Numerical implementation of the Manakov-PMD equation with precomputed M(Ω) matrices

The Manakov-PMD equation can be integrated with the same numerical efficiency as the coarse-step method by using precomputed M(Ω) matrices, which entirely avoids the somewhat ad-hoc rescaling of coefficients necessary in the coarse-step method.

Typical kernel size and number of sparse random matrices over Galois fields: a statistical physics approach

Using methods of statistical physics, we study the average number and kernel size of general sparse random matrices over GF(q), with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q-th complex roots of unity. This representation facilitates the derivation of the average kernel size of random matrices using the replica approach, under the replica symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average number of random matrices for any general connectivity profile. We present numerical results for particular distributions.

Properties of sparse random matrices over finite fields

Typical properties of sparse random matrices over finite (Galois) fields are studied, in the limit of large matrices, using techniques from the physics of disordered systems. For the case of a finite field GF(q) with prime order q, we present results for the average kernel dimension, average dimension of the eigenvector spaces and the distribution of the eigenvalues. The number of matrices for a given distribution of entries is also calculated for the general case. The significance of these results to error-correcting codes and random graphs is also discussed.

Genotypic and phenotypic properties of coagulase-negative staphylococci causing dialysis catheter-related sepsis

Sixty coagulase-negative staphylococcus (CNS) isolates were recovered from the blood cultures or peritoneal dialysate effluent of 43 patients on renal dialysis. The patients had either renal dialysis catheter-related sepsis (CRS) or continuous ambulatory peritoneal dialysis (CAPD)-associated peritonitis. Isolates were characterized by biotyping, and genotyped by pulsed-field gel electrophoresis (PFGE). Phenotypic properties of the strains were also investigated. Several genotypes were identified with no one specific strain of CNS being associated with CRS. However, closely related strains were isolated from several patients within the units studied, suggesting horizontal transfer of micro-organisms. Genotypic macro-restriction profiles did not concur with phenotypic profiles or biotypes, confirming that genotyping is required for epidemiological studies. All staphylococcal strains were investigated for the production of phenotypic characteristics. Significant differences were predominantly seen in the production of lipase, esterase and elastase in strains isolated from the renal patients with CRS and CAPD-associated peritonitis, compared with a non-septic control group. These phenotypic characteristics may therefore have a role in the maintenance of CRS in renal patients. © 2003 The Hospital Infection Society. Published by Elsevier Science Ltd. All rights reserved.

Phenotypic and genotypic characterisation of Clostrum Difficile

Clostridium difficile is at present one of the most common nosocomial infections in the developed world. Hypervirulent strains (PCR ribotype 027) of C. difficile which produce enhanced levels of toxins have also been associated with other characteristics such as a greater rate of sporulation and resistance to fluoroquinolones. Infection due to C. difficile PCR ribotype 027 has also been associated with greater rates of morbidity and mortality. The aim of this thesis was to investigate both the phenotypic and genotypic characteristics of two populations of toxigenic clinical isolates of C. difficile which were recovered from two separate hospital trusts within the UK. Phenotypic characterisation of the isolates was undertaken using analytical profile indexes (APIs), minimum inhibitory concentrations(MICs) and S-layer protein typing. In addition to this, isolates were also investigated for the production of a range of extracellular enzymes as potential virulence factors. Genotypic characterisation was performed using a random amplification of polymorphic DNA(RAPD) PCR protocol which was fully optimised in this study, and the gold standard method, PCR ribotyping. The discriminatory power of both methods was compared and the similarity between the different isolates also analysed. Associations between the phenotypic and genotypic characteristics and the recovery location of the isolate were then investigated. Extracellular enzyme production and API testing revealed little variation between the isolates; with S-layer typing demonstrating low discrimination. Minimum inhibitory concentrations did not identify any resistance towards either vancomycin or metronidazole; there were however significant differences in the distribution of antibiogram profiles of isolates recovered from the two different trusts. The RAPD PCR protocol was successfully optimised and alongside PCR ribotyping, effectively typed all of the clinical isolates and also identified differences in the number of types defined between the two locations. Both PCR ribotyping and RAPD demonstrated similar discriminatory power; however, the two genotyping methods did not generate amplicons that mapped directly onto each other and therefore clearly characterised isolates based on different genomic markers. The RAPD protocol also identified different subtypes within PCR ribotypes, therefore demonstrating that all isolates defined as a particular PCR ribotype were not the same strain. No associations could be demonstrated between the phenotypic and genotypic characteristics observed; however, the location from which an isolate was recovered did appear to influence antibiotic resistance and genotypic characteristics. The phenotypic and genotypic characteristics observed amongst the C. difficile isolates in this study, may provide a basis for the identification of further targets which may be potentially incorporated into future methods for the characterisation of C. difficile isolates.

