Average error exponent in Gallager low-density parity-check codes

We present a theoretical method for a direct evaluation of the average error exponent in Gallager error-correcting codes using methods of statistical physics. Results for the binary symmetric channel(BSC)are presented for codes of both finite and infinite connectivity.

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.

Accommodating intraocular lenses:a review of design concepts, usage and assessment methods

The correction of presbyopia and restoration of true accommodative function to the ageing eye is the focus of much ongoing research and clinical work. A range of accommodating intraocular lenses (AIOLs) implanted during cataract surgery has been developed and they are designed to change either their position or shape in response to ciliary muscle contraction to generate an increase in dioptric power. Two main design concepts exist. First, axial shift concepts rely on anterior axial movement of one or two optics creating accommodative ability. Second, curvature change designs are designed to provide significant amplitudes of accommodation with little physical displacement. Single-optic devices have been used most widely, although the true accommodative ability provided by forward shift of the optic appears limited and recent findings indicate that alternative factors such as flexing of the optic to alter ocular aberrations may be responsible for the enhanced near vision reported in published studies. Techniques for analysing the performance of AIOLs have not been standardised and clinical studies have reported findings using a wide range of both subjective and objective methods, making it difficult to gauge the success of these implants. There is a need for longitudinal studies using objective methods to assess long-term performance of AIOLs and to determine if true accommodation is restored by the designs available. While dual-optic and curvature change IOLs are designed to provide greater amplitudes of accommodation than is possible with single-optic devices, several of these implants are in the early stages of development and require significant further work before human use is possible. A number of challenges remain and must be addressed before the ultimate goal of restoring youthful levels of accommodation to the presbyopic eye can be achieved.

Development of a questionnaire to assess the relative subjective benefits of presbyopia correction

Purpose To develop a standardized questionnaire of near visual function and satisfaction to complement visual function evaluations of presbyopic corrections. Setting Eye Clinic, School of Life and Health Sciences, Aston University, Midland Eye Institute and Solihull Hospital, Birmingham, United Kingdom. Design Questionnaire development. Methods A preliminary 26-item questionnaire of previously used near visual function items was completed by patients with monofocal intraocular lenses (IOLs), multifocal IOLs, accommodating IOLs, multifocal contact lenses, or varifocal spectacles. Rasch analysis was used for item reduction, after which internal and test–retest reliabilities were determined. Construct validity was determined by correlating the resulting Near Activity Visual Questionnaire (NAVQ) scores with near visual acuity and critical print size (CPS), which was measured using the Minnesota Low Vision Reading Test chart. Discrimination ability was assessed through receiver-operating characteristic (ROC) curve analysis. Results One hundred fifty patients completed the questionnaire. Item reduction resulted in a 10-item NAVQ with excellent separation (2.92), internal consistency (Cronbach a = 0.95), and test–retest reliability (intraclass correlation coefficient = 0.72). Correlations of questionnaire scores with near visual acuity (r = 0.32) and CPS (r = 0.27) provided evidence of validity, and discrimination ability was excellent (area under ROC curve = 0.91). Conclusion Results show the NAVQ is a reliable, valid instrument that can be incorporated into the evaluation of presbyopic corrections.

Comparison of near visual acuity and reading metrics in presbyopia correction

PURPOSE: To provide a consistent standard for the evaluation of different types of presbyopic correction. SETTING: Eye Clinic, School of Life and Health Sciences, Aston University, Birmingham, United Kingdom. METHODS: Presbyopic corrections examined were accommodating intraocular lenses (IOLs), simultaneous multifocal and monovision contact lenses, and varifocal spectacles. Binocular near visual acuity measured with different optotypes (uppercase letters, lowercase letters, and words) and reading metrics assessed with the Minnesota Near Reading chart (reading acuity, critical print size [CPS], CPS reading speed) were intercorrelated (Pearson product moment correlations) and assessed for concordance (intraclass correlation coefficients [ICC]) and agreement (Bland-Altman analysis) for indication of clinical usefulness. RESULTS: Nineteen accommodating IOL cases, 40 simultaneous contact lens cases, and 38 varifocal spectacle cases were evaluated. Other than CPS reading speed, all near visual acuity and reading metrics correlated well with each other (r>0.70, P<.001). Near visual acuity measured with uppercase letters was highly concordant (ICC, 0.78) and in close agreement with lowercase letters (+/- 0.17 logMAR). Near word acuity agreed well with reading acuity (+/- 0.16 logMAR), which in turn agreed well with near visual acuity measured with uppercase letters 0.16 logMAR). Concordance (ICC, 0.18 to 0.46) and agreement (+/- 0.24 to 0.30 logMAR) of CPS with the other near metrics was moderate. CONCLUSION: Measurement of near visual ability in presbyopia should be standardized to include assessment of near visual acuity with logMAR uppercase-letter optotypes, smallest logMAR print size that maintains maximum reading speed (CPS), and reading speed. J Cataract Refract Surg 2009; 35:1401-1409 (C) 2009 ASCRS and ESCRS

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.

