GPU accelerated algorithms for computing matrix function vector products with applications to exponential integrators and fractional diffusion

The efficient computation of matrix function vector products has become an important area of research in recent times, driven in particular by two important applications: the numerical solution of fractional partial differential equations and the integration of large systems of ordinary differential equations. In this work we consider a problem that combines these two applications, in the form of a numerical solution algorithm for fractional reaction diffusion equations that after spatial discretisation, is advanced in time using the exponential Euler method. We focus on the efficient implementation of the algorithm on Graphics Processing Units (GPU), as we wish to make use of the increased computational power available with this hardware. We compute the matrix function vector products using the contour integration method in [N. Hale, N. Higham, and L. Trefethen. Computing Aα, log(A), and related matrix functions by contour integrals. SIAM J. Numer. Anal., 46(5):2505–2523, 2008]. Multiple levels of preconditioning are applied to reduce the GPU memory footprint and to further accelerate convergence. We also derive an error bound for the convergence of the contour integral method that allows us to pre-determine the appropriate number of quadrature points. Results are presented that demonstrate the effectiveness of the method for large two-dimensional problems, showing a speedup of more than an order of magnitude compared to a CPU-only implementation.

The Jean Chretien Pledge to Africa act: Patent law and humanitarian aid

This article evaluates the implementation of the WTO General Council Decision in 2003, which resolved that developed nations could export patented pharmaceutical drugs to member states in order to address public health issues - such as HIV/AIDS, tuberculosis, malaria and other epidemics. The Jean Chretien Pledge to Africa Act 2004 (Canada) provides authorisation for the export of pharmaceutical drugs from Canada to developing countries to address public health epidemics. The European Union has issued draft regulations governing the export of pharmaceutical drugs. A number of European countries - including Norway, the Netherlands, France, and Switzerland - are seeking to pass domestic legislation to give force to the WTO General Council Decision. Australia has shown little initiative in seeking to implement such international agreements dealing with access to essential medicines. It is argued that Australia should implement humanitarian legislation to embody the WTO General Council Decision, emulating models in Canada, Norway, and the European Union. Ideally, there should be no right of first refusal; the list of pharmaceutical drugs should be open-ended; and the eligible importing countries should not be limited to members of the WTO.

Extending genetic linkage analysis to diffusion tensor images to map single gene effects on brain fiber architecture

We extended genetic linkage analysis - an analysis widely used in quantitative genetics - to 3D images to analyze single gene effects on brain fiber architecture. We collected 4 Tesla diffusion tensor images (DTI) and genotype data from 258 healthy adult twins and their non-twin siblings. After high-dimensional fluid registration, at each voxel we estimated the genetic linkage between the single nucleotide polymorphism (SNP), Val66Met (dbSNP number rs6265), of the BDNF gene (brain-derived neurotrophic factor) with fractional anisotropy (FA) derived from each subject's DTI scan, by fitting structural equation models (SEM) from quantitative genetics. We also examined how image filtering affects the effect sizes for genetic linkage by examining how the overall significance of voxelwise effects varied with respect to full width at half maximum (FWHM) of the Gaussian smoothing applied to the FA images. Raw FA maps with no smoothing yielded the greatest sensitivity to detect gene effects, when corrected for multiple comparisons using the false discovery rate (FDR) procedure. The BDNF polymorphism significantly contributed to the variation in FA in the posterior cingulate gyrus, where it accounted for around 90-95% of the total variance in FA. Our study generated the first maps to visualize the effect of the BDNF gene on brain fiber integrity, suggesting that common genetic variants may strongly determine white matter integrity.

Investigating the population structure of Queensland invasive Streptococcus pneumoniae isolates in children: Using a modified multi-locus variable number of tandem repeat analysis and a novel minimum SNPs capsular typing method

This research investigated the use of DNA fingerprinting to characterise the bacteria Streptococcus pneumoniae or pneumococcus, and hence gain insight into the development of new vaccines or antibiotics. Different bacterial DNA fingerprinting methods were studied, and a novel method was developed and validated, which characterises different cell coatings that pneumococci produce. This method was used to study the epidemiology of pneumococci in Queensland before and after the introduction of the current pneumococcal vaccine. This study demonstrated that pneumococcal disease is highly prevalent in children under four years, that the bacteria can `switch' its cell coating to evade the vaccine, and that some DNA fingerprinting methods are more discriminatory than others. This has an impact on understanding which strains are more prone to cause invasive disease. Evidence of the excellent research findings have been published in high impact internationally refereed journals.

