Fusional vergence measurements for eso versus exo deviations: is there a difference?

Purpose: The aims of this study were to compare angle of deviation, fusional vergence measurements and fusion reserve ratio between esophoria and exophoria. Methods: A cross-sectional study was performed in children with best-corrected visual acuity of 0.0 LogMAR in either eye, compensated heterophoria within 10 prism dioptres (PD), full ocular rotations, presence of fusional vergence and stereopsis (60 seconds of arc or better). Fusional amplitudes were compared between angle of deviation (2, 4, 6, 8 and 10 PD) in esophoria and exophoria. The fusion reserve ratio was calculated (to assess the effect of the underlying angle of deviation) as fusional convergence divided by prism alternating cover test measurements. Results: Two-hundred and eleven children (7.65±1.16 years) were recruited to this study. Exophoria was most common for near (n=181; 85.8%) and distance (n=20; 9.5%). Esophoria was present in 22 children for near (10.4%) and in 1 child for distance (0.5%). No significant differences were found between fusional amplitudes and angle of deviation for near (p>0.05). Children with exophoria of 10PD had a slight, but not, significant (p=0.264) increase in fusional convergence from 2PD (19.95±5.09) to 10PD (26.67±5.77). In esophoric children the variation of fusional convergence was smaller from 2P (25.00±0.00) to 10PD (22.50±3.54) and non significant (p=0.185). The fusion reserve ratio was significantly smaller in children with higher deviations (i.e. 10PD) for both esophoria (p=0.003) and exophoria (p>0.001). The fusion reserve ratio ranged between 12.50 (2PD) and 2.25±0.35 (10PD) for esophoria and between 9.98±2.55 (2PD) and 2.67±0.58 (10PD) for exophoria. Conclusions: Angle of deviation is not an efficient measure to predict fusional amplitudes. The fusion reserve ratio appears to be a better measurement to assess the effect of the underlying angle of deviation on fusional convergence. More studies are necessary to understand better the relationship between fusion amplitudes and angle of deviation.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

Difference-based meta-analytic procedures for between-participant and/or within-participant designs : a tutorial review for sports and exercise scientists

The aim of this paper is to provide a contemporary summary of statistical and non-statistical meta-analytic procedures that have relevance to the type of experimental designs often used by sport scientists when examining differences/change in dependent measure(s) as a result of one or more independent manipulation(s). Using worked examples from studies on observational learning in the motor behaviour literature, we adopt a random effects model and give a detailed explanation of the statistical procedures for the three types of raw score difference-based analyses applicable to between-participant, within-participant, and mixed-participant designs. Major merits and concerns associated with these quantitative procedures are identified and agreed methods are reported for minimizing biased outcomes, such as those for dealing with multiple dependent measures from single studies, design variation across studies, different metrics (i.e. raw scores and difference scores), and variations in sample size. To complement the worked examples, we summarize the general considerations required when conducting and reporting a meta-analysis, including how to deal with publication bias, what information to present regarding the primary studies, and approaches for dealing with outliers. By bringing together these statistical and non-statistical meta-analytic procedures, we provide the tools required to clarify understanding of key concepts and principles.

Pathologising difference, governing personality

Recent research has stressed the integral part played by teachers in both preliminary diagnosis and ongoing treatment of a range of conduct and personality disorders. Teachers are not only required to be aware of a variety of new categories of difference (Attention Deficit Disorder, Selective Mutism, Borderline Personality Disorder, Antisocial Personality Disorder, to name but a few), but are also now lauded for extending the role of education into new areas of social management. This paper will take issue with this understanding on two counts: first, teachers have always sought to mould the personalities of students, and the pathologisation of specific forms of conduct is simply a new tactic within a very old and familiar strategy. Second, schools do not simply discover disorders such as ADD as objective facts of nature. Rather, they are part of the process through which such differences are created, and by which individuals can be more effectively governed.