A Crank--Nicolson ADI spectral method for a two-dimensional riesz space fractional nonlinear reaction-diffusion equation

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank--Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived method is stable and convergent of order $2$ in time. An optimal error estimate in space is also obtained by introducing a new orthogonal projector. The present method is extended to solve the fractional FitzHugh--Nagumo model. Numerical results are provided to verify the theoretical analysis.

A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation

The fractional Fokker-Planck equation is an important physical model for simulating anomalous diffusions with external forces. Because of the non-local property of the fractional derivative an interesting problem is to explore high accuracy numerical methods for fractional differential equations. In this paper, a space-time spectral method is presented for the numerical solution of the time fractional Fokker-Planck initial-boundary value problem. The proposed method employs the Jacobi polynomials for the temporal discretization and Fourier-like basis functions for the spatial discretization. Due to the diagonalizable trait of the Fourier-like basis functions, this leads to a reduced representation of the inner product in the Galerkin analysis. We prove that the time fractional Fokker-Planck equation attains the same approximation order as the time fractional diffusion equation developed in [23] by using the present method. That indicates an exponential decay may be achieved if the exact solution is sufficiently smooth. Finally, some numerical results are given to demonstrate the high order accuracy and efficiency of the new numerical scheme. The results show that the errors of the numerical solutions obtained by the space-time spectral method decay exponentially.

Wake angle for surface gravity waves on a finite depth fluid

Linear water wave theory suggests that wave patterns caused by a steadily moving disturbance are contained within a wedge whose half-angle depends on the depth-based Froude number $F_H$. For the problem of flow past an axisymmetric pressure distribution in a finite-depth channel, we report on the apparent angle of the wake, which is the angle of maximum peaks. For moderately deep channels, the dependence of the apparent wake angle on the Froude number is very different to the wedge angle, and varies smoothly as $F_H$ passes through the critical value $F_H=1$. For shallow water, the two angles tend to follow each other more closely, which leads to very large apparent wake angles for certain regimes.

MRI reveals individual level deformities in the growing scoliotic spine that clinically are masked by the Cobb angle

Clinically, the Cobb angle method measures the overall scoliotic curve in the coronal plane but does not measure individual vertebra and disc wedging. The contributions of the vertebrae and discs in the growing scoliotic spine were measured using sequential MRI scans to investigate coronal plane deformity progression with growth. Sequential MRI data showed complex patterns of deformity progression. Changes to the wedging of individual vertebrae and discs may occur in patients who have no increase in overall Cobb angle measure; the Cobb method alone may be insufficient to capture the complex mechanisms of deformity progression.

Is there evidence to support the use of the angle of peak torque as a marker of hamstring injury and re-injury risk?

Hamstring strain injuries are the predominant injury in many sports, costing athletes and clubs a significant financial and performance burden. Therefore the ability to identify and intervene with individuals who are considered at a high risk of injury is important. One measure which has grown in popularity as an outcome variable following hamstring intervention/prevention studies and rehabilitation is the angle of peak knee flexor torque. This current opinion article will firstly introduce the measure and the processes behind it. Secondly, this article will summarise how the angle of peak knee flexor torque has been suggested to measure hamstring strain injury risk. Finally various limitations will be presented and outlined as to how they may influence the measure. These include the lack of muscle specificity, the common concentric contraction mode of assessment, reliability of the measure, various neural contributions (such as rate of force development and neuromuscular inhibition) as well as the lack of prospective data showing any predictive value in the measure.

Sequential MRI reveals individual level deformities in the growing scoliotic spine that are clinically masked by the Cobb angle

Introduction Clinically, the Cobb angle method measures the overall scoliotic curve in the coronal plane but does not measure individual vertebra and disc wedging. The contributions of the vertebrae and discs in the growing scoliotic spine were measured to investigate coronal plane deformity progression with growth. Methods A 0.49mm isotropic 3D MRI technique was developed to investigate the level-by-level changes that occur in the growing spine of a group of Adolescent Idiopathic Scoliosis (AIS) patients, who received two to four sequential scans (spaced 3-12 months apart). The coronal plane wedge angles of each vertebra and disc in the major curve were measured to capture any changes that occurred during their adolescent growth phase. Results Seventeen patients had at least two scans. Mean patient age was 12.9 years (SD 1.5 years). Sixteen were classified as right-sided major thoracic Lenke Type 1 (one left sided). Mean standing Cobb angle at initial presentation was 31° (SD 12°). Six received two scans, nine three scans and two four scans, with 65% showing a Cobb angle progression of 5° or more between scans. Overall, there was no clear pattern of deformity progression of individual vertebrae and discs, nor between patients who progressed and those who didn’t. There were measurable changes in the wedging of the vertebrae and discs in all patients. In sequential scans, change in direction of wedging was also seen. In several patients there was reverse wedging in the discs that counteracted increased wedging of the vertebrae such that no change in overall Cobb angle was seen. Conclusion Sequential MRI data showed complex patterns of deformity progression. Changes to the wedging of individual vertebrae and discs may occur in patients who have no increase in Cobb angle measure; the Cobb method alone may be insufficient to capture the complex mechanisms of deformity progression.