Modified hydrogel matrices in fibre optic sensors

Common problems encountered in clinical sensing are those of non-biocompatibility, and slow response time of the device. The latter, also applying to chemical sensors, is possibly due to a lack of understanding of polymer support or membrane properties and hence failure to optimise membranes chosen for specific sensor applications. Hydrogels can be described as polymers which swell in water. In addition to this, the presence of water in the polymer matrix offers some control of biocompatibility. They thus provide a medium through which rapid transport of a sensed species to an incorporated reagent could occur. This work considers the feasibility of such a system, leading to the design and construction of an optical sensor test bed. The development of suitable membrane systems and of suitable coating techniques in order to apply them to the fibre optics is described. Initial results obtained from hydrogel coatings implied that the refractive index change in the polymer matrix, due to a change in water content with pH is the major factor contributing to the sensor response. However the presence of the colourimetric reagent was also altering the output signal obtained. An analysis of factors contributing to the overall response, such as colour change and membrane composition were made on both the test bed, via optical response, and on whole membranes via measurement of water content change. The investigation of coatings with low equilibrium water contents, of less than 10% was carried out and in fact a clearer signal response from the test bed was noted. Again these membranes were suprisingly responding via refractive index change, with the reagent playing a primary role in obtaining a sensible or non-random response, although not in a colourimetric fashion. A photographic study of these coatings revealed some clues as to the physical nature of these coatings and hence partially explained this phenomenon. A study of the transport properties of the most successful membrane, on a coated wire electrode and also on the fibre optic test bed, in a series of test environments, indicated that the reagent was possibly acting as an ion exchanger and hence having a major influence on transport and therefore sensor characteristics.

Phenotypic and genotypic analysis of intestinal spirochacies

Pulsed field gel electrophoresis of 82 intestinal spirochaete isolates showed specific differentiation of Serpulina pilosicoli and Serpulina hyodysenteriae although considerable heterogeneity was observed, especially amongst S. pilosicoli isolates. In several cases genotypically similar isolates originated from different animals suggesting that cross-species transmission may have occurred. The Caco-2 and Caco-21HT29 cell models have been proposed as potentially realistic models of intestinal infection. Quantitation of adhesion to the cells showed isolate 3 82/91 (from a bacteraemia) to adhere at significantly greater numbers than any other isolate tested. This isolate produced a PFGE profile which differed from other S. pilosicoli isolates and so would be of interest for further study. Comparison of bacteraemic and other S. pilosicoli isolates suggested that bacteraemic isolates were not more specifically adapted for adhesion to, or invasion of the epithelial cell layer than other S. pilosicoli isolates. Genotypically similar isolates from differing animal origins adhered to the Caco-2 model at similar levels. Generation of a random genomic library of S. pilosicoli and screening with species specific monoclonal antibody has enabled the identification of a gene sequence encoding a protein which showed significant homology with an ancestral form of the enzyme pyruvate oxidoreductase. Immunoscreening with polyclonal serum identified the sequences of two gene clusters and a probable arylsulphatase. One gene cluster represented a ribosomal gene cluster which has a similar molecular arrangement to Borrelia burgdorjeri, Treponema pallidum and Thermatoga maritima. The other gene cluster contained an ABC transporter protein, sorbitol dehydrogenase and phosphomannose isomerase. An ELISA type assay was used to demonstrate that isolates of S. pilosicoli could adhere to components of the extracellular matrix such as collagen (type 1), fibronectin, laminin, and porcine gastric mucin.

