Supplement : Efficient weak second-order stochastic Runge-Kutta methods for non-commutative Stratonvich stochastic differential equations

This paper gives a modification of a class of stochastic Runge–Kutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly.

Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions

We consider time-space fractional reaction diffusion equations in two dimensions. This equation is obtained from the standard reