Magnification factors for the SOM and GTM algorithms

Magnification factors specify the extent to which the area of a small patch of the latent (or `feature') space of a topographic mapping is magnified on projection to the data space, and are of considerable interest in both neuro-biological and data analysis contexts. Previous attempts to consider magnification factors for the self-organizing map (SOM) algorithm have been hindered because the mapping is only defined at discrete points (given by the reference vectors). In this paper we consider the batch version of SOM, for which a continuous mapping can be defined, as well as the Generative Topographic Mapping (GTM) algorithm of Bishop et al. (1997) which has been introduced as a probabilistic formulation of the SOM. We show how the techniques of differential geometry can be used to determine magnification factors as continuous functions of the latent space coordinates. The results are illustrated here using a problem involving the identification of crab species from morphological data.

Typical case behaviour of spin systems in random graph and composite ensembles

This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed using a statistical analysis of a simple branch and bound algorithm. The algorithm can be formulated in the large system limit as a branching process, for which critical properties can be analysed. Far from the critical point a set of differential equations may be used to model the process, and these are solved by numerical integration and exact bounding methods. The multi-access channel problem is formulated as an equilibrium statistical physics problem for the case of bit transmission on a channel with power control and synchronisation. A sparse code division multiple access method is considered and the optimal detection properties are examined in typical case by use of the replica method, and compared to detection performance achieved by interactive decoding methods. These codes are found to have phenomena closely resembling the well-understood dense codes. The composite model is introduced as an abstraction of canonical sparse and dense disordered spin models. The model includes couplings due to both dense and sparse topologies simultaneously. The new type of codes are shown to outperform sparse and dense codes in some regimes both in optimal performance, and in performance achieved by iterative detection methods in finite systems.

Pair breaking and bound states in disordered superconductors

We study the effects of inhomogeneous pairing interactions and impurities in short-coherence-length superconductors. Within the Born approximation, the effects of pairing disorder and magnetic impurities are identical. The T-matrices for pairing disorder sites with and without an impurity give rise to bound states within the BCS (Bardeen-Cooper-Schrieffer) gap, consistent with scanning tunnelling microscopy results on Bi2Sr2CaCu2O8+δ with Zn or Ni impurities.

A branch and efficiency algorithm for the optimal design of supply chain networks

Supply chain operations directly affect service levels. Decision on amendment of facilities is generally decided based on overall cost, leaving out the efficiency of each unit. Decomposing the supply chain superstructure, efficiency analysis of the facilities (warehouses or distribution centers) that serve customers can be easily implemented. With the proposed algorithm, the selection of a facility is based on service level maximization and not just cost minimization as this analysis filters all the feasible solutions utilizing Data Envelopment Analysis (DEA) technique. Through multiple iterations, solutions are filtered via DEA and only the efficient ones are selected leading to cost minimization. In this work, the problem of optimal supply chain networks design is addressed based on a DEA based algorithm. A Branch and Efficiency (B&E) algorithm is deployed for the solution of this problem. Based on this DEA approach, each solution (potentially installed warehouse, plant etc) is treated as a Decision Making Unit, thus is characterized by inputs and outputs. The algorithm through additional constraints named “efficiency cuts”, selects only efficient solutions providing better objective function values. The applicability of the proposed algorithm is demonstrated through illustrative examples.

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.

A methodology for analysis and control of discrete event dynamic systems

The rapid developments in computer technology have resulted in a widespread use of discrete event dynamic systems (DEDSs). This type of system is complex because it exhibits properties such as concurrency, conflict and non-determinism. It is therefore important to model and analyse such systems before implementation to ensure safe, deadlock free and optimal operation. This thesis investigates current modelling techniques and describes Petri net theory in more detail. It reviews top down, bottom up and hybrid Petri net synthesis techniques that are used to model large systems and introduces on object oriented methodology to enable modelling of larger and more complex systems. Designs obtained by this methodology are modular, easy to understand and allow re-use of designs. Control is the next logical step in the design process. This thesis reviews recent developments in control DEDSs and investigates the use of Petri nets in the design of supervisory controllers. The scheduling of exclusive use of resources is investigated and an efficient Petri net based scheduling algorithm is designed and a re-configurable controller is proposed. To enable the analysis and control of large and complex DEDSs, an object oriented C++ software tool kit was developed and used to implement a Petri net analysis tool, Petri net scheduling and control algorithms. Finally, the methodology was applied to two industrial DEDSs: a prototype can sorting machine developed by Eurotherm Controls Ltd., and a semiconductor testing plant belonging to SGS Thomson Microelectronics Ltd.