Meta-analysis of the population and phenotypic expression of CYP2C9/2C19 polymorphism on drug metabolism in different ethnicities

The term "pharmacogenetics" has been defined as the scientific study of inherited factors that affect the human drug response. Many pharmacogenetie studies have been published since 1995 and have focussed on the principal enzyme family involved in drug metabolism, the cytochrome P450 family, particularly cytochrome P4502C9 and 2C19. In order to investigate the pharmacogenetic aspect of pharmacotherapy, the relevant studies describing the association of pharmacogenetic factor(s) in drug responses must be retrieved from existing literature using a systematic review approach. In addition, the estimation of variant allele prevalence for the gene under study between different ethnic populations is important for pharmacogenetic studies. In this thesis, the prevalence of CYP2C9/2C19 alleles between different ethnicities has been estimated through meta-analysis and the population genetic principle. The clinical outcome of CYP2C9/2C19 allelic variation on the pharmacotherapy of epilepsy has been investigated; although many new antiepileptic drugs have been launched into the market, carbamazepine, phenobarbital and phenytoin are still the major agents in the pharmacotherapy of epilepsy. Therefore, phenytoin was chosen as a model AED and the effect of CYP2C9/2C19 genetic polymorphism on phenytoin metabolism was further examined.An estimation of the allele prevalence was undertaken for three CYP2C9/2C19 alleles respectively using a meta-analysis of studies that fit the Hardy-Weinberg equilibrium. The prevalence of CYP2C9*1 is approximately 81%, 96%, 97% and 94% in Caucasian, Chinese, Japanese, African populations respectively; the pooled prevalence of CYP2C19*1 is about 86%, 57%, 58% and 85% in these ethnic populations respectively. However, the studies of association between CYP2C9/2C19 polymorphism and phenytoin metabolism failed to achieve any qualitative or quantitative conclusion. Therefore, mephenytoin metabolism was examined as a probe drug for association between CYP2C19 polymorphism and mephenytoin metabolic ratio. Similarly, analysis of association between CYP2C9 polymorphism and warfarin dose requirement was undertaken.It was confirmed that subjects carrying two mutated CYP2C19 alleles have higher S/R mephenytoin ratio due to deficient CYP2C19 enzyme activity. The studies of warfarin and CYP2C9 polymorphism did not provide a conclusive result due to poor comparability between studies.The genetic polymorphism of drug metabolism enzymes has been studied extensively, however other genetic factors, such as multiple drug resistance genes (MDR) and genes encoding ion channels, which may contribute to variability in function of drug transporters and targets, require more attention in future pharmacogenetic studies of antiepileptic drugs.

Drug/Water interactions in hydrogel matrices

The primary aim of this research has been the investigation of the role of water structuring effects in the widely different extents of irritancy displayed by certain antibiotics. The compounds involved were members of the Lincomycin group of antibiotics. The aqueous solution behaviour of these co~pounds was studied using techniques such as vapour pressure osmometry end differential scanning calorimetry (D.S.C.). The effects of the antibiotics on water structure in hydrogel membrane preparations In which the equilibrium water content (E.W.C.) and constituent amounts of freezing and non-freezing water ware varied were also investigated using D.S.C. The permeability of water swollen hydrogel preparations to aqueous antibiotic solutions as well as other solutes were studied. A series of hydrogel preparations into which the antibiotics had been incorporated during polymerisation were developed and used in studies of the effects of the antibiotics end their water structure modifications on the permeation of a range of solutes.

The controlled release of macromolecules from macroporous hydrophyllic polymer matrices

