Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy

This article aims to fill in the gap of the second-order accurate schemes for the time-fractional subdiffusion equation with unconditional stability. Two fully discrete schemes are first proposed for the time-fractional subdiffusion equation with space discretized by finite element and time discretized by the fractional linear multistep methods. These two methods are unconditionally stable with maximum global convergence order of $O(\tau+h^{r+1})$ in the $L^2$ norm, where $\tau$ and $h$ are the step sizes in time and space, respectively, and $r$ is the degree of the piecewise polynomial space. The average convergence rates for the two methods in time are also investigated, which shows that the average convergence rates of the two methods are $O(\tau^{1.5}+h^{r+1})$. Furthermore, two improved algorithms are constrcted, they are also unconditionally stable and convergent of order $O(\tau^2+h^{r+1})$. Numerical examples are provided to verify the theoretical analysis. The comparisons between the present algorithms and the existing ones are included, which show that our numerical algorithms exhibit better performances than the known ones.

A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients

In this paper, we derive a new nonlinear two-sided space-fractional diffusion equation with variable coefficients from the fractional Fick’s law. A semi-implicit difference method (SIDM) for this equation is proposed. The stability and convergence of the SIDM are discussed. For the implementation, we develop a fast accurate iterative method for the SIDM by decomposing the dense coefficient matrix into a combination of Toeplitz-like matrices. This fast iterative method significantly reduces the storage requirement of O(n2)O(n2) and computational cost of O(n3)O(n3) down to n and O(nlogn)O(nlogn), where n is the number of grid points. The method retains the same accuracy as the underlying SIDM solved with Gaussian elimination. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

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.

Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation

In this paper, we consider a two-sided space-fractional diffusion equation with variable coefficients on a finite domain. Firstly, based on the nodal basis functions, we present a new fractional finite volume method for the two-sided space-fractional diffusion equation and derive the implicit scheme and solve it in matrix form. Secondly, we prove the stability and convergence of the implicit fractional finite volume method and conclude that the method is unconditionally stable and convergent. Finally, some numerical examples are given to show the effectiveness of the new numerical method, and the results are in excellent agreement with theoretical analysis.

Numeracy counts in the statistical reasoning equation

The relationship between mathematics and statistical reasoning frequently receives comment (Vere-Jones 1995, Moore 1997); however most of the research into the area tends to focus on maths anxiety. Gnaldi (Gnaldi 2003) showed that in a statistics course for psychologists, the statistical understanding of students at the end of the course depended on students’ basic numeracy, rather than the number or level of previous mathematics courses the student had undertaken. As part of a study into the development of statistical thinking at the interface between secondary and tertiary education, students enrolled in an introductory data analysis subject were assessed regarding their statistical reasoning ability, basic numeracy skills and attitudes towards statistics. This work reports on the relationships between these factors and in particular the importance of numeracy to statistical reasoning.

Meltdown : a tool to help in the interpretation of thermal melt curves acquired by differential scanning fluorimetry

The output of a differential scanning fluorimetry (DSF) assay is a series of melt curves, which need to be interpreted to get value from the assay. An application that translates raw thermal melt curve data into more easily assimilated knowledge is described. This program, called “Meltdown,” conducts four main activities—control checks, curve normalization, outlier rejection, and melt temperature (Tm) estimation—and performs optimally in the presence of triplicate (or higher) sample data. The final output is a report that summarizes the results of a DSF experiment. The goal of Meltdown is not to replace human analysis of the raw fluorescence data but to provide a meaningful and comprehensive interpretation of the data to make this useful experimental technique accessible to inexperienced users, as well as providing a starting point for detailed analyses by more experienced users.

Differential segmentation responses to an alcohol social marketing program

Objective This study seeks establish whether meaningful subgroups exist within a 14-16 year old adolescent population and if these segments respond differently to the Game On: Know Alcohol (GOKA) intervention, a school-based alcohol social marketing program. Methodology This study is part of a larger cluster randomized controlled evaluation of the Game On: Know Alcohol (GOKA) program implemented in 14 schools in 2013/2014. TwoStep cluster analysis was conducted to segment 2114 high school adolescents (14-16 years old) on the basis of 22 demographic, behavioral and psychographic variables. Program effects on knowledge, attitudes, behavioral intentions, social norms, expectancies and refusal self-efficacy of identified segments was subsequently examined. Results Three segments were identified: (1) Abstainers (2) Bingers (3) Moderate Drinkers. Program effects varied significantly across segments. The strongest positive change effects post participation were observed for the Bingers, while mixed effects were evident for Moderate Drinkers and Abstainers. Conclusions These findings provide preliminary empirical evidence supporting application of social marketing segmentation in alcohol education programs. Development of targeted programs that meet the unique needs of each of the three identified segments is indicated to extend the social marketing footprint in alcohol education.

