes in film morphology, from continuous surface coating to open porous format, were achieved by variation of processing parameters such as collagen:PCL ratio and the weight of the starting lyophilised collagen mat. Collagenase digestion indicated that the collagen content of 1:4 and 1:8 collagen:PCL biocomposites was almost totally accessible for enzymatic digestion indicating a high degree of collagen exposure for interaction with other ECM proteins or cells contacting the biomaterial surface. Much reduced collagen exposure (around 50%) was measured for the 1:20 collagen:PCL materials. These findings were consistent with the SEM examination of collagen:PCL biocomposites which revealed a highly porous morphology for the 1:4 and 1:8 blends but virtually complete coverage of the collagen component by PCL in the1:20 samples. Investigations of the attachment and spreading characteristics of human osteoblast (HOB) cells on PCL films and collagen:PCL materials respectively, indicated that HOB cells poorly recognised PCL but attachment and spreading were much improved on the biocomposites. The non-chemically crosslinked, collagen:PCL biocomposites described are expected to provide a useful addition to the range of biomaterials and matrix systems for tissue engineering.

Improving returnable transport equipment management with an autonomous approach

Challenges of returnable transport equipment (RTE) management continue to heighten as the popularity of their usage magnifies. Logistics companies are investigating the implementation of radio-frequency identification (RFID) technology to alleviate problems such as loss prevention and stock reduction. However, the research within this field is limited and fails to fully explore with depth, the wider network improvements that can be made to optimize the supply chain through efficient RTE management. This paper, investigates the nature of RTE network management building on current research and practices, filling a gap in the literature, through the investigation of a product-centric approach where the paradigms of “intelligent products” and “autonomous objects” are explored. A network optimizing approach with RTE management is explored, encouraging advanced research development of the RTE paradigm to align academic research with problematic areas in industry. Further research continues with the development of an agent-based software system, ready for application to a real-case study distribution network, producing quantitative results for further analysis. This is pivotal on the endeavor to developing agile support systems, fully utilizing an information-centric environment and encouraging RTE to be viewed as critical network optimizing tools rather than costly waste.

Achieving cost competitiveness with an agent based integrated process planning and production scheduling system

From a manufacturing perspective, the efficiency of manufacturing operations (such as process planning and production scheduling) are the key element for enhancing manufacturing competence. Process planning and production scheduling functions have been traditionally treated as two separate activities, and have resulted in a range of inefficiencies. These include infeasible process plans, non-available/overloaded resources, high production costs, long production lead times, and so on. Above all, it is unlikely that the dynamic changes can be efficiently dealt with. Despite much research has been conducted to integrate process planning and production scheduling to generate optimised solutions to improve manufacturing efficiency, there is still a gap to achieve the competence required for the current global competitive market. In this research, the concept of multi-agent system (MAS) is adopted as a means to address the aforementioned gap. A MAS consists of a collection of intelligent autonomous agents able to solve complex problems. These agents possess their individual objectives and interact with each other to fulfil the global goal. This paper describes a novel use of an autonomous agent system to facilitate the integration of process planning and production scheduling functions to cope with unpredictable demands, in terms of uncertainties in product mix and demand pattern. The novelty lies with the currency-based iterative agent bidding mechanism to allow process planning and production scheduling options to be evaluated simultaneously, so as to search for an optimised, cost-effective solution. This agent based system aims to achieve manufacturing competence by means of enhancing the flexibility and agility of manufacturing enterprises.

Detection of signals corrupted by the combination of Gaussian and Non-Gaussian noise

The detection of signals in the presence of noise is one of the most basic and important problems encountered by communication engineers. Although the literature abounds with analyses of communications in Gaussian noise, relatively little work has appeared dealing with communications in non-Gaussian noise. In this thesis several digital communication systems disturbed by non-Gaussian noise are analysed. The thesis is divided into two main parts. In the first part, a filtered-Poisson impulse noise model is utilized to calulate error probability characteristics of a linear receiver operating in additive impulsive noise. Firstly the effect that non-Gaussian interference has on the performance of a receiver that has been optimized for Gaussian noise is determined. The factors affecting the choice of modulation scheme so as to minimize the deterimental effects of non-Gaussian noise are then discussed. In the second part, a new theoretical model of impulsive noise that fits well with the observed statistics of noise in radio channels below 100 MHz has been developed. This empirical noise model is applied to the detection of known signals in the presence of noise to determine the optimal receiver structure. The performance of such a detector has been assessed and is found to depend on the signal shape, the time-bandwidth product, as well as the signal-to-noise ratio. The optimal signal to minimize the probability of error of; the detector is determined. Attention is then turned to the problem of threshold detection. Detector structure, large sample performance and robustness against errors in the detector parameters are examined. Finally, estimators of such parameters as. the occurrence of an impulse and the parameters in an empirical noise model are developed for the case of an adaptive system with slowly varying conditions.

Odour pollution problems within the district of the Wrekin council

This thesis is concerned with various aspects of Air Pollution due to smell, the impact it has on communities exposed to it, the means by which it may be controlled and the manner in which a local authority may investigate the problems it causes. The approach is a practical one drawing on examples occurring within a Local Authority's experience and for that reason the research is anecdotal and is not a comprehensive treatise on the full range of options available. Odour Pollution is not yet a well organised discipline and might be considered esoteric as it is necessary to incorporate elements of science and the humanities. It has been necessary to range widely across a number of aspects of the subject so that discussion is often restricted but many references have been included to enable a reader to pursue a particular point in greater depth. In a `fuzzy' subject there is often a yawning gap separating theory and practice, thus case studies have been used to illustrate the interplay of various disciplines in resolution of a problem. The essence of any science is observation and measurement. Observation has been made of the spread of odour pollution through a community and also of relevant meterological data so that a mathematical model could be constructed and its predictions checked. It has been used to explore the results of some options for odour control. Measurements of odour perception and human behaviour seldom have the precision and accuracy of the physical sciences. However methods of social research enabled individual perception of odour pollution to be quantified and an insight gained into reaction of a community exposed to it. Odours have four attributes that can be measured and together provide a complete description of its perception. No objective techniques of measurement have yet been developed but in this thesis simple, structured procedures of subjective assessment have been improvised and their use enabled the functioning of the components of an odour control system to be assessed. Such data enabled the action of the system to be communicated using terms that are understood by a non specialist audience.

On the solution of a class of capital investment problems

In this work the solution of a class of capital investment problems is considered within the framework of mathematical programming. Upon the basis of the net present value criterion, the problems in question are mainly characterized by the fact that the cost of capital is defined as a non-decreasing function of the investment requirements. Capital rationing and some cases of technological dependence are also included, this approach leading to zero-one non-linear programming problems, for which specifically designed solution procedures supported by a general branch and bound development are presented. In the context of both this development and the relevant mathematical properties of the previously mentioned zero-one programs, a generalized zero-one model is also discussed. Finally,a variant of the scheme, connected with the search sequencing of optimal solutions, is presented as an alternative in which reduced storage limitations are encountered.