This work has used novel polymer design and fabrication technology to generate bead form polymer based systems, with variable, yet controlled release properties, specifically for the delivery of macromolecules, essentially peptides of therapeutic interest. The work involved investigation of the potential interaction between matrix ultrastructural morphology, in vitro release kinetics, bioactivity and immunoreactivity of selected macromolecules with limited hydrolytic stability, delivered from controlled release vehicles. The underlying principle involved photo-polymerisation of the monomer, hydroxyethyl methacrylate, around frozen ice crystals, leading to the production of a macroporous hydrophilic matrix. Bead form matrices were fabricated in controllable size ranges in the region of 100µm - 3mm in diameter. The initial stages of the project involved the study of how variables, delivery speed of the monomer and stirring speed of the non solvent, affectedthe formation of macroporous bead form matrices. From this an optimal bench system for bead production was developed. Careful selection of monomer, solvents, crosslinking agent and polymerisation conditions led to a variable but controllable distribution of pore sizes (0.5 - 4µm). Release of surrogate macromolecules, bovine serum albumin and FITC-linked dextrans, enabled factors relating to the size and solubility of the macromolecule on the rate of release to be studied. Incorporation of bioactive macromolecules allowed retained bioactivity to be determined (glucose oxidase and interleukin-2), whilst the release of insulin enabled determination of both bioactivity (using rat epididymal fat pad) and immunoreactivity (RIA). The work carried out has led to the generation of macroporous bead form matrices, fabricated from a tissue biocompatible hydrogel, capable of the sustained, controlled release of biologically active peptides, with potential use in the pharmaceutical and agrochemical industries.

The durability of glass fibre reinforced cements made with new cementitious matrices

Widespread use of glass fibre reinforced cement (GRC) has been impeded by concerns over its durability. Three degradation mechanisms are proposed - fibre corrosion, Ca(OHh precipitation and matrix densification - although their relative importance is debated. Matrices with reduced alkalinities and Ca(OH)2 contents are being developed; the aim of this study was to investigate their hydration and interaction with alkali-resistant fibres to determine the factors controlling their long-term durability, and assess the relevancy of accelerated ageing. The matrices studied were: OPC/calcium-sulphoaluminate cement plus metakaolin (C); OPC plus metakaolin (M); blast-furnace slag cement plus a micro-silica based additive (D); and OPC (O). Accelerated ageing included hot water and cyclic regimes prior to tensile testing. Investigations included pore solution expression, XRD, DTA/TG, SEM and optical petrography. Bond strength was determined from crack spacings using microstructural parameters obtained from a unique image analysis technique. It was found that, for the new matrices - pore solution alkalinities were lower; Ca(OH)2 was absent or quickly consumed; different hydrates were formed at higher immersion temperatures; degradation under 65°C immersion was an order of magnitude slower, and no interfilamental Ca(OH)2 was observed .It was concluded that: fibre weakening caused by flaw growth was the primary degradation mechanism and was successfully modelled on stress corrosion/static fatigue principles. OPC inferiority was attributed partly to its higher alkalinity but chiefly to the growth of Ca(OH)2 aggravating the degradation; and hot water ageing although useful in model formulation and contrasting the matrices, changed the intrinsic nature of the composites rather than simply accelerating the degradation mechanisms.

Spectra of modular and small-world matrices

We compute spectra of symmetric random matrices describing graphs with general modular structure and arbitrary inter- and intra-module degree distributions, subject only to the constraint of finite mean connectivities. We also evaluate spectra of a certain class of small-world matrices generated from random graphs by introducing shortcuts via additional random connectivity components. Both adjacency matrices and the associated graph Laplacians are investigated. For the Laplacians, we find Lifshitz-type singular behaviour of the spectral density in a localized region of small |?| values. In the case of modular networks, we can identify contributions of local densities of state from individual modules. For small-world networks, we find that the introduction of short cuts can lead to the creation of satellite bands outside the central band of extended states, exhibiting only localized states in the band gaps. Results for the ensemble in the thermodynamic limit are in excellent agreement with those obtained via a cavity approach for large finite single instances, and with direct diagonalization results.

Statnote 31:analysis of covariance

Analysis of covariance (ANCOVA) is a useful method of ‘error control’, i.e., it can reduce the size of the error variance in an experimental or observational study. An initial measure obtained before the experiment, which is closely related to the final measurement, is used to adjust the final measurements, thus reducing the error variance. When this method is used to reduce the error term, the X variable must not itself be affected by the experimental treatments, because part of the treatment effect would then also be removed. Hence, the method can only be safely used when X is measured before an experiment. A further limitation of the analysis is that only the linear effect of Y on X is being removed and it is possible that Y could be a curvilinear function of X. A question often raised is whether ANCOVA should be used routinely in experiments rather than a randomized blocks or split-plot design, which may also reduce the error variance. The answer to this question depends on the relative precision of the difference methods with reference to each scenario. Considerable judgment is often required to select the best experimental design and statistical help should be sought at an early stage of an investigation.