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.

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.

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.

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.

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.

Modeling of spectral and statistical properties of a random distributed feedback fiber laser

For the first time we report full numerical NLSE-based modeling of generation properties of random distributed feedback fiber laser based on Rayleigh scattering. The model which takes into account the random backscattering via its average strength only describes well power and spectral properties of random DFB fiber lasers. The influence of dispersion and nonlinearity on spectral and statistical properties is investigated. The evidence of non-gaussian intensity statistics is found. © 2013 Optical Society of America.

Cleavage initiation in the intercritically reheated coarse-grained heat affected zone:Part II. Failure criteria and statistical effects

In part 1 of this article, cleavage initiation in the intercritically reheated coarse-grained heat affected zone (IC CG HAZ) of high-strength low-alloy (HSLA) steels was determined to occur between two closely spaced blocky MA particles. Blunt notch, crack tip opening displacement (CTOD), and precracked Charpy testing were used in this investigation to determine the failure criteria required for cleavage initiation to occur by this mechanism in the IC CG HAZ. It was found that the attainment of a critical level of strain was required in addition to a critical level of stress. This does not occur in the case of high strain rate testing, for example, during precracked Charpy testing. A different cleavage initiation mechanism is then found to operate. The precise fracture criteria and microstructural requirements (described in part I of this article) result in competition between potential cleavage initiation mechanisms in the IC CG HAZ.

Temporal and statistical properties of the ytterbium doped fiber laser

Recently, temporal and statistical properties of quasi-CW fiber lasers have attracted a great attention. In particular, properties of Raman fiber laser (RFLs) have been studied both numerically and experimentally [1,2]. Experimental investigation is more challengeable, as the full generation optical bandwidth (typically hundreds of GHz for RFLs) is much bigger than real-time bandwidth of oscilloscopes (up to 60GHz for the newest models). So experimentally measured time dynamics is highly bandwidth averaged and do not provide precise information about overall statistical properties. To overpass this, one can use the spectral filtering technique to study temporal and statistical properties within optical bandwidth comparable with measurement bandwidth [3] or indirect measurements [4]. Ytterbium-doped fiber lasers (YDFL) are more suitable for experimental investigation, as their generation spectrum usually 10 times narrower. Moreover, recently ultra-narrow-band generation has been demonstrated in YDFL [5] which provides in principle possibility to measure time dynamics and statistics in real time using conventional oscilloscopes. © 2013 IEEE.

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.

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).

Numerical modelling of spectral, temporal and statistical properties of Raman fiber lasers

Efficient numerical modelling of the power, spectral and statistical properties of partially coherent quasi-CW Raman fiber laser radiation is presented. XPM between pump wave and generated Stokes wave is not important in the generation spectrum broadening and XPM term can be omitted in propagation equation what sufficiently speeds-up simulations. The time dynamics of Raman fiber laser (RFL) is stochastic exhibiting events several times more intense that the mean value on the ps timescale. However, the RFL has different statistical properties on different time scales. The probability density function of spectral power density is exponential for the generation modes located either in the spectrum centre or spectral wings while the phases are distributed uniformly. The pump wave preserves the initial Gaussian statistics during propagation in the laser cavity. Intense pulses in the pump wave are evolved under the SPM influence and are not disturbed by the dispersion. Contrarily, in the generated wave the dispersion plays a significant role that results in stochastic behavior. © 2012 Elsevier B.V. All rights reserved.

Intensity dynamics and statistical properties of random distributed feedback fiber laser

We present first experimental investigation of fast-intensity dynamics of random distributed feedback (DFB) fiber lasers. We found that the laser dynamics are stochastic on a short time scale and exhibit pronounced fluctuations including generation of extreme events. We also experimentally characterize statistical properties of radiation of random DFB fiber lasers. We found that statistical properties deviate from Gaussian and depend on the pump power.

Physiologically based pharmacokinetic modelling in drug delivery

The application of pharmacokinetic modelling within the drug development field essentially allows one to develop a quantitative description of the temporal behaviour of a compound of interest at a tissue/organ level, by identifying and defining relationships between a dose of a drug and dependent variables. In order to understand and characterise the pharmacokinetics of a drug, it is often helpful to employ pharmacokinetic modelling using empirical or mechanistic approaches. Pharmacokinetic models can be developed within mathematical and statistical commercial software such as MATLAB using traditional mathematical and computation coding, or by using the Simbiology Toolbox available within MATLAB for a graphical user interface approach to developing pharmacokinetic (PBPK) models. For formulations dosed orally, a prerequisite for clinical activity is the entry of the drug into the systemic circulation.