Sequential MRI of growing scoliotic spines reveals individual level deformities that are clinically masked by the cobb angle

INTRODUCTION. Clinically, the Cobb angle method measures the overall scoliotic curve in the coronal plane but does not measure individual vertebra and disc wedging. The contributions of the vertebrae and discs in the growing scoliotic spine were measured to investigate coronal plane deformity progression with growth. METHODS. A 0.49mm isotropic 3D MRI technique was developed to investigate the level-by-level changes that occur in the growing spine of a group of Adolescent Idiopathic Scoliosis (AIS) patients, who received two to four sequential scans (spaced 3-12 months apart). The coronal plane wedge angles of each vertebra and disc in the major curve were measured to capture any changes that occurred during their adolescent growth phase. RESULTS. Seventeen patients had at least two scans. Mean patient age was 12.9 years (SD 1.5 years). Sixteen were classified as right-sided major thoracic Lenke Type 1 (one left sided). Mean standing Cobb angle at initial presentation was 31° (SD 12°). Six received two scans, nine three scans and two four scans, with 65% showing a Cobb angle progression of 5° or more between scans. Overall, there was no clear pattern of deformity progression of individual vertebrae and discs, nor between patients who progressed and those who didn’t. There were measurable changes in the wedging of the vertebrae and discs in all patients. In sequential scans, change in direction of wedging was also seen. In several patients there was reverse wedging in the discs that counteracted increased wedging of the vertebrae such that no change in overall Cobb angle was seen. CONCLUSION. Sequential MRI data showed complex patterns of deformity progression. Changes to the wedging of individual vertebrae and discs may occur in patients who have no increase in Cobb angle measure; the Cobb method alone may be insufficient to capture the complex mechanisms of deformity progression.

Supine to standing cobb angle change in idiopathic scoliosis: The effect of endplate preselection

INTRODUCTION Standing radiographs are the ‘gold standard’ for clinical assessment of adolescent idiopathic scoliosis (AIS), with the Cobb Angle used to measure the severity and progression of the scoliotic curve. Supine imaging modalities can provide valuable 3D information on scoliotic anatomy, however, due to changes in gravitational loading direction, the geometry of the spine alters between the supine and standing position which in turn affects the Cobb Angle measurement. Previous studies have consistently reported a 7-10° [1-3] Cobb Angle increase from supine to standing, however, none have reported the effect of endplate pre-selection and which (if any) curve parameters affect the supine to standing Cobb Angle difference. CONCLUSION There is a statistically significant relationship between supine to standing Cobb Angle change and fulcrum flexibility. Therefore, this difference can be considered a measure of spinal flexibility. Pre-selecting vertebral endplates causes only minor changes.

Sequential MRI reveals individual level deformities in the growing scoliotic spine that are not seen clinically by the cobb angle

Clinically, the Cobb angle method measures the overall scoliotic curve in the coronal plane but does not measure individual vertebra and disc wedging. The contributions of the vertebrae and discs in the growing scoliotic spine were measured to investigate coronal plane deformity progression with growth. Sequential MRI data in this project showed complex patterns of deformity progression. Changes to the wedging of individual vertebrae and discs may occur in patients who have no increase in Cobb angle measure; the Cobb method alone may be insufficient to capture the complex mechanisms of deformity progression.

Fourier spectral methods for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains ofRn. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.

Genome-wide association study identifies susceptibility loci for open angle glaucoma at TMCO1 and CDKN2B-AS1

We report a genome-wide association study for open-angle glaucoma (OAG) blindness using a discovery cohort of 590 individuals with severe visual field loss (cases) and 3,956 controls. We identified associated loci at TMCO1 (rs4656461[G] odds ratio (OR) = 1.68, P = 6.1 × 10-10) and CDKN2B-AS1 (rs4977756[A] OR = 1.50, P = 4.7 × 10-9). We replicated these associations in an independent cohort of cases with advanced OAG (rs4656461 P = 0.010; rs4977756 P = 0.042) and two additional cohorts of less severe OAG (rs4656461 combined discovery and replication P = 6.00 × 10-14, OR = 1.51, 95% CI 1.35-1.68; rs4977756 combined P = 1.35 × 10-14, OR = 1.39, 95% CI 1.28-1.51). We show retinal expression of genes at both loci in human ocular tissues. We also show that CDKN2A and CDKN2B are upregulated in the retina of a rat model of glaucoma. © 2011 Nature America, Inc. All rights reserved.

