A simple implementation of a normal mixture approach to differential gene expression in multiclass microarrays

Motivation: An important problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. We provide a straightforward and easily implemented method for estimating the posterior probability that an individual gene is null. The problem can be expressed in a two-component mixture framework, using an empirical Bayes approach. Current methods of implementing this approach either have some limitations due to the minimal assumptions made or with more specific assumptions are computationally intensive. Results: By converting to a z-score the value of the test statistic used to test the significance of each gene, we propose a simple two-component normal mixture that models adequately the distribution of this score. The usefulness of our approach is demonstrated on three real datasets.

Methods of studying the planar distribution of objects in histological sections of brain tissue

This article reviews the statistical methods that have been used to study the planar distribution, and especially clustering, of objects in histological sections of brain tissue. The objective of these studies is usually quantitative description, comparison between patients or correlation between histological features. Objects of interest such as neurones, glial cells, blood vessels or pathological features such as protein deposits appear as sectional profiles in a two-dimensional section. These objects may not be randomly distributed within the section but exhibit a spatial pattern, a departure from randomness either towards regularity or clustering. The methods described include simple tests of whether the planar distribution of a histological feature departs significantly from randomness using randomized points, lines or sample fields and more complex methods that employ grids or transects of contiguous fields, and which can detect the intensity of aggregation and the sizes, distribution and spacing of clusters. The usefulness of these methods in understanding the pathogenesis of neurodegenerative diseases such as Alzheimer's disease and Creutzfeldt-Jakob disease is discussed. © 2006 The Royal Microscopical Society.

Testing term structure estimation methods:evidence from the UK STRIPs market

Prices and yields of UK government zero-coupon bonds are used to test alternative yield curve estimation models. Zero-coupon bonds permit a more pure comparison, as the models are providing only the interpolation service and also not making estimation feasible. It is found that better yield curves estimates are obtained by fitting to the yield curve directly rather than fitting first to the discount function. A simple procedure to set the smoothness of the fitted curves is developed, and a positive relationship between oversmoothness and the fitting error is identified. A cubic spline function fitted directly to the yield curve provides the best overall balance of fitting error and smoothness, both along the yield curve and within local maturity regions.

Mathematical methods in power system stability studies

In this thesis various mathematical methods of studying the transient and dynamic stabiIity of practical power systems are presented. Certain long established methods are reviewed and refinements of some proposed. New methods are presented which remove some of the difficulties encountered in applying the powerful stability theories based on the concepts of Liapunov. Chapter 1 is concerned with numerical solution of the transient stability problem. Following a review and comparison of synchronous machine models the superiority of a particular model from the point of view of combined computing time and accuracy is demonstrated. A digital computer program incorporating all the synchronous machine models discussed, and an induction machine model, is described and results of a practical multi-machine transient stability study are presented. Chapter 2 reviews certain concepts and theorems due to Liapunov. In Chapter 3 transient stability regions of single, two and multi~machine systems are investigated through the use of energy type Liapunov functions. The treatment removes several mathematical difficulties encountered in earlier applications of the method. In Chapter 4 a simple criterion for the steady state stability of a multi-machine system is developed and compared with established criteria and a state space approach. In Chapters 5, 6 and 7 dynamic stability and small signal dynamic response are studied through a state space representation of the system. In Chapter 5 the state space equations are derived for single machine systems. An example is provided in which the dynamic stability limit curves are plotted for various synchronous machine representations. In Chapter 6 the state space approach is extended to multi~machine systems. To draw conclusions concerning dynamic stability or dynamic response the system eigenvalues must be properly interpreted, and a discussion concerning correct interpretation is included. Chapter 7 presents a discussion of the optimisation of power system small sjgnal performance through the use of Liapunov functions.

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.

Data analysis methods in optometry: is there a difference between two samples? Part 2.

In this second article, statistical ideas are extended to the problem of testing whether there is a true difference between two samples of measurements. First, it will be shown that the difference between the means of two samples comes from a population of such differences which is normally distributed. Second, the 't' distribution, one of the most important in statistics, will be applied to a test of the difference between two means using a simple data set drawn from a clinical experiment in optometry. Third, in making a t-test, a statistical judgement is made as to whether there is a significant difference between the means of two samples. Before the widespread use of statistical software, this judgement was made with reference to a statistical table. Even if such tables are not used, it is useful to understand their logical structure and how to use them. Finally, the analysis of data, which are known to depart significantly from the normal distribution, will be described.

