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.

Applying quantitative methods in the assessment of outcomes of pharmacotherapy of psoriasis

Healthcare providers and policy makers are faced with an ever-increasing number of medical publications. Searching for relevant information and keeping up to date with new research findings remains a constant challenge. It has been widely acknowledged that narrative reviews of the literature are susceptible to several types of bias and a systematic approach may protect against these biases. The aim of this thesis was to apply quantitative methods in the assessment of outcomes of topical therapies for psoriasis. In particular, to systematically examine the comparative efficacy, tolerability and cost-effectiveness of topical calcipotriol in the treatment of mild-to-moderate psoriasis. Over the years, a wide range of techniques have been used to evaluate the severity of psoriasis and the outcomes from treatment. This lack of standardisation complicates the direct comparison of results and ultimately the pooling of outcomes from different clinical trials. There is a clear requirement for more comprehensive tools for measuring drug efficacy and disease severity in psoriasis. Ideally, the outcome measures need to be simple, relevant, practical, and widely applicable, and the instruments should be reliable, valid and responsive. The results of the meta-analysis reported herein show that calcipotriol is an effective antipsoriatic agent. In the short-tenn, the pooled data found calcipotriol to be more effective than calcitriol, tacalcitol, coal tar and short-contact dithranol. Only potent corticosteroids appeared to have comparable efficacy, with less short-term side-effects. Potent corticosteroids also added to the antipsoriatic effect of calcipotriol, and appeared to suppress the occurrence of calcipotriol-induced irritation. There was insufficient evidence to support any large effects in favour of improvements in efficacy when calcipotriol is used in combination with systemic therapies in patients with severe psoriasis. However, there was a total absence of long-term morbidity data on the effectiveness of any of the interventions studied. Decision analysis showed that, from the perspective of the NHS as payer, the relatively small differences in efficacy between calcipotriol and short-contact dithranol lead to large differences in the direct cost of treating patients with mildto-moderate plaque psoriasis. Further research is needed to examine the clinical and economic issues affecting patients under treatment for psoriasis in the UK. In particular, the maintenance value and cost/benefit ratio for the various treatment strategies, and the assessment of patient's preferences has not yet been adequately addressed for this chronic recurring disease.

Quantitative methods in neuropathology

The last decade has seen a considerable increase in the application of quantitative methods in the study of histological sections of brain tissue and especially in the study of neurodegenerative disease. These disorders are characterised by the deposition and aggregation of abnormal or misfolded proteins in the form of extracellular protein deposits such as senile plaques (SP) and intracellular inclusions such as neurofibrillary tangles (NFT). Quantification of brain lesions and studying the relationships between lesions and normal anatomical features of the brain, including neurons, glial cells, and blood vessels, has become an important method of elucidating disease pathogenesis. This review describes methods for quantifying the abundance of a histological feature such as density, frequency, and 'load' and the sampling methods by which quantitative measures can be obtained including plot/quadrat sampling, transect sampling, and the point-quarter method. In addition, methods for determining the spatial pattern of a histological feature, i.e., whether the feature is distributed at random, regularly, or is aggregated into clusters, are described. These methods include the use of the Poisson and binomial distributions, pattern analysis by regression, Fourier analysis, and methods based on mapped point patterns. Finally, the statistical methods available for studying the degree of spatial correlation between pathological lesions and neurons, glial cells, and blood vessels are described.

Sociolinguistics:quantitative methods

Variationist sociolinguistics was one of the first branches of linguistics to adopt a quantitative approach to data analysis (e.g., Fischer, 1958; Labov, 1963, 1966, 1969; Wolfram, 1969).

Advanced mean field methods:theory and practice

A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Because exact computations are infeasible in such cases and Monte Carlo sampling techniques may reach their limits, there is a need for methods that allow for efficient approximate computations. One of the simplest approximations is based on the mean field method, which has a long history in statistical physics. The method is widely used, particularly in the growing field of graphical models. Researchers from disciplines such as statistical physics, computer science, and mathematical statistics are studying ways to improve this and related methods and are exploring novel application areas. Leading approaches include the variational approach, which goes beyond factorizable distributions to achieve systematic improvements; the TAP (Thouless-Anderson-Palmer) approach, which incorporates correlations by including effective reaction terms in the mean field theory; and the more general methods of graphical models. Bringing together ideas and techniques from these diverse disciplines, this book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling.

Quantifying the pathology of neurodegenerative disorders:Quantitative measurements, sampling strategies and data analysis

The use of quantitative methods has become increasingly important in the study of neurodegenerative disease. Disorders such as Alzheimer's disease (AD) are characterized by the formation of discrete, microscopic, pathological lesions which play an important role in pathological diagnosis. This article reviews the advantages and limitations of the different methods of quantifying the abundance of pathological lesions in histological sections, including estimates of density, frequency, coverage, and the use of semiquantitative scores. The major sampling methods by which these quantitative measures can be obtained from histological sections, including plot or quadrat sampling, transect sampling, and point-quarter sampling, are also described. In addition, the data analysis methods commonly used to analyse quantitative data in neuropathology, including analyses of variance (ANOVA) and principal components analysis (PCA), are discussed. These methods are illustrated with reference to particular problems in the pathological diagnosis of AD and dementia with Lewy bodies (DLB).

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.

The propensity to disrupt and the disruption nucleolus of a characteristic function game

Gately [1974] recently introduced the concept of an individual player's “propensity to disrupt” a payoff vector in a three-person characteristic function game. As a generalisation of this concept we propose the “disruption nucleolus” of ann-person game. The properties and computational possibilities of this concept are analogous to those of the nucleolus itself. Two numerical examples are given.