Development of height-weight based equation for assessment of body composition in Sri Lankan children

Objective To develop a height and weight based equation to estimate total body water (TBW) in Sri Lankan children. Methods Cross sectional descriptive study done involving 5–15 year old healthy children. Height and weight were measured. TBW was assessed using isotope dilution method (D2O) and fat free mass (FFM) calculated. Multiple regression analysis was used to develop prediction equation and validated using PRESS statistical technique. Height, weight and sex code (male=1; female=0) were used as prediction variables. Results This study provides height and weight equation for the prediction of TBW in Sri Lankan children. To the best of our knowledge there are no published height weight prediction equations validated on South Asian populations. Conclusion Results of this study need to be affirmed by more studies on other closely related populations by using multicomponent body composition.

Comparative analysis and distribution of Omega-3 lcPUFA Biosynthesis genes in marine molluscs

Recent research has identified marine molluscs as an excellent source of omega-3 long-chain polyunsaturated fatty acids (lcPUFAs), based on their potential for endogenous synthesis of lcPUFAs. In this study we generated a representative list of fatty acyl desaturase (Fad) and elongation of very long-chain fatty acid (Elovl) genes from major orders of Phylum Mollusca, through the interrogation of transcriptome and genome sequences, and various publicly available databases. We have identified novel and uncharacterised Fad and Elovl sequences in the following species: Anadara trapezia, Nerita albicilla, Nerita melanotragus, Crassostrea gigas, Lottia gigantea, Aplysia californica, Loligo pealeii and Chlamys farreri. Based on alignments of translated protein sequences of Fad and Elovl genes, the haeme binding motif and histidine boxes of Fad proteins, and the histidine box and seventeen important amino acids in Elovl proteins, were highly conserved. Phylogenetic analysis of aligned reference sequences was used to reconstruct the evolutionary relationships for Fad and Elovl genes separately. Multiple, well resolved clades for both the Fad and Elovl sequences were observed, suggesting that repeated rounds of gene duplication best explain the distribution of Fad and Elovl proteins across the major orders of molluscs. For Elovl sequences, one clade contained the functionally characterised Elovl5 proteins, while another clade contained proteins hypothesised to have Elovl4 function. Additional well resolved clades consisted only of uncharacterised Elovl sequences. One clade from the Fad phylogeny contained only uncharacterised proteins, while the other clade contained functionally characterised delta-5 desaturase proteins. The discovery of an uncharacterised Fad clade is particularly interesting as these divergent proteins may have novel functions. Overall, this paper presents a number of novel Fad and Elovl genes suggesting that many mollusc groups possess most of the required enzymes for the synthesis of lcPUFAs.

The relationship between number of fruits, vegetables, and noncore foods tried at age 14 months and food preferences, dietary intake patterns, fussy eating behavior, and weight status at age 3.7 years

Objective We examined whether exposure to a greater number of fruits, vegetables, and noncore foods (ie, nutrient poor and high in saturated fats, added sugars, or added salt) at age 14 months was related to children’s preference for and intake of these foods as well as maternal-reported food fussiness and measured child weight status at age 3.7 years. Methods This study reports secondary analyses of longitudinal data from mothers and children (n=340) participating in the NOURISH randomized controlled trial. Exposure was quantified as the number of food items (n=55) tried by a child from specified lists at age 14 months. At age 3.7 years, food preferences, intake patterns, and fussiness (also at age 14 months) were assessed using maternal-completed, established questionnaires. Child weight and length/height were measured by study staff at both age points. Multivariable linear regression models were tested to predict food preferences, intake patterns, fussy eating, and body mass index z score at age 3.7 years adjusting for a range of maternal and child covariates. Results Having tried a greater number of vegetables, fruits, and noncore foods at age 14 months predicted corresponding preferences and higher intakes at age 3.7 years but did not predict child body mass index z score. Adjusting for fussiness at age 14 months, having tried more vegetables at age 14 months was associated with lower fussiness at age 3.7 years. Conclusions These prospective analyses support the hypothesis that early taste and texture experiences influence subsequent food preferences and acceptance. These findings indicate introduction to a variety of fruits and vegetables and limited noncore food exposure from an early age are important strategies to improve later diet quality.