Data methods in optometry. Part 6: fitting a regression line to data

1. Fitting a linear regression to data provides much more information about the relationship between two variables than a simple correlation test. A goodness of fit test of the line should always be carried out. Hence, r squared estimates the strength of the relationship between Y and X, ANOVA whether a statistically significant line is present, and the ‘t’ test whether the slope of the line is significantly different from zero. 2. Always check whether the data collected fit the assumptions for regression analysis and, if not, whether a transformation of the Y and/or X variables is necessary. 3. If the regression line is to be used for prediction, it is important to determine whether the prediction involves an individual y value or a mean. Care should be taken if predictions are made close to the extremities of the data and are subject to considerable error if x falls beyond the range of the data. Multiple predictions require correction of the P values. 3. If several individual regression lines have been calculated from a number of similar sets of data, consider whether they should be combined to form a single regression line. 4. If the data exhibit a degree of curvature, then fitting a higher-order polynomial curve may provide a better fit than a straight line. In this case, a test of whether the data depart significantly from a linear regression should be carried out.

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.

The application of methods of uncertain reasoning to the biological classification of river water quality

This thesis presents an investigation into the application of methods of uncertain reasoning to the biological classification of river water quality. Existing biological methods for reporting river water quality are critically evaluated, and the adoption of a discrete biological classification scheme advocated. Reasoning methods for managing uncertainty are explained, in which the Bayesian and Dempster-Shafer calculi are cited as primary numerical schemes. Elicitation of qualitative knowledge on benthic invertebrates is described. The specificity of benthic response to changes in water quality leads to the adoption of a sensor model of data interpretation, in which a reference set of taxa provide probabilistic support for the biological classes. The significance of sensor states, including that of absence, is shown. Novel techniques of directly eliciting the required uncertainty measures are presented. Bayesian and Dempster-Shafer calculi were used to combine the evidence provided by the sensors. The performance of these automatic classifiers was compared with the expert's own discrete classification of sampled sites. Variations of sensor data weighting, combination order and belief representation were examined for their effect on classification performance. The behaviour of the calculi under evidential conflict and alternative combination rules was investigated. Small variations in evidential weight and the inclusion of evidence from sensors absent from a sample improved classification performance of Bayesian belief and support for singleton hypotheses. For simple support, inclusion of absent evidence decreased classification rate. The performance of Dempster-Shafer classification using consonant belief functions was comparable to Bayesian and singleton belief. Recommendations are made for further work in biological classification using uncertain reasoning methods, including the combination of multiple-expert opinion, the use of Bayesian networks, and the integration of classification software within a decision support system for water quality assessment.

Physics-inspired methods for networking and communications

Advances in statistical physics relating to our understanding of large-scale complex systems have recently been successfully applied in the context of communication networks. Statistical mechanics methods can be used to decompose global system behavior into simple local interactions. Thus, large-scale problems can be solved or approximated in a distributed manner with iterative lightweight local messaging. This survey discusses how statistical physics methodology can provide efficient solutions to hard network problems that are intractable by classical methods. We highlight three typical examples in the realm of networking and communications. In each case we show how a fundamental idea of statistical physics helps solve the problem in an efficient manner. In particular, we discuss how to perform multicast scheduling with message passing methods, how to improve coding using the crystallization process, and how to compute optimal routing by representing routes as interacting polymers.

A simple method for the fabrication of intrinsically apodized chirped fibre Bragg gratings

A new and simple fabrication technique is reported for the UV inscription of intrinsically apodized chirped fibre gratings at an arbitrary Bragg wavelength employing a single chirped phase-mask in a scanning Talbot interferometer set-up. Chirped gratings have been successfully produced over a large wavelength range and with bandwidths up to 5 nm. These gratings exhibit the time-delay response of a small ripple effect. In the present paper a comparison with previously reported fabrication methods is given, showing the advantages and disadvantages of the different methods.

Bit error rate estimation methods for QPSK CO-OFDM transmission

Coherent optical orthogonal frequency division multiplexing (CO-OFDM) is an attractive transmission technique to virtually eliminate intersymbol interference caused by chromatic dispersion and polarization-mode dispersion. Design, development, and operation of CO-OFDM systems require simple, efficient, and reliable methods of their performance evaluation. In this paper, we demonstrate an accurate bit error rate estimation method for QPSK CO-OFDM transmission based on the probability density function of the received QPSK symbols. By comparing with other known approaches, including data-aided and nondata-aided error vector magnitude, we show that the proposed method offers the most accurate estimate of the system performance for both single channel and wavelength division multiplexing QPSK CO-OFDM transmission systems. © 2014 IEEE.