Investigating the impact of project definition clarity on project performance: Structural equation modeling study

Having a clear project definition is crucial for successful construction projects. It affects design quality, project communication between stakeholders and final project performance in terms of cost, schedule and quality. This study examines the relationship between project definition and final project performance through a structural equation model comprising 4 latent constructs and 6 path hypotheses using data from a questionnaire survey of 120 general contractors in the Malaysian construction industry. The results show that in the study population, all three items impact the project performance, but the link between design quality and project performance is indirect. Instead, the clarity of project definition affects project performance indirectly through design quality and project communication and design quality affects project performance indirectly through project communication. The primary contribution is to provide quantitative confirmation of the more general statements made in the literature from around the world and therefore adds to and consolidates existing knowledge. Practical implications derived from the finding are also proposed for various project stakeholders. Furthermore, as lack of the clarity of project definition is a very common occurrence in construction projects globally, these findings have important ramifications for all construction projects in expanding and clarifying existing knowledge on what is needed for the successful delivery of construction projects.

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.

Differential interaction between the C2B domain of synaptotagmin-I and the Drosophila stonedA and stonedB proteins

The stoned locus in Drosophila encodes two proteins StonedA (STNA) and StonedB (STNB), both of which have been suggested to act as adaptins in mediating synaptic vesicle recycling. A combination of immunological, genetic and biochemical studies have shown an interaction of STNA and STNB with the C2B domain of Synaptotagmin-I (SYT-1), an integral synaptic vesicle protein that mediates Ca2+-dependent exocytosis, as well as endocytosis. The C2B domain of SYT-1 contains an AP-2 binding site that controls the size of recycled vesicles, and a C-terminal tryptophan-containing motif that acts as an internalization signal. Investigation of SYT-1 mutations in Drosophila has shown that altering the Ca2+ binding region of the C2B domain, results in a reduction in the rate of vesicle recycling, implicating this region in SYT-I endocytosis. In this poster, we report the molecular dissection of the interactions between the STNA and STNB proteins and the C2B domain of SYT-1. Deletion of the AP-2 binding site decreased the binding of both STNA and STNB. However, C-terminal deletions of the C2B domain significantly increased STNB binding. In contrast, the same C-terminal deletions reduced the affinity of the C2B domain for STNA. The possible interactions of both STNB and STNA with the Ca2+ binding region of SYT-1 will be also investigated.

An evaluation of differential reinforcement of other behavior, differential reinforcement of incompatible behavior, and restitution for the management of aggressive behaviors

A 46 year old institutionalized retarded woman was referred for treatment because of frequent verbal abuse and physically aggressive behaviors. A multicomponent behavioral intervention consisting of differential reinforcement of other behaviors, differential reinforcement of incompatible behaviors, and restitution was implemented. A sequential withdrawal design was used in order to evaluate the effects of components of the original intervention, and to provide a measure of response maintenance. Results indicated a marked decrease in verbal abuse and elimination of physical aggression. Verbal abuse recurred when the restitution procedure was withdrawn. The relative efficacy of the different interventions is discussed with respect to the behavioral management of aggression.

Differential processing of thematic and categorical conceptual relations in spoken word production

Studies of semantic context effects in spoken word production have typically distinguished between categorical (or taxonomic) and associative relations. However, associates tend to confound semantic features or morphological representations, such as whole-part relations and compounds (e.g., BOAT-anchor, BEE-hive). Using a picture-word interference paradigm and functional magnetic resonance imaging (fMRI), we manipulated categorical (COW-rat) and thematic (COW-pasture) TARGET-distractor relations in a balanced design, finding interference and facilitation effects on naming latencies, respectively, as well as differential patterns of brain activation compared with an unrelated distractor condition. While both types of distractor relation activated the middle portion of the left middle temporal gyrus (MTG) consistent with retrieval of conceptual or lexical representations, categorical relations involved additional activation of posterior left MTG, consistent with retrieval of a lexical cohort. Thematic relations involved additional activation of the left angular gyrus. These results converge with recent lesion evidence implicating the left inferior parietal lobe in processing thematic relations and may indicate a potential role for this region during spoken word production.

The differential impact of monetary policy announcements and explanatory minutes releases on the Australian interest rate futures market

Unlike US and Continental European jurisdictions, Australian monetary policy announcements are not followed promptly by projections materials or comprehensive summaries that explain the decision process. This information is disclosed 2 weeks later when the explanatory minutes of the Reserve Bank board meeting are released. This paper is the first study to exploit the features of the Australian monetary policy environment in order to examine the differential impact of monetary policy announcements and explanatory statements on the Australian interest rate futures market. We find that both monetary policy announcements and explanatory minutes releases have a significant impact on the implied yield and volatility of Australian interest rate futures contracts. When the differential impact of these announcements is examined using the full sample, no statistically significant difference is found. However, when the sample is partitioned based on stable periods and the Global Financial Crisis, a differential impact is evident. Further, contrary to the findings of Kim and Nguyen (2008), Lu et al. (2009), and Smales (2012a), the response along the yield curve, is found to be indifferent between the short and medium terms.

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.

A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems

In order to simulate stiff biochemical reaction systems, an explicit exponential Euler scheme is derived for multidimensional, non-commutative stochastic differential equations with a semilinear drift term. The scheme is of strong order one half and A-stable in mean square. The combination with this and the projection method shows good performance in numerical experiments dealing with an alternative formulation of the chemical Langevin equation for a human ether a-go-go related gene ion channel mode