Early mathematical learning: Number processing skills and executive function at 5 and 8 years of age

This research investigated differences and associations in performance in number processing and executive function for children attending primary school in a large Australian metropolitan city. In a cross-sectional study, performance of 25 children in the first full-time year of school, (Prep; mean age = 5.5 years) and 21 children in Year 3 (mean age = 8.5 years) completed three number processing tasks and three executive function tasks. Year 3 children consistently outperformed the Prep year children on measures of accuracy and reaction time, on the tasks of number comparison, calculation, shifting, and inhibition but not on number line estimation. The components of executive function (shifting, inhibition, and working memory) showed different patterns of correlation to performance on number processing tasks across the early years of school. Findings could be used to enhance teachers’ understanding about the role of the cognitive processes employed by children in numeracy learning, and so inform teachers’ classroom practices.

Ortho-Dihydroxyl-9,10-anthraquinone dyes as visible-light sensitizers that exhibit a high turnover number for hydrogen evolution

Pt/TiO2 sensitized by the cheap and organic ortho-dihydroxyl-9,10-anthraquinone dyes, such as Alizarin and Alizarin Red, achieved a TON of approximately 10 000 (TOF > 250 h−1 for the first ten hours) during >80 hours of visible light irradiation (>420 nm) for photocatalytic hydrogen evolution when triethanolamine was used as the sacrificial donor. The stability and activity enhancements can be attributed to the two highly serviceable redox reactions involving the 9,10-dicarbonyl and ortho-dihydroxyl groups of the anthracene ring, respectively

Numerical analysis of a new space-time variable fractional order advection-dispersion equation

Many physical processes appear to exhibit fractional order behavior that may vary with time and/or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider a new space–time variable fractional order advection–dispersion equation on a finite domain. The equation is obtained from the standard advection–dispersion equation by replacing the first-order time derivative by Coimbra’s variable fractional derivative of order α(x)∈(0,1]α(x)∈(0,1], and the first-order and second-order space derivatives by the Riemann–Liouville derivatives of order γ(x,t)∈(0,1]γ(x,t)∈(0,1] and β(x,t)∈(1,2]β(x,t)∈(1,2], respectively. We propose an implicit Euler approximation for the equation and investigate the stability and convergence of the approximation. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

On the effect of Reynolds number for flow past three side-by-side square cylinders for unequal gap spacings

Flow patterns and aerodynamic characteristics behind three side-by-side square cylinders has been found depending upon the unequal gap spacing (g1 = s1/d and g2 = s2/d) between the three cylinders and the Reynolds number (Re) using the Lattice Boltzmann method. The effect of Reynolds numbers on the flow behind three cylinders are numerically studied for 75 ≤ Re ≤ 175 and chosen unequal gap spacings such as (g1, g2) = (1.5, 1), (3, 4) and (7, 6). We also investigate the effect of g2 while keeping g1 fixed for Re = 150. It is found that a Reynolds number have a strong effect on the flow at small unequal gap spacing (g1, g2) = (1.5, 1.0). It is also found that the secondary cylinder interaction frequency significantly contributes for unequal gap spacing for all chosen Reynolds numbers. It is observed that at intermediate unequal gap spacing (g1, g2) = (3, 4) the primary vortex shedding frequency plays a major role and the effect of secondary cylinder interaction frequencies almost disappear. Some vortices merge near the exit and as a result small modulation found in drag and lift coefficients. This means that with the increase in the Reynolds numbers and unequal gap spacing shows weakens wakes interaction between the cylinders. At large unequal gap spacing (g1, g2) = (7, 6) the flow is fully periodic and no small modulation found in drag and lift coefficients signals. It is found that the jet flows for unequal gap spacing strongly influenced the wake interaction by varying the Reynolds number. These unequal gap spacing separate wake patterns for different Reynolds numbers: flip-flopping, in-phase and anti-phase modulation synchronized, in-phase and anti-phase synchronized. It is also observed that in case of equal gap spacing between the cylinders the effect of gap spacing is stronger than the Reynolds number. On the other hand, in case of unequal gap spacing between the cylinders the wake patterns strongly depends on both unequal gap spacing and Reynolds number. The vorticity contour visualization, time history analysis of drag and lift coefficients, power spectrum analysis of lift coefficient and force statistics are systematically discussed for all chosen unequal gap spacings and Reynolds numbers to fully understand this valuable and practical problem.

