Mathematical and numerical modelling of dispersion-managed solitons, autosolitons and self-similar optical pulses

This thesis presents theoretical investigation of three topics concerned with nonlinear optical pulse propagation in optical fibres. The techniques used are mathematical analysis and numerical modelling. Firstly, dispersion-managed (DM) solitons in fibre lines employing a weak dispersion map are analysed by means of a perturbation approach. In the case of small dispersion map strengths the average pulse dynamics is described by a perturbation approach (NLS) equation. Applying a perturbation theory, based on the Inverse Scattering Transform method, an analytic expression for the envelope of the DM soliton is derived. This expression correctly predicts the power enhancement arising from the dispersion management.Secondly, autosoliton transmission in DM fibre systems with periodical in-line deployment of nonlinear optical loop mirrors (NOLMs) is investigated. The use of in-line NOLMs is addressed as a general technique for all-optical passive 2R regeneration of return-to-zero data in high speed transmission system with strong dispersion management. By system optimisation, the feasibility of ultra-long single-channel and wavelength-division multiplexed data transmission at bit-rates ³ 40 Gbit s-1 in standard fibre-based systems is demonstrated. The tolerance limits of the results are defined.Thirdly, solutions of the NLS equation with gain and normal dispersion, that describes optical pulse propagation in an amplifying medium, are examined. A self-similar parabolic solution in the energy-containing core of the pulse is matched through Painlevé functions to the linear low-amplitude tails. The analysis provides a full description of the features of high-power pulses generated in an amplifying medium.

Numerical and statistical analysis of long-haul undersea optical communication systems

Firstly, we numerically model a practical 20 Gb/s undersea configuration employing the Return-to-Zero Differential Phase Shift Keying data format. The modelling is completed using the Split-Step Fourier Method to solve the Generalised Nonlinear Schrdinger Equation. We optimise the dispersion map and per-channel launch power of these channels and investigate how the choice of pre/post compensation can influence the performance. After obtaining these optimal configurations, we investigate the Bit Error Rate estimation of these systems and we see that estimation based on Gaussian electrical current systems is appropriate for systems of this type, indicating quasi-linear behaviour. The introduction of narrower pulses due to the deployment of quasi-linear transmission decreases the tolerance to chromatic dispersion and intra-channel nonlinearity. We used tools from Mathematical Statistics to study the behaviour of these channels in order to develop new methods to estimate Bit Error Rate. In the final section, we consider the estimation of Eye Closure Penalty, a popular measure of signal distortion. Using a numerical example and assuming the symmetry of eye closure, we see that we can simply estimate Eye Closure Penalty using Gaussian statistics. We also see that the statistics of the logical ones dominates the statistics of the logical ones dominates the statistics of signal distortion in the case of Return-to-Zero On-Off Keying configurations.

New oil modified acrylic polymer for pH sensitive drug release:experimental results and statistical analysis

We report results of an experimental study, complemented by detailed statistical analysis of the experimental data, on the development of a more effective control method of drug delivery using a pH sensitive acrylic polymer. New copolymers based on acrylic acid and fatty acid are constructed from dodecyl castor oil and a tercopolymer based on methyl methacrylate, acrylic acid and acryl amide were prepared using this new approach. Water swelling characteristics of fatty acid, acrylic acid copolymer and tercopolymer respectively in acid and alkali solutions have been studied by a step-change method. The antibiotic drug cephalosporin and paracetamol have also been incorporated into the polymer blend through dissolution with the release of the antibiotic drug being evaluated in bacterial stain media and buffer solution. Our results show that the rate of release of paracetamol getss affected by the pH factor and also by the nature of polymer blend. Our experimental data have later been statistically analyzed to quantify the precise nature of polymer decay rates on the pH density of the relevant polymer solvents. The time evolution of the polymer decay rates indicate a marked transition from a linear to a strictly non-linear regime depending on the whether the chosen sample is a general copolymer (linear) or a tercopolymer (non-linear). Non-linear data extrapolation techniques have been used to make probabilistic predictions about the variation in weight percentages of retained polymers at all future times, thereby quantifying the degree of efficacy of the new method of drug delivery.