Verstehen, was zählt. Ein Forschungsbericht über quantitative Arbeitsformen im Linguistik- und Deutsch-als-Fremdsprache-Unterricht in Großbritannien

UK schools and universities are trying to remedy a nationally recognized skills shortage in quantitative methods among graduates. This article describes and analyses a research project in German Studies funded by the Economic and Social Research Council (ESRC) aimed at addressing the issue. The interdisciplinary pilot project introduced quantitative methods into undergraduate curricula not only in Linguistics, but also in German Studies.

Statistical mechanics of low-density parity-check codes

We review recent theoretical progress on the statistical mechanics of error correcting codes, focusing on low-density parity-check (LDPC) codes in general, and on Gallager and MacKay-Neal codes in particular. By exploiting the relation between LDPC codes and Ising spin systems with multispin interactions, one can carry out a statistical mechanics based analysis that determines the practical and theoretical limitations of various code constructions, corresponding to dynamical and thermodynamical transitions, respectively, as well as the behaviour of error-exponents averaged over the corresponding code ensemble as a function of channel noise. We also contrast the results obtained using methods of statistical mechanics with those derived in the information theory literature, and show how these methods can be generalized to include other channel types and related communication problems.

Average and reliability error exponents in low-density parity-check codes

We present a theoretical method for a direct evaluation of the average and reliability error exponents in low-density parity-check error-correcting codes using methods of statistical physics. Results for the binary symmetric channel are presented for codes of both finite and infinite connectivity.

DEA-R:ratio-based comparative efficiency model, its mathematical relation to DEA and its use in applications

We propose a new mathematical model for efficiency analysis, which combines DEA methodology with an old idea-Ratio Analysis. Our model, called DEA-R, treats all possible ratios "output/input" as outputs within the standard DEA model. Although DEA and DEA-R generate different summary measures for efficiency, the two measures are comparable. Our mathematical and empirical comparisons establish the validity of DEA-R model in its own right. The key advantage of DEA-R over DEA is that it allows effective integration of the model with experts' opinions via flexible restrictive conditions on individual "output/input" pairs. © 2007 Springer Science+Business Media, LLC.

A study in the application of domestic solar assisted heat pumps for heating and cooling

In the present work, the more important parameters of the heat pump system and of solar assisted heat pump systems were analysed in a quantitative way. Ideal and real Rankine cycles applied to the heat pump, with and without subcooling and superheating were studied using practical recommended values for their thermodynamics parameters. Comparative characteristics of refrigerants here analysed looking for their applicability in heat pumps for domestic heating and their effect in the performance of the system. Curves for the variation of the coefficient of performance as a function of condensing and evaporating temperatures were prepared for R12. Air, water and earth as low-grade heat sources and basic heat pump design factors for integrated heat pumps and thermal stores and for solar assisted heat pump-series, parallel and dual-systems were studied. The analysis of the relative performance of these systems demonstrated that the dual system presents advantages in domestic applications. An account of energy requirements for space and hater heating in the domestic sector in the O.K. is presented. The expected primary energy savings by using heat pumps to provide for the heating demand of the domestic sector was found to be of the order of 7%. The availability of solar energy in the U.K. climatic conditions and the characteristics of the solar radiation here studied. Tables and graphical representations in order to calculate the incident solar radiation over a tilted roof were prepared and are given in this study in section IV. In order to analyse and calculate the heating load for the system, new mathematical and graphical relations were developed in section V. A domestic space and water heating system is described and studied. It comprises three main components: a solar radiation absorber, the normal roof of a house, a split heat pump and a thermal store. A mathematical study of the heat exchange characteristics in the roof structure was done. This permits to evaluate the energy collected by the roof acting as a radiation absorber and its efficiency. An indication of the relative contributions from the three low-grade sources: ambient air, solar boost and heat loss from the house to the roof space during operation is given in section VI, together with the average seasonal performance and the energy saving for a prototype system tested at the University of Aston. The seasonal performance as found to be 2.6 and the energy savings by using the system studied 61%. A new store configuration to reduce wasted heat losses is also discussed in section VI.

When do conservation planning methods deliver? Quantifying the consequences of uncertainty

The rapid global loss of biodiversity has led to a proliferation of systematic conservation planning methods. In spite of their utility and mathematical sophistication, these methods only provide approximate solutions to real-world problems where there is uncertainty and temporal change. The consequences of errors in these solutions are seldom characterized or addressed. We propose a conceptual structure for exploring the consequences of input uncertainty and oversimpli?ed approximations to real-world processes for any conservation planning tool or strategy. We then present a computational framework based on this structure to quantitatively model species representation and persistence outcomes across a range of uncertainties. These include factors such as land costs, landscape structure, species composition and distribution, and temporal changes in habitat. We demonstrate the utility of the framework using several reserve selection methods including simple rules of thumb and more sophisticated tools such as Marxan and Zonation. We present new results showing how outcomes can be strongly affected by variation in problem characteristics that are seldom compared across multiple studies. These characteristics include number of species prioritized, distribution of species richness and rarity, and uncertainties in the amount and quality of habitat patches. We also demonstrate how the framework allows comparisons between conservation planning strategies and their response to error under a range of conditions. Using the approach presented here will improve conservation outcomes and resource allocation by making it easier to predict and quantify the consequences of many different uncertainties and assumptions simultaneously. Our results show that without more rigorously generalizable results, it is very dif?cult to predict the amount of error in any conservation plan. These results imply the need for standard practice to include evaluating the effects of multiple real-world complications on the behavior of any conservation planning method.

A mean field theory of coded CDMA systems

We present a mean field theory of code-division multiple access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems.