Description and critical appraisal of principal components analysis (PCA) methodology applied to pulsed-field gel electrophoresis profiles of methicillin-resistant Staphylococcus aureus isolates

Principal components analysis (PCA) has been described for over 50 years; however, it is rarely applied to the analysis of epidemiological data. In this study PCA was critically appraised in its ability to reveal relationships between pulsed-field gel electrophoresis (PFGE) profiles of methicillin- resistant Staphylococcus aureus (MRSA) in comparison to the more commonly employed cluster analysis and representation by dendrograms. The PFGE type following SmaI chromosomal digest was determined for 44 multidrug-resistant hospital-acquired methicillin-resistant S. aureus (MR-HA-MRSA) isolates, two multidrug-resistant community-acquired MRSA (MR-CA-MRSA), 50 hospital-acquired MRSA (HA-MRSA) isolates (from the University Hospital Birmingham, NHS Trust, UK) and 34 community-acquired MRSA (CA-MRSA) isolates (from general practitioners in Birmingham, UK). Strain relatedness was determined using Dice band-matching with UPGMA clustering and PCA. The results indicated that PCA revealed relationships between MRSA strains, which were more strongly correlated with known epidemiology, most likely because, unlike cluster analysis, PCA does not have the constraint of generating a hierarchic classification. In addition, PCA provides the opportunity for further analysis to identify key polymorphic bands within complex genotypic profiles, which is not always possible with dendrograms. Here we provide a detailed description of a PCA method for the analysis of PFGE profiles to complement further the epidemiological study of infectious disease. © 2005 Elsevier B.V. All rights reserved.

Increasing the rigour and trustworthiness of participatory evaluations : learnings from the field

Participatory evaluation and participatory action research (PAR) are increasingly used in community-based programs and initiatives and there is a growing acknowledgement of their value. These methodologies focus more on knowledge generated and constructed through lived experience than through social science (Vanderplaat 1995). The scientific ideal of objectivity is usually rejected in favour of a holistic approach that acknowledges and takes into account the diverse perspectives, values and interpretations of participants and evaluation professionals. However, evaluation rigour need not be lost in this approach. Increasing the rigour and trustworthiness of participatory evaluations and PAR increases the likelihood that results are seen as credible and are used to continually improve programs and policies.----- Drawing on learnings and critical reflections about the use of feminist and participatory forms of evaluation and PAR over a 10-year period, significant sources of rigour identified include:----- • participation and communication methods that develop relations of mutual trust and open communication----- • using multiple theories and methodologies, multiple sources of data, and multiple methods of data collection----- • ongoing meta-evaluation and critical reflection----- • critically assessing the intended and unintended impacts of evaluations, using relevant theoretical models----- • using rigorous data analysis and reporting processes----- • participant reviews of evaluation case studies, impact assessments and reports.

Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion

Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A^(-α/2)b, where A ∈ ℝ^(n×n) is a large, sparse symmetric positive definite matrix and b ∈ ℝ^n is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LL^T is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L^(-T)z, with x = A^(-1/2)z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form ϕn = A^(-α/2)b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t^(-α/2) and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A^(-α/2)b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.

Temperature and electric field dependent mobility in poly„3-hexylthiophene diodes

Current-voltage (I-V) curves of Poly(3-hexyl-thiophene) (P3HT) diodes have been collected to investigate the polymer hole-dominated charge transport. At room temperature and at low electric fields the I-V characteristic is purely Ohmic whereas at medium-high electric fields, experimental data shows that the hole transport is Trap Dominated - Space Charge Limited Current (TD-SCLC). In this regime, it is possible to extract the I-V characteristic of the P3HT/Al junction showing the ideal Schottky diode behaviour over five orders of magnitude. At high-applied electric fields, holes’ transport is found to be in the trap free SCLC regime. We have measured and modelled in this regime the holes’ mobility to evaluate its dependence from the electric field applied and the temperature of the device.

Applied batch cryptography

The material presented in this thesis may be viewed as comprising two key parts, the first part concerns batch cryptography specifically, whilst the second deals with how this form of cryptography may be applied to security related applications such as electronic cash for improving efficiency of the protocols. The objective of batch cryptography is to devise more efficient primitive cryptographic protocols. In general, these primitives make use of some property such as homomorphism to perform a computationally expensive operation on a collective input set. The idea is to amortise an expensive operation, such as modular exponentiation, over the input. Most of the research work in this field has concentrated on its employment as a batch verifier of digital signatures. It is shown that several new attacks may be launched against these published schemes as some weaknesses are exposed. Another common use of batch cryptography is the simultaneous generation of digital signatures. There is significantly less previous work on this area, and the present schemes have some limited use in practical applications. Several new batch signatures schemes are introduced that improve upon the existing techniques and some practical uses are illustrated. Electronic cash is a technology that demands complex protocols in order to furnish several security properties. These typically include anonymity, traceability of a double spender, and off-line payment features. Presently, the most efficient schemes make use of coin divisibility to withdraw one large financial amount that may be progressively spent with one or more merchants. Several new cash schemes are introduced here that make use of batch cryptography for improving the withdrawal, payment, and deposit of electronic coins. The devised schemes apply both to the batch signature and verification techniques introduced, demonstrating improved performance over the contemporary divisible based structures. The solutions also provide an alternative paradigm for the construction of electronic cash systems. Whilst electronic cash is used as the vehicle for demonstrating the relevance of batch cryptography to security related applications, the applicability of the techniques introduced extends well beyond this.

Correcting mean-field approximations for birth-death-movement processes

On the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of spatial correlations and can have a negative impact upon population growth. Usually, such effects are neglected in modeling studies and simple phenomenological descriptions, such as the logistic model, are used to model population growth. In this work we outline some methods for analyzing exclusion processes which include agent proliferation, death and motility in two and three spatial dimensions with spatially homogeneous initial conditions. The mean-field description for these types of processes is of logistic form; we show that, under certain parameter conditions, such systems may display large deviations from the mean field, and suggest computationally tractable methods to correct the logistic-type description.

Corrected mean-field models for spatially-dependent advection-diffusion-reaction phenomena

In the exclusion-process literature, mean-field models are often derived by assuming that the occupancy status of lattice sites is independent. Although this assumption is questionable, it is the foundation of many mean-field models. In this work we develop methods to relax the independence assumption for a range of discrete exclusion process-based mechanisms motivated by applications from cell biology. Previous investigations that focussed on relaxing the independence assumption have been limited to studying initially-uniform populations and ignored any spatial variations. By ignoring spatial variations these previous studies were greatly simplified due to translational invariance of the lattice. These previous corrected mean-field models could not be applied to many important problems in cell biology such as invasion waves of cells that are characterised by moving fronts. Here we propose generalised methods that relax the independence assumption for spatially inhomogeneous problems, leading to corrected mean-field descriptions of a range of exclusion process-based models that incorporate (i) unbiased motility, (ii) biased motility, and (iii) unbiased motility with agent birth and death processes. The corrected mean-field models derived here are applicable to spatially variable processes including invasion wave type problems. We show that there can be large deviations between simulation data and traditional mean-field models based on invoking the independence assumption. Furthermore, we show that the corrected mean-field models give an improved match to the simulation data in all cases considered.