Pragmatic algorithms for implementing geostatistics with large datasets

With the ability to collect and store increasingly large datasets on modern computers comes the need to be able to process the data in a way that can be useful to a Geostatistician or application scientist. Although the storage requirements only scale linearly with the number of observations in the dataset, the computational complexity in terms of memory and speed, scale quadratically and cubically respectively for likelihood-based Geostatistics. Various methods have been proposed and are extensively used in an attempt to overcome these complexity issues. This thesis introduces a number of principled techniques for treating large datasets with an emphasis on three main areas: reduced complexity covariance matrices, sparsity in the covariance matrix and parallel algorithms for distributed computation. These techniques are presented individually, but it is also shown how they can be combined to produce techniques for further improving computational efficiency.

Classification and contextual enhancement of remotely sensed data

The aims of the project were twofold: 1) To investigate classification procedures for remotely sensed digital data, in order to develop modifications to existing algorithms and propose novel classification procedures; and 2) To investigate and develop algorithms for contextual enhancement of classified imagery in order to increase classification accuracy. The following classifiers were examined: box, decision tree, minimum distance, maximum likelihood. In addition to these the following algorithms were developed during the course of the research: deviant distance, look up table and an automated decision tree classifier using expert systems technology. Clustering techniques for unsupervised classification were also investigated. Contextual enhancements investigated were: mode filters, small area replacement and Wharton's CONAN algorithm. Additionally methods for noise and edge based declassification and contextual reclassification, non-probabilitic relaxation and relaxation based on Markov chain theory were developed. The advantages of per-field classifiers and Geographical Information Systems were investigated. The conclusions presented suggest suitable combinations of classifier and contextual enhancement, given user accuracy requirements and time constraints. These were then tested for validity using a different data set. A brief examination of the utility of the recommended contextual algorithms for reducing the effects of data noise was also carried out.

Variability of the permetric response in normals and in glaucoma

This study investigated the variability of response associated with various perimetric techniques, with the aim of improving the clinical interpretation of automated static threshold perirnetry. Evaluation of a third generation of perimetric threshold algorithms (SITA) demonstrated a reduction in test duration by approximately 50% both in normal subjects and in glaucoma patients. SITA produced a slightly higher, but clinically insignificant, Mean Sensitivity than with the previous generations of algorithms. This was associated with a decreased between-subject variability in sensitivity and hence, lower confidence intervals for normality. In glaucoma, the SITA algorithms gave rise to more statistically significant visual field defects and a similar between-visit repeatability to the Full Threshold and FASTPAC algorithms. The higher estimated sensitivity observed with SITA compared to Full Threshold and FASTPAC were not attributed to a reduction in the fatigue effect. The investigation of a novel method of maintaining patient fixation, a roving fixation target which paused immediately prior lo the stimulus presentation, revealed a greater degree of fixational instability with the roving fixation target compared to the conventional static fixation target. Previous experience with traditional white-white perimetry did not eradicate the learning effect in short-wavelength automated perimetry (SWAP) in a group of ocular hypertensive patients. The learning effect was smaller in an experienced group of patients compared to a naive group of patients, but was still at a significant level to require that patients should undertake a series of at least three familiarisation tests with SWAP.

INTAMAP: the design and implementation of an interoperable automated interpolation web service

INTAMAP is a Web Processing Service for the automatic spatial interpolation of measured point data. Requirements were (i) using open standards for spatial data such as developed in the context of the Open Geospatial Consortium (OGC), (ii) using a suitable environment for statistical modelling and computation, and (iii) producing an integrated, open source solution. The system couples an open-source Web Processing Service (developed by 52°North), accepting data in the form of standardised XML documents (conforming to the OGC Observations and Measurements standard) with a computing back-end realised in the R statistical environment. The probability distribution of interpolation errors is encoded with UncertML, a markup language designed to encode uncertain data. Automatic interpolation needs to be useful for a wide range of applications and the algorithms have been designed to cope with anisotropy, extreme values, and data with known error distributions. Besides a fully automatic mode, the system can be used with different levels of user control over the interpolation process.