Clinical characteristics of unilateral myopic anisometropia in a juvenile optometric practice population

Purpose: A retrospective study of longitudinal case histories, undertaken to establish the clinical and statistical characteristics of unilateral myopic anisometropia (UMA) amongst the juvenile and adolescent population at an optometric practice, is reported. UMA was defined as that specific refractive state where an unequivocally myopic eye is paired with a 'piano' [spherical equivalent refraction, (SER) = ±0.25 Dioptres (D)] companion eye. Methods: The clinical records of all patients aged <19 years on file at an established independent optometric practice were categorised as 'myopic' (SER ≤-0.50 D), 'hypermetropie' (≥+0.75 D) or 'emmetropic' (≥-0.37≤+0.62 D). Subsequently all juvenile patients matching the UMA criterion, together with a case-matched group of bilaterally myopic individuals, were selected as the comparative study populations. Results: A total of 14.4% (n = 21 of 146) of the juvenile myopic case histories were identified as cases of UMA. More than half of these UMA cases emerged between the ages of 11.5 and 13.5 years. There was a marked female gender bias. The linear gradient of the age-related mean refractive trend in the myopic eye of the UMA population was not statistically significantly different (p > 0.1) to that fitted to the ametropic progression recorded in either eye of the case-matched population of young bilateral myopes; uniquely the slope associated with the companion eye of UMA cases was statistically significantly (p < 0.025) less steep. Compared with bilateral myopes fewer cases of UMA required a refractive correction to relieve visual or asthenopic symptoms, and this initial correction was dispensed on average 1 year later (at age 12.7 years) in UMA patients. Conclusions: Individuals identified as demonstrating clinically-defined UMA can be considered as distinct but functionally normal cases on the continuum of human refractive error. However, any unilaterally-acting determining factor(s) underlying the genesis of the condition remain obscure. © 2004 The College of Optometrists.

Surgical correction of astigmatism during cataract surgery

High levels of corneal astigmatism are prevalent in a significant proportion of the population. During cataract surgery pre-existing astigmatism can be corrected using single or paired incisions on the steep axis of the cornea, using relaxing incisions or with the use of a toric intraocular lens. This review provides an overview of the conventional methods of astigmatic correction during cataract surgery and in particular, discusses the various types of toric lenses presently available and the techniques used in determining the correct axis for the placement of such lenses. Furthermore, the potential causes of rotation in toric lenses are identified, along with techniques for assessing and quantifying the amount of rotation and subsequent management options for addressing post-operative rotation.

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 Part 4: an introduction to analysis of variance (ANOVA)

In any investigation in optometry involving more that two treatment or patient groups, an investigator should be using ANOVA to analyse the results assuming that the data conform reasonably well to the assumptions of the analysis. Ideally, specific null hypotheses should be built into the experiment from the start so that the treatments variation can be partitioned to test these effects directly. If 'post-hoc' tests are used, then an experimenter should examine the degree of protection offered by the test against the possibilities of making either a type 1 or a type 2 error. All experimenters should be aware of the complexity of ANOVA. The present article describes only one common form of the analysis, viz., that which applies to a single classification of the treatments in a randomised design. There are many different forms of the analysis each of which is appropriate to the analysis of a specific experimental design. The uses of some of the most common forms of ANOVA in optometry have been described in a further article. If in any doubt, an investigator should consult a statistician with experience of the analysis of experiments in optometry since once embarked upon an experiment with an unsuitable design, there may be little that a statistician can do to help.

Data analysis methods in optometry. Part 5: correlation

1. Pearson's correlation coefficient only tests whether the data fit a linear model. With large numbers of observations, quite small values of r become significant and the X variable may only account for a minute proportion of the variance in Y. Hence, the value of r squared should always be calculated and included in a discussion of the significance of r. 2. The use of r assumes that a bivariate normal distribution is present and this assumption should be examined prior to the study. If Pearson's r is not appropriate, then a non-parametric correlation coefficient such as Spearman's rs may be used. 3. A significant correlation should not be interpreted as indicating causation especially in observational studies in which there is a high probability that the two variables are correlated because of their mutual correlations with other variables. 4. In studies of measurement error, there are problems in using r as a test of reliability and the ‘intra-class correlation coefficient’ should be used as an alternative. A correlation test provides only limited information as to the relationship between two variables. Fitting a regression line to the data using the method known as ‘least square’ provides much more information and the methods of regression and their application in optometry will be discussed in the next article.

