A preconditioned numerical solver for stiff nonlinear reaction-diffusion equations with fractional Laplacians that avoids dense matrices

The numerical solution of fractional partial differential equations poses significant computational challenges in regard to efficiency as a result of the spatial nonlocality of the fractional differential operators. The dense coefficient matrices that arise from spatial discretisation of these operators mean that even one-dimensional problems can be difficult to solve using standard methods on grids comprising thousands of nodes or more. In this work we address this issue of efficiency for one-dimensional, nonlinear space-fractional reaction–diffusion equations with fractional Laplacian operators. We apply variable-order, variable-stepsize backward differentiation formulas in a Jacobian-free Newton–Krylov framework to advance the solution in time. A key advantage of this approach is the elimination of any requirement to form the dense matrix representation of the fractional Laplacian operator. We show how a banded approximation to this matrix, which can be formed and factorised efficiently, can be used as part of an effective preconditioner that accelerates convergence of the Krylov subspace iterative solver. Our approach also captures the full contribution from the nonlinear reaction term in the preconditioner, which is crucial for problems that exhibit stiff reactions. Numerical examples are presented to illustrate the overall effectiveness of the solver.

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.

The subordinated processes controlled by a family of subordinators and corresponding Fokker-Planck type equations

In this work, we consider subordinated processes controlled by a family of subordinators which consist of a power function of a time variable and a negative power function of an α-stable random variable. The effect of parameters in the subordinators on the subordinated process is discussed. By suitable variable substitutions and the Laplace transform technique, the corresponding fractional Fokker–Planck-type equations are derived. We also compute their mean square displacements in a free force field. By choosing suitable ranges of parameters, the resulting subordinated processes may be subdiffusive, normal diffusive or superdiffusive

Using quantitative wastewater analysis to measure daily usage of conventional and emerging illicit drugs at an annual music festival

Introduction and Aims Wastewater analysis provides a non-intrusive way of measuring drug use within a population. We used this approach to determine daily use of conventional illicit drugs [cannabis, cocaine, methamphetamine and 3,4-methylenedioxymethamphetamine (MDMA)] and emerging illicit psychostimulants (benzylpiperazine, mephedrone and methylone) in two consecutive years (2010 and 2011) at an annual music festival. Design and Methods Daily composite wastewater samples, representative of the festival, were collected from the on-site wastewater treatment plant and analysed for drug metabolites. Data over 2 years were compared using Wilcoxon matched-pair test. Data from 2010 festival were compared with data collected at the same time from a nearby urban community using equivalent methods. Results Conventional illicit drugs were detected in all samples whereas emerging illicit psychostimulants were found only on specific days. The estimated per capita consumption of MDMA, cocaine and cannabis was similar between the two festival years. Statistically significant (P < 0.05; Z = −2.0–2.2) decreases were observed in use of methamphetamine and one emerging illicit psychostimulant (benzyl piperazine). Only consumption of MDMA was elevated at the festival compared with the nearby urban community. Discussion and Conclusions Rates of substance use at this festival remained relatively consistent over two monitoring years. Compared with the urban community, drug use among festival goers was only elevated for MDMA, confirming its popularity in music settings. Our study demonstrated that wastewater analysis can objectively capture changes in substance use at a music setting without raising major ethical issues. It would potentially allow effective assessments of drug prevention strategies in such settings in the future.

Challenges and opportunities in using wastewater analysis to measure drug use in a small prison facility

Introduction and Aims Wastewater analysis (WWA) is intended to be a direct and objective method of measuring substance use in large urban populations. It has also been used to measure prison substance use in two previous studies. The application of WWA in this context has raised questions as to how best it might be used to measure illicit drug use in prisons, and whether it can also be used to measure prescription misuse. We applied WWA to a small regional prison to measure the use of 12 licit and illicit substances. We attempted to measure the non-medical use of methadone and buprenorphine and to compare our findings with the results of the prison's mandatory drug testing (MDT). Design and Methods Representative daily composite samples were collected for two periods of 12 consecutive days in May to July 2013 and analysed for 18 drug metabolites. Prescription data and MDT results were obtained from the prison and compared with the substance use estimates calculated from WWA data. Results Daily use of methamphetamine, methadone, buprenorphine and codeine was detected, while sporadic detection of ketamine and methylone was also observed. Overall buprenorphine misuse appeared to be greater than methadone misuse. Discussion and Conclusions Compared with MDT, WWA provides a more comprehensive picture of prison substance use. WWA also has the potential to measure the misuse of medically prescribed substances. However, a great deal of care must be exercised in quantifying the usage of any substance in small populations, such as in prisons.