CDMA multiuser detection, neural networks, and statistical mechanics

A novel approach, based on statistical mechanics, to analyze typical performance of optimum code-division multiple-access (CDMA) multiuser detectors is reviewed. A `black-box' view ot the basic CDMA channel is introduced, based on which the CDMA multiuser detection problem is regarded as a `learning-from-examples' problem of the `binary linear perceptron' in the neural network literature. Adopting Bayes framework, analysis of the performance of the optimum CDMA multiuser detectors is reduced to evaluation of the average of the cumulant generating function of a relevant posterior distribution. The evaluation of the average cumulant generating function is done, based on formal analogy with a similar calculation appearing in the spin glass theory in statistical mechanics, by making use of the replica method, a method developed in the spin glass theory.

Assessing pupil and school performance by non-parametric and parametric techniques

This paper discusses the use of the non-parametric free disposal hull (FDH) and the parametric multi-level model (MLM) as alternative methods for measuring pupil and school attainment where hierarchical structured data are available. Using robust FDH estimates, we show how to decompose the overall inefficiency of a unit (a pupil) into a unit specific and a higher level (a school) component. By a sample of entry and exit attainments of 3017 girls in British ordinary single sex schools, we test the robustness of the non-parametric and parametric estimates. Finally, the paper uses the traditional MLM model in a best practice framework so that pupil and school efficiencies can be computed.

Assessing pupil and school performance by non-parametric and parametric techniques

Often observations are nested within other units. This is particularly the case in the educational sector where school performance in terms of value added is the result of school contribution as well as pupil academic ability and other features relating to the pupil. Traditionally, the literature uses parametric (i.e. it assumes a priori a particular function on the production process) Multi-Level Models to estimate the performance of nested entities. This paper discusses the use of the non-parametric (i.e. without a priori assumptions on the production process) Free Disposal Hull model as an alternative approach. While taking into account contextual characteristics as well as atypical observations, we show how to decompose non-parametrically the overall inefficiency of a pupil into a unit specific and a higher level (i.e. a school) component. By a sample of entry and exit attainments of 3017 girls in British ordinary single sex schools, we test the robustness of the non-parametric and parametric estimates. We find that the two methods agree in the relative measures of the scope for potential attainment improvement. Further, the two methods agree on the variation in pupil attainment and the proportion attributable to pupil and school level.

Immunological and biochemical techniques in the analysis of tear proteins

This study is concerned with the analysis of tear proteins, paying particular attention to the state of the tears (e.g. non-stimulated, reflex, closed), created during sampling, and to assess their interactions with hydrogel contact lenses. The work has involved the use of a variety of biochemical and immunological analytical techniques for the measurement of proteins, (a), in tears, (b), on the contact lens, and (c), in the eluate of extracted lenses. Although a diverse range of tear components may contribute to contact lens spoilation, proteins were of particular interest in this study because of their theoretical potential for producing immunological reactions. Although normal host proteins in their natural state are generally not treated as dangerous or non-self, those which undergo denaturation or suffer a conformational change may provoke an excessive and unnecessary immune response. A novel on-lens cell based assay has been developed and exploited in order to study the role of the ubiquitous cell adhesion glycoprotein, vitronectin, in tears and contact lens wear under various parameters. Vitronectin, whose levels are known to increase in the closed eye environment and shown here to increase during contact lens wear, is an important immunoregulatory protein and may be a prominent marker of inflammatory activity. Immunodiffusion assays were developed and optimised for use in tear analysis, and in a series of subsequent studies used for example in the measurement of albumin, lactoferrin, IgA and IgG. The immunodiffusion assays were then applied in the estimation of the closed eye environment; an environment which has been described as sustaining a state of sub-clinical inflammation. The role and presence of a lesser understood and investigated protein, kininogen, was also estimated, in particular, in relation to contact lens wear. Difficulties arise when attempting to extract proteins from the contact lens in order to examine the individual nature of the proteins involved. These problems were partly alleviated with the use of the on-lens cell assay and a UV spectrophotometry assay, which can analyse the lens surface and bulk respectively, the latter yielding only total protein values. Various lens extraction methods were investigated to remove protein from the lens and the most efficient was employed in the analysis of lens extracts. Counter immunoelectrophoresis, an immunodiffusion assay, was then applied to the analysis of albumin, lactoferrin, IgA and IgG in the resultant eluates.