A soft-computing-based method for the automatic discovery of fuzzy rules in databases:uses for academic research and management support in marketing

The study here highlights the potential that analytical methods based on Knowledge Discovery in Databases (KDD) methodologies have to aid both the resolution of unstructured marketing/business problems and the process of scholarly knowledge discovery. The authors present and discuss the application of KDD in these situations prior to the presentation of an analytical method based on fuzzy logic and evolutionary algorithms, developed to analyze marketing databases and uncover relationships among variables. A detailed implementation on a pre-existing data set illustrates the method. © 2012 Published by Elsevier Inc.

Nonlinear speech analysis algorithms mapped to a standard metric achieve clinically useful quantification of average Parkinson's disease symptom severity

The standard reference clinical score quantifying average Parkinson's disease (PD) symptom severity is the Unified Parkinson's Disease Rating Scale (UPDRS). At present, UPDRS is determined by the subjective clinical evaluation of the patient's ability to adequately cope with a range of tasks. In this study, we extend recent findings that UPDRS can be objectively assessed to clinically useful accuracy using simple, self-administered speech tests, without requiring the patient's physical presence in the clinic. We apply a wide range of known speech signal processing algorithms to a large database (approx. 6000 recordings from 42 PD patients, recruited to a six-month, multi-centre trial) and propose a number of novel, nonlinear signal processing algorithms which reveal pathological characteristics in PD more accurately than existing approaches. Robust feature selection algorithms select the optimal subset of these algorithms, which is fed into non-parametric regression and classification algorithms, mapping the signal processing algorithm outputs to UPDRS. We demonstrate rapid, accurate replication of the UPDRS assessment with clinically useful accuracy (about 2 UPDRS points difference from the clinicians' estimates, p < 0.001). This study supports the viability of frequent, remote, cost-effective, objective, accurate UPDRS telemonitoring based on self-administered speech tests. This technology could facilitate large-scale clinical trials into novel PD treatments.

Nonlinear pulse shaping and polarization dynamics in mode-locked fibre lasers

We review our recent progress on the study of new nonlinear mechanisms of pulse shaping in passively mode-locked fibre lasers. These include a mode-locking regime featuring pulses with a triangular distribution of the intensity, and spectral compression arising from nonlinear pulse propagation. We also report on our recent experimental studies unveiling new families of vector solitons with precessing states of polarization for multipulsing and bound-state soliton operations in a carbon nanotube mode-locked fibre laser with anomalous dispersion cavity. © 2013 IEEE.

Adaptive resource allocation for multicast orthogonal frequency division multiple access systems with guaranteed BER and rate

In this paper, we propose a resource allocation scheme to minimize transmit power for multicast orthogonal frequency division multiple access systems. The proposed scheme allows users to have different symbol error rate (SER) across subcarriers and guarantees an average bit error rate and transmission rate for all users. We first provide an algorithm to determine the optimal bits and target SER on subcarriers. Because the worst-case complexity of the optimal algorithm is exponential, we further propose a suboptimal algorithm that separately assigns bit and adjusts SER with a lower complexity. Numerical results show that the proposed algorithm can effectively improve the performance of multicast orthogonal frequency division multiple access systems and that the performance of the suboptimal algorithm is close to that of the optimal one. Copyright © 2012 John Wiley & Sons, Ltd. This paper proposes optimal and suboptimal algorithms for minimizing transmitting power of multicast orthogonal frequency division multiple access systems with guaranteed average bit error rate and data rate requirement. The proposed scheme allows users to have different symbol error rate across subcarriers and guarantees an average bit error rate and transmission rate for all users. Copyright © 2012 John Wiley & Sons, Ltd.

Nonlinear pulse shaping and polarization dynamics in mode-locked fibre lasers

We review our recent progress on the study of new nonlinear mechanisms of pulse shaping in passively mode-locked fibre lasers. These include a mode-locking regime featuring pulses with a triangular distribution of the intensity, and spectral compression arising from nonlinear pulse propagation. We also report on our recent experimental studies unveiling new families of vector solitons with precessing states of polarization for multipulsing and bound-state soliton operations in a carbon nanotube mode-locked fibre laser with anomalous dispersion cavity. © 2013 IEEE.