Data methods in optometry Part 9: experimental design and analysis of variance

The key to the correct application of ANOVA is careful experimental design and matching the correct analysis to that design. The following points should therefore, be considered before designing any experiment: 1. In a single factor design, ensure that the factor is identified as a 'fixed' or 'random effect' factor. 2. In more complex designs, with more than one factor, there may be a mixture of fixed and random effect factors present, so ensure that each factor is clearly identified. 3. Where replicates can be grouped or blocked, the advantages of a randomised blocks design should be considered. There should be evidence, however, that blocking can sufficiently reduce the error variation to counter the loss of DF compared with a randomised design. 4. Where different treatments are applied sequentially to a patient, the advantages of a three-way design in which the different orders of the treatments are included as an 'effect' should be considered. 5. Combining different factors to make a more efficient experiment and to measure possible factor interactions should always be considered. 6. The effect of 'internal replication' should be taken into account in a factorial design in deciding the number of replications to be used. Where possible, each error term of the ANOVA should have at least 15 DF. 7. Consider carefully whether a particular factorial design can be considered to be a split-plot or a repeated measures design. If such a design is appropriate, consider how to continue the analysis bearing in mind the problem of using post hoc tests in this situation.

Visual acuity measures do not reliably detect childhood refractive error - an epidemiological study

Purpose To investigate the utility of uncorrected visual acuity measures in screening for refractive error in white school children aged 6-7-years and 12-13-years. Methods The Northern Ireland Childhood Errors of Refraction (NICER) study used a stratified random cluster design to recruit children from schools in Northern Ireland. Detailed eye examinations included assessment of logMAR visual acuity and cycloplegic autorefraction. Spherical equivalent refractive data from the right eye were used to classify significant refractive error as myopia of at least 1DS, hyperopia as greater than +3.50DS and astigmatism as greater than 1.50DC, whether it occurred in isolation or in association with myopia or hyperopia. Results Results are presented from 661 white 12-13-year-old and 392 white 6-7-year-old school-children. Using a cut-off of uncorrected visual acuity poorer than 0.20 logMAR to detect significant refractive error gave a sensitivity of 50% and specificity of 92% in 6-7-year-olds and 73% and 93% respectively in 12-13-year-olds. In 12-13-year-old children a cut-off of poorer than 0.20 logMAR had a sensitivity of 92% and a specificity of 91% in detecting myopia and a sensitivity of 41% and a specificity of 84% in detecting hyperopia. Conclusions Vision screening using logMAR acuity can reliably detect myopia, but not hyperopia or astigmatism in school-age children. Providers of vision screening programs should be cognisant that where detection of uncorrected hyperopic and/or astigmatic refractive error is an aspiration, current UK protocols will not effectively deliver.

A projected process kriging algorithm for sensor networks with heterogeneous error characteristics

Large monitoring networks are becoming increasingly common and can generate large datasets from thousands to millions of observations in size, often with high temporal resolution. Processing large datasets using traditional geostatistical methods is prohibitively slow and in real world applications different types of sensor can be found across a monitoring network. Heterogeneities in the error characteristics of different sensors, both in terms of distribution and magnitude, presents problems for generating coherent maps. An assumption in traditional geostatistics is that observations are made directly of the underlying process being studied and that the observations are contaminated with Gaussian errors. Under this assumption, sub–optimal predictions will be obtained if the error characteristics of the sensor are effectively non–Gaussian. One method, model based geostatistics, assumes that a Gaussian process prior is imposed over the (latent) process being studied and that the sensor model forms part of the likelihood term. One problem with this type of approach is that the corresponding posterior distribution will be non–Gaussian and computationally demanding as Monte Carlo methods have to be used. An extension of a sequential, approximate Bayesian inference method enables observations with arbitrary likelihoods to be treated, in a projected process kriging framework which is less computationally intensive. The approach is illustrated using a simulated dataset with a range of sensor models and error characteristics.

Bayesian error bars for regression

Regression problems are concerned with predicting the values of one or more continuous quantities, given the values of a number of input variables. For virtually every application of regression, however, it is also important to have an indication of the uncertainty in the predictions. Such uncertainties are expressed in terms of the error bars, which specify the standard deviation of the distribution of predictions about the mean. Accurate estimate of error bars is of practical importance especially when safety and reliability is an issue. The Bayesian view of regression leads naturally to two contributions to the error bars. The first arises from the intrinsic noise on the target data, while the second comes from the uncertainty in the values of the model parameters which manifests itself in the finite width of the posterior distribution over the space of these parameters. The Hessian matrix which involves the second derivatives of the error function with respect to the weights is needed for implementing the Bayesian formalism in general and estimating the error bars in particular. A study of different methods for evaluating this matrix is given with special emphasis on the outer product approximation method. The contribution of the uncertainty in model parameters to the error bars is a finite data size effect, which becomes negligible as the number of data points in the training set increases. A study of this contribution is given in relation to the distribution of data in input space. It is shown that the addition of data points to the training set can only reduce the local magnitude of the error bars or leave it unchanged. Using the asymptotic limit of an infinite data set, it is shown that the error bars have an approximate relation to the density of data in input space.