Biochemical markers and contact lens wear

The project objective was to develop a reliable selection procedure to match contact lens materials with individual wearers by the identification of a biochemical marker for assessment of in-eye performance of contact lenses. There is a need for such a procedure as one of the main reasons for contact lens wearers ceasing wearing contact lenses is poor end of day comfort i.e. the lenses become intolerable to the wearer as the day progresses. The selection of an optimal material for individual wearers has the potential benefit to reduce drop Qut, hence increasing the overall contact lens population, and to improve contact lens comfort for established wearers. Using novel analytical methods and statistical techniques, we were able to investigate the interactions between the composition of the tear film and of the biofilm deposited on the contact lenses and contact lens performance. The investigations were limited to studying the lipid components of the tear film; the lipid layer, which plays a key role in preventing evaporation and stabilising the tear film, has been reported to be significantly thinner and of different mixing characteristics during contact lens wear. Different lipid families were found to influence symptomatology, in vivo tear film structure and stability as well as ocular integrity. Whereas the symptomatology was affected by both the tear film lipid composition and the nature of the lipid deposition, the structure of the tear film and its stability were mainly influenced by the tear film lipid composition. The ocular integrity also appeared to be influenced by the nature of the lipid deposition. Potential markers within the lipid species have been identified and could be applied as follows: When required in order to identify a problematic wearer or to match the contact lens material to the contact lens wearer, tear samples collected by the clinician could be dispatched to an analytical laboratory where lipid analysis could be carried out by HPLC. A colorimetric kit based on the lipid markers could also be developed and used by clinician directly in the practice; such a kit would involve tear sampling and classification according to the colour into "Problem", "Border line" and "Good" contact lens wearers groups. A test kit would also have wider scope for marketing in other areas such as general dry-eye pathology.

Sample size estimation and statistical power analyses

The concept of sample size and statistical power estimation is now something that Optometrists that want to perform research, whether it be in practice or in an academic institution, cannot simply hide away from. Ethics committees, journal editors and grant awarding bodies are now increasingly requesting that all research be backed up with sample size and statistical power estimation in order to justify any study and its findings. This article presents a step-by-step guide of the process for determining sample sizeand statistical power. It builds on statistical concepts presented in earlier articles in Optometry Today by Richard Armstrong and Frank Eperjesi.

A combination of cyclone and vert techniques for the management of construction projects

Many planning and control tools, especially network analysis, have been developed in the last four decades. The majority of them were created in military organization to solve the problem of planning and controlling research and development projects. The original version of the network model (i.e. C.P.M/PERT) was transplanted to the construction industry without the consideration of the special nature and environment of construction projects. It suited the purpose of setting up targets and defining objectives, but it failed in satisfying the requirement of detailed planning and control at the site level. Several analytical and heuristic rules based methods were designed and combined with the structure of C.P.M. to eliminate its deficiencies. None of them provides a complete solution to the problem of resource, time and cost control. VERT was designed to deal with new ventures. It is suitable for project evaluation at the development stage. CYCLONE, on the other hand, is concerned with the design and micro-analysis of the production process. This work introduces an extensive critical review of the available planning techniques and addresses the problem of planning for site operation and control. Based on the outline of the nature of site control, this research developed a simulation based network model which combines part of the logics of both VERT and CYCLONE. Several new nodes were designed to model the availability and flow of resources, the overhead and operating cost and special nodes for evaluating time and cost. A large software package is written to handle the input, the simulation process and the output of the model. This package is designed to be used on any microcomputer using MS-DOS operating system. Data from real life projects were used to demonstrate the capability of the technique. Finally, a set of conclusions are drawn regarding the features and limitations of the proposed model, and recommendations for future work are outlined at the end of this thesis.