A comparison of denoising methods for X-ray fluoroscopic images

Fluoroscopic images exhibit severe signal-dependent quantum noise, due to the reduced X-ray dose involved in image formation, that is generally modelled as Poisson-distributed. However, image gray-level transformations, commonly applied by fluoroscopic device to enhance contrast, modify the noise statistics and the relationship between image noise variance and expected pixel intensity. Image denoising is essential to improve quality of fluoroscopic images and their clinical information content. Simple average filters are commonly employed in real-time processing, but they tend to blur edges and details. An extensive comparison of advanced denoising algorithms specifically designed for both signal-dependent noise (AAS, BM3Dc, HHM, TLS) and independent additive noise (AV, BM3D, K-SVD) was presented. Simulated test images degraded by various levels of Poisson quantum noise and real clinical fluoroscopic images were considered. Typical gray-level transformations (e.g. white compression) were also applied in order to evaluate their effect on the denoising algorithms. Performances of the algorithms were evaluated in terms of peak-signal-to-noise ratio (PSNR), signal-to-noise ratio (SNR), mean square error (MSE), structural similarity index (SSIM) and computational time. On average, the filters designed for signal-dependent noise provided better image restorations than those assuming additive white Gaussian noise (AWGN). Collaborative denoising strategy was found to be the most effective in denoising of both simulated and real data, also in the presence of image gray-level transformations. White compression, by inherently reducing the greater noise variance of brighter pixels, appeared to support denoising algorithms in performing more effectively. © 2012 Elsevier Ltd. All rights reserved.

Refinement methods for software architecture design using the software architecture model

Modern software systems are often large and complicated. To better understand, develop, and manage large software systems, researchers have studied software architectures that provide the top level overall structural design of software systems for the last decade. One major research focus on software architectures is formal architecture description languages, but most existing research focuses primarily on the descriptive capability and puts less emphasis on software architecture design methods and formal analysis techniques, which are necessary to develop correct software architecture design. ^ Refinement is a general approach of adding details to a software design. A formal refinement method can further ensure certain design properties. This dissertation proposes refinement methods, including a set of formal refinement patterns and complementary verification techniques, for software architecture design using Software Architecture Model (SAM), which was developed at Florida International University. First, a general guideline for software architecture design in SAM is proposed. Second, specification construction through property-preserving refinement patterns is discussed. The refinement patterns are categorized into connector refinement, component refinement and high-level Petri nets refinement. These three levels of refinement patterns are applicable to overall system interaction, architectural components, and underlying formal language, respectively. Third, verification after modeling as a complementary technique to specification refinement is discussed. Two formal verification tools, the Stanford Temporal Prover (STeP) and the Simple Promela Interpreter (SPIN), are adopted into SAM to develop the initial models. Fourth, formalization and refinement of security issues are studied. A method for security enforcement in SAM is proposed. The Role-Based Access Control model is formalized using predicate transition nets and Z notation. The patterns of enforcing access control and auditing are proposed. Finally, modeling and refining a life insurance system is used to demonstrate how to apply the refinement patterns for software architecture design using SAM and how to integrate the access control model. ^ The results of this dissertation demonstrate that a refinement method is an effective way to develop a high assurance system. The method developed in this dissertation extends existing work on modeling software architectures using SAM and makes SAM a more usable and valuable formal tool for software architecture design. ^

Navigating health sources on the Internet: A mixed-methods examination of online consumer reviews and expert text on psychotropic drugs

Purpose. The Internet has provided an unprecedented opportunity for psychotropic medication consumers, a traditionally silenced group in clinical trial research, to have voice by contributing to the construction of drug knowledge in an immediate, direct manner. Currently, there are no systematic appraisals of the potential of online consumer drug reviews to contribute to drug knowledge. The purpose of this research was to explore the content of drug information on various websites representing themselves as consumer- and expert-constructed, and as a practical consideration, to examine how each source may help and hinder treatment decision-making.^ Methodology. A mixed-methods research strategy utilizing a grounded theory approach was used to analyze drug information on 5 exemplar websites (3 consumer- and 2 expertconstructed) for 2 popularly prescribed psychotropic drugs (escitalopram and quetiapine). A stratified simple random sample was used to select 1,080 consumer reviews from the websites (N=7,114) through February 2009. Text was coded using QDA Miner 3.2 software by Provalis Research. A combination of frequency tables, descriptive excerpts from text, and chi-square tests for association were used throughout analyses.^ Findings. The most frequently mentioned effects by consumers taking either drug were related to psychological/behavioral symptoms and sleep. Consumers reported many of the same effects as found on expert health sites, but provided more descriptive language and situational examples. Expert labels of less serious on certain effects were not congruent with the sometimes tremendous burden described by consumers. Consumers mentioned more than double the themes mentioned in expert text, and demonstrated a diversity and range of discourses around those themes.^ Conclusions. Drug effects from each source were complete relative to the information provided in the other, but each also offered distinct advantages. Expert health sites provided concise summaries of medications’ effects, while consumer reviews had the added advantage of concrete descriptions and greater context. In short, consumer reviews better prepared potential consumers for what it’s like to take psychotropic drugs. Both sources of information benefit clinicians and consumers in making informed treatment-related decisions. Social work practitioners are encouraged to thoughtfully utilize online consumer drug reviews as a legitimate additional source for assisting clients in learning about treatment options.^