Development and validation of a questionnaire to measure health professionals' attitudes toward identification of female victimes of domestic violence

Background Domestic violence against women is a major public health problem and violations of women’s human rights. Health professionals could play an important role in screening for the victims. From the evidence to date, it is unclear whether health professionals do play an active role in identification of the victims. Objectives To develop a reliable and valid instrument to measure health professionals’ attitude to identifying female victims of domestic violence. Methods A primary questionnaire was constructed in accordance with established guidelines using the Theory of Planned Behaviour Ajzen (1975) to develop an instrument to measure health professionals’ attitudes in identifying female victim of DV. An expert panel was used to establish content validity. Focus groups amongst a group of health professionals (N = 5) of the target population were performed to confirm face validity. A pilot study (N = 30 nurses and doctors) was undertaken to elicit the feasibility and reliability of the questionnaire. The questionnaire was also administered a second time after one week to check the stability of the tests. Results Feedbacks of the expert panel’s and group discussion confirmed that the questionnaire had the content and face validity. Cronbach’s alpha values for all the items were greater than 0.7. Strong correlations between the direct and indirect measures confirmed that the indirect measures were well constructed. High test-retest correlations confirmed that the measures were reliable in the sense of temporal stability. Significance This tool has the potential to be used by researchers in expanding the knowledge base in this important area.

Ability of commonly used prediction equations to predict resting energy expenditure in children with inflammatory bowel disease

Background: Paediatric onset inflammatory bowel disease (IBD) may cause alterations in energy requirements and invalidate the use of standard prediction equations. Our aim was to evaluate four commonly used prediction equations for resting energy expenditure (REE) in children with IBD. Methods: Sixty-three children had repeated measurements of REE as part of a longitudinal research study yielding a total of 243 measurements. These were compared with predicted REE from Schofield, Oxford, FAO/WHO/UNU, and Harris-Benedict equations using the Bland-Altman method. Results: Mean (±SD) age of the patients was 14.2 (2.4) years. Mean measured REE was 1566 (336) kcal per day compared with 1491 (236), 1441 (255), 1481 (232), and 1435 (212) kcal per day calculated from Schofield, Oxford, FAO/WHO/UNU, and Harris-Benedict, respectively. While the Schofield equation demonstrated the least difference between measured and predicted REE, it, along with the other equations tested, did not perform uniformly across all subjects, indicating greater errors at either end of the spectrum of energy expenditure. Smaller differences were found for all prediction equations for Crohn's disease compared with ulcerative colitis. Conclusions: Of the commonly used equations, the equation of Schofield should be used in pediatric patients with IBD when measured values are not able to be obtained. (Inflamm Bowel Dis 2010;) Copyright © 2010 Crohn's & Colitis Foundation of America, Inc.

Validity of currently used cutoff values of body mass index as a measure of obesity in Sri Lankan children

The aim of the study was to determine the reliability of body mass index based (BMI) cutoff values in diagnosing obesity among Sri Lankan children. Height, weight, waist circumference (WC) and hip circumference (HC) in 282 children were measured. Total body water was determined by deuterium dilution and fat mass (FM) derived using age and gender specific constants. A percentage FM of 30% for girls and 25% for boys were considered as cutoff levels for obesity. Two hundred and eighty two children (M/F: 158/124) were studied and 99 (80%) girls and 72 (45.5%) boys were obese based on % body fat. Eight (6.4%) girls and nine (5.7%) boys were obese based on International Obesity Task Force (IOTF) cutoff values. Percentage FM and WC centile charts were able to diagnose a significant proportion of children as true obese children. The FM and BMI were closely associated in both girls (r = 0.82, p < 0.001) and boys (r = 0.87, p < 0.001). Percentage FM and BMI had a very low but significant association; girls (r = 0.32, p < 0.001) and boys (r = 0.68, p < 0.001). FM had a significant association with WC and HC. BMI based cutoff values had a specificity of 100% but a very low sensitivity, varying between 8% and 23.6%. BMI is a poor indicator of the percentage fat and the commonly used cutoff values were not sensitive to detect cases of childhood obesity in Sri Lankan children.

Applying POVM to model non-orthogonality in quantum cognition

Much of the work currently occurring in the field of Quantum Interaction (QI) relies upon Projective Measurement. This is perhaps not optimal, cognitive states are not nearly as well behaved as standard quantum mechanical systems; they exhibit violations of repeatability, and the operators that we use to describe measurements do not appear to be naturally orthogonal in cognitive systems. Here we attempt to map the formalism of Positive Operator Valued Measure (POVM) theory into the domain of semantic memory, showing how it might be used to construct Bell-type inequalities.