Clinical studies of spatial and temporal aspects of vision: an investigation using psychophysical and electrophysiological techniques

Separate physiological mechanisms which respond to spatial and temporal stimulation have been identified in the visual system. Some pathological conditions may selectively affect these mechanisms, offering a unique opportunity to investigate how psychophysical and electrophysiological tests reflect these visual processes, and thus enhance the use of the tests in clinical diagnosis. Amblyopia and optical blur were studied, representing spatial visual defects of neural and optical origin, respectively. Selective defects of the visual pathways were also studied - optic neuritis which affects the optic nerve, and dementia of the Alzheimer type in which the higher association areas are believed to be affected, but the primary projections spared. Seventy control subjects from 10 to 79 years of age were investigated. This provided material for an additional study of the effect of age on the psychophysical and electrophysiological responses. Spatial processing was measured by visual acuity, the contrast sensitivity function, or spatial modulation transfer function (MTF), and the pattern reversal and pattern onset-offset visual evoked potential (VEP). Temporal, or luminance, processing was measured by the de Lange curve, or temporal MTF, and the flash VEP. The pattern VEP was shown to reflect the integrity of the optic nerve, geniculo striate pathway and primary projections, and was related to high temporal frequency processing. The individual components of the flash VEP differed in their characteristics. The results suggested that the P2 component reflects the function of the higher association areas and is related to low temporal frequency processing, while the Pl component reflects the primary projection areas. The combination of a delayed flash P2 component and a normal latency pattern VEP appears to be specific to dementia of the Alzheimer type and represents an important diagnostic test for this condition.

Apparatus and test methods for measuring the impact of golf balls on turf and their application in the field

An apparatus was developed to project spinning golf balls directly onto golf greens. This employed a modified baseball/practice machine with two counter-rotating pneumatic wheels. The speed of the wheels could be varied independently allowing backspin to be given to the ball. The ball was projected into a darkened enclosure where the motion of the ball before and after impacting with the turf was recorded using a still camera and a stroboscope. The resulting photographs contained successive images of the ball on a single frame of film. The apparatus was tested on eighteen golf courses resulting in 721 photographs of impacts. Statistical analysis was carried out on the results of the photographs and from this, two types of green emerged. On the first, the ball tended to rebound with topspin, while on the second, the ball retained backspin after impact if the initial backspin was greater than about 350 rads-1. Eleven tests were devised to determine the characteristics of greens and statistical techniques were used to analyse the relationships between these tests. These showed the effects of the green characteristics on ball/turf impacts. It was found that the ball retained backspin on greens that were freely drained and had less than 60% of Poa annua (annual meadow grass) in their swards. Visco-elastic models were used to simulate the impact of the ball with the turf. Impacts were simulated by considering the ball to be rigid and the turf to be a two layered system consisting of springs and dampers. The model showed good agreement with experiment and was used to simulate impacts from two different shots onto two contrasting types of green.

Quantitative neuropathology:data collection and statistical analysis

The use of quantitative methods has become increasingly important in the study of neuropathology and especially in neurodegenerative disease. Disorders such as Alzheimer's disease (AD) and the frontotemporal dementias (FTD) are characterized by the formation of discrete, microscopic, pathological lesions which play an important role in pathological diagnosis. This chapter reviews the advantages and limitations of the different methods of quantifying pathological lesions in histological sections including estimates of density, frequency, coverage, and the use of semi-quantitative scores. The sampling strategies by which these quantitative measures can be obtained from histological sections, including plot or quadrat sampling, transect sampling, and point-quarter sampling, are described. In addition, data analysis methods commonly used to analysis quantitative data in neuropathology, including analysis of variance (ANOVA), polynomial curve fitting, multiple regression, classification trees, and principal components analysis (PCA), are discussed. These methods are illustrated with reference to quantitative studies of a variety of neurodegenerative disorders.