Two-scale computational modelling of water flow in unsaturated soils containing irregular-shaped inclusions

The focus of this paper is two-dimensional computational modelling of water flow in unsaturated soils consisting of weakly conductive disconnected inclusions embedded in a highly conductive connected matrix. When the inclusions are small, a two-scale Richards’ equation-based model has been proposed in the literature taking the form of an equation with effective parameters governing the macroscopic flow coupled with a microscopic equation, defined at each point in the macroscopic domain, governing the flow in the inclusions. This paper is devoted to a number of advances in the numerical implementation of this model. Namely, by treating the micro-scale as a two-dimensional problem, our solution approach based on a control volume finite element method can be applied to irregular inclusion geometries, and, if necessary, modified to account for additional phenomena (e.g. imposing the macroscopic gradient on the micro-scale via a linear approximation of the macroscopic variable along the microscopic boundary). This is achieved with the help of an exponential integrator for advancing the solution in time. This time integration method completely avoids generation of the Jacobian matrix of the system and hence eases the computation when solving the two-scale model in a completely coupled manner. Numerical simulations are presented for a two-dimensional infiltration problem.

Post-transcriptional regulation in the nucleus and cytoplasm: study of mean time to threshold (MTT) and narrow escape problem

Messenger RNAs (mRNAs) can be repressed and degraded by small non-coding RNA molecules. In this paper, we formulate a coarsegrained Markov-chain description of the post-transcriptional regulation of mRNAs by either small interfering RNAs (siRNAs) or microRNAs (miRNAs). We calculate the probability of an mRNA escaping from its domain before it is repressed by siRNAs/miRNAs via cal- culation of the mean time to threshold: when the number of bound siRNAs/miRNAs exceeds a certain threshold value, the mRNA is irreversibly repressed. In some cases,the analysis can be reduced to counting certain paths in a reduced Markov model. We obtain explicit expressions when the small RNA bind irreversibly to the mRNA and we also discuss the reversible binding case. We apply our models to the study of RNA interference in the nucleus, examining the probability of mRNAs escaping via small nuclear pores before being degraded by siRNAs. Using the same modelling framework, we further investigate the effect of small, decoy RNAs (decoys) on the process of post-transcriptional regulation, by studying regulation of the tumor suppressor gene, PTEN : decoys are able to block binding sites on PTEN mRNAs, thereby educing the number of sites available to siRNAs/miRNAs and helping to protect it from repression. We calculate the probability of a cytoplasmic PTEN mRNA translocating to the endoplasmic reticulum before being repressed by miRNAs. We support our results with stochastic simulations

Spatially explicit structural equation modeling

Structural equation modeling (SEM) is a powerful statistical approach for the testing of networks of direct and indirect theoretical causal relationships in complex data sets with intercorrelated dependent and independent variables. SEM is commonly applied in ecology, but the spatial information commonly found in ecological data remains difficult to model in a SEM framework. Here we propose a simple method for spatially explicit SEM (SE-SEM) based on the analysis of variance/covariance matrices calculated across a range of lag distances. This method provides readily interpretable plots of the change in path coefficients across scale and can be implemented using any standard SEM software package. We demonstrate the application of this method using three studies examining the relationships between environmental factors, plant community structure, nitrogen fixation, and plant competition. By design, these data sets had a spatial component, but were previously analyzed using standard SEM models. Using these data sets, we demonstrate the application of SE-SEM to regularly spaced, irregularly spaced, and ad hoc spatial sampling designs and discuss the increased inferential capability of this approach compared with standard SEM. We provide an R package, sesem, to easily implement spatial structural equation modeling.