Development of multi-rotor localised surveillance using multi-spectral sensors for plant biosecurity

This report describes a proof of concept for multi-rotor localised surveillance using a multi-spectral sensor for plant biosecurity applications. A literature review was conducted on previous applications using airborne multispectral imaging for plant biosecurity purposes. A ready built platform was purchased and modified in order to fit and provide suitable clearance for a Tetracam Mini-MCA multispectral camera. The appropriate risk management documents were developed allowing the platform and the multi-spectral camera to be tested extensively. However, due to technical difficulties with the platform the Mini- MCA was not mounted to the platform. Once a suitable platform is developed, future extensions can be conducted into the suitability of the Mini-MCA for airborne surveillance of Australian crops.

Constrained Linear Spectral Unmixing Technique for Regional Land Cover Mapping Using MODIS Data

Over the last few decades, there has been a significant land cover (LC) change across the globe due to the increasing demand of the burgeoning population and urban sprawl. In order to take account of the change, there is a need for accurate and up-to-date LC maps. Mapping and monitoring of LC in India is being carried out at national level using multi-temporal IRS AWiFS data. Multispectral data such as IKONOS, Landsat-TM/ETM+, IRS-ICID LISS-III/IV, AWiFS and SPOT-5, etc. have adequate spatial resolution (similar to 1m to 56m) for LC mapping to generate 1:50,000 maps. However, for developing countries and those with large geographical extent, seasonal LC mapping is prohibitive with data from commercial sensors of limited spatial coverage. Superspectral data from the MODIS sensor are freely available, have better temporal (8 day composites) and spectral information. MODIS pixels typically contain a mixture of various LC types (due to coarse spatial resolution of 250, 500 and 1000 in), especially in more fragmented landscapes. In this context, linear spectral unmixing would be useful for mapping patchy land covers, such as those that characterise much of the Indian subcontinent. This work evaluates the existing unmixing technique for LC mapping using MODIS data, using end-members that are extracted through Pixel Purity Index (PPI), Scatter plot and N-dimensional visualisation. The abundance maps were generated for agriculture, built up, forest, plantations, waste land/others and water bodies. The assessment of the results using ground truth and a LISS-III classified map shows 86% overall accuracy, suggesting the potential for broad-scale applicability of the technique with superspectral data for natural resource planning and inventory applications. Index Terms-Remote sensing, digital

Small-angle neutron scattering study of micellar structures of dimeric surfactants

Dimeric or gemini surfactants consist of two hydrophobic chains and two hydrophilic head groups co; valently connected by a hydrocarbon spacer. Small-angle neutron scattering measurements from bis-cationic C16H33N+(CH3)(2)-(CH2)(m)-N+(CH3)(2)C(16)H(33)2Br(-) dimeric surfactants, referred to-as 16-m-16, for different length of hydrocarbon spacers m-3-6, 8, 10, and 12, are reported. The measurements have been carried out at various concentrations: C=2.5 and 10 mM for all m and C=30 and 50 mM for m greater than or equal to 5. It is found that micellar structure depends on the length of the spacer. Micelles are disks for m=3, cylindrical for m=4, and prolate ellipsoidals for other values of m. These structural results are in agreement with the theoretical predictions based on the packing parameter. It has also been observed that conformation of the spacer and the hydrophobic chains in the interior of the micelle change as the length of the spacer is increased. The concentration dependence for m greater than or equal to 5 shows that the effect of surfactant concentration on the size of the micelle is more pronounced for m=5 and 12 than for the intermediate spacers. The fractional charge on the micelle increases with the increase in spacer length and decreases when the concentration is increased.

1H and 13C NMR spectra of some unsymmetric N,N-dipyridyl ureas: spectral assignments and molecular conformation

Abstract: The H-1 NMR spectra of N-(2-pyridyl), N'-(3-pyridyl)ureas and N-(2-pyridyl), N'-(4-pyridyl)ureas in CDCl3 and (CD3)(2)CO have been assigned with the aid of COSY and NOE experiments and chemical shift and coupling constant correlations, The C-13 NMR spectra in CDCl3 were analysed utilizing the HETCOR and proton coupled spectra, The H-1 NMR spectra, NOE effects and MINDO/3 calculations have been utilized to show that the molecular conformation of these compounds has the 2-pyridyl ring coplanar with the urea plane with the N-H group hydrogen bonded to the nitrogen of the 2-pyridyl group on the other urea nitrogen while the 3/4-pyridyl group rotates rapidly about the N-C-3/N-C-4 bond.