Impact of ethnicity upon body composition assessment in Sri Lankan Australian children

Objectives: Obesity is a disease with excess body fat where health is adversely affected. Therefore it is prudent to make the diagnosis of obesity based on the measure of percentage body fat. Body composition of a group of Australian children of Sri Lankan origin were studied to evaluate the applicability of some bedside techniques in the measurement of percentage body fat. Methods: Height (H) and weight (W) was measured and BMI (W/H2) calculated. Bioelectrical impedance analysis (BIA) was measured using tetra polar technique with an 800 μA current of 50 Hz frequency. Total body water was used as a reference method and was determined by deuterium dilution and fat free mass and hence fat mass (FM) derived using age and gender specific constants. Percentage FM was estimated using four predictive equations, which used BIA and anthropometric measurements. Results: Twenty-seven boys and 15 girls were studied with mean ages being 9.1 years and 9.6 years, respectively. Girls had a significantly higher FM compared to boys. The mean percentage FM of boys (22.9 ± 8.7%) was higher than the limit for obesity and for girls (29.0 ± 6.0%) it was just below the cut-off. BMI was comparatively low. All but BIA equation in boys under estimated the percentage FM. The impedance index and weight showed a strong association with total body water (r 2 = 0.96, P < 0.001). Except for BIA in boys all other techniques under diagnosed obesity. Conclusions: Sri Lankan Australian children appear to have a high percentage of fat with a low BMI and some of the available indirect techniques are not helpful in the assessment of body composition. Therefore ethnic and/or population specific predictive equations have to be developed for the assessment of body composition, especially in a multicultural society using indirect methods such as BIA or anthropometry.

Comparison of measured sleeping metabolic rate and predicted basal metabolic rate during the first year of life : evidence of a bias changing with increasing metabolic rate

Objective: To compare measurements of sleeping metabolic rate (SMR) in infancy with predicted basal metabolic rate (BMR) estimated by the equations of Schofield. Methods: Some 104 serial measurements of SMR by indirect calorimetry were performed in 43 healthy infants at 1.5, 3, 6, 9 and 12 months of age. Predicted BMR was calculated using the weight only (BMR-wo) and weight and height (BMR-wh) equations of Schofield for 0-3-y-olds. Measured SMR values were compared with both predictive values by means of the Bland-Altman statistical test. Results: The mean measured SMR was 1.48 MJ/day. The mean predicted BMR values were 1.66 and 1.47 MJ/day for the weight only and weight and height equations, respectively. The Bland-Altman analysis showed that BMR-wo equation on average overestimated SMR by 0.18 MJ/day (11%) and the BMR-wh equation underestimated SMR by 0.01 MJ/day (1%). However the 95% limits of agreement were wide: -0.64 to + 0.28 MJ/day (28%) for the former equation and -0.39 to + 0.41 MJ/day (27%) for the latter equation. Moreover there was a significant correlation between the mean of the measured and predicted metabolic rate and the difference between them. Conclusions: The wide variation seen in the difference between measured and predicted metabolic rate and the bias probably with age indicates there is a need to measure actual metabolic rate for individual clinical care in this age group.

Wife beating: A measure to deal with marital disharmony or a license for misconduct

Wife beating is not a new phenomena rather it has been practiced from pre historic time till date. This was due to the fact that in all the civilizations and under all religions, woman was considered subjugated to men. Her natural physical weakness had also made her vulnerable for violence. Islam reinforced womanhood by protecting her rights and providing her respect in the family and society at large. However, it is not interpreted accurately in male dominant society due to the existence of a patriarchal social setup. Adding to the ignorance regarding the position of women in Islam, the presence of injustice and mal practices in contemporary Muslim societies has been taken up as a weak point of Islam by non Muslims as well by less informed Muslims. The reasons for denying women’s rights in Pakistani society could be summed up as lack of education, ignorance about Islamic teachings, feudal and tribal cultural traditions, male dominated patriarchal attitudes, poverty, unemployment and misinterpretations regarding precise teachings of Quran and Sunnah. There are many misconceptions regarding the stance of Islam on wife beating as well. It is commonly understood that Islam gives permission for wife beating in the Quranic verse 4:34. This article will describe the relationship between husband and wife in the light of Quranic verse4:34 and will explore the sanctions of wife beating and its dimensions. Furthermore, it will aim to remove misunderstandings and prejudged opinions related to the concerned issue, in the light of Quran and Sunnah.

An integrated mathematical approach to measure the capacity of MMTS

This article focusses upon multi-modal transportation systems (MMTS) and the issues surrounding the determination of system capacity. For that purpose a multi-objective framework is advocated that integrates all the different modes and many different competing capacity objectives. This framework is analytical in nature and facilitates a variety of capacity querying and capacity expansion planning.

Working covariance model selection for generalized estimating equations

We investigate methods for data-based selection of working covariance models in the analysis of correlated data with generalized estimating equations. We study two selection criteria: Gaussian pseudolikelihood and a geodesic distance based on discrepancy between model-sensitive and model-robust regression parameter covariance estimators. The Gaussian pseudolikelihood is found in simulation to be reasonably sensitive for several response distributions and noncanonical mean-variance relations for longitudinal data. Application is also made to a clinical dataset. Assessment of adequacy of both correlation and variance models for longitudinal data should be routine in applications, and we describe open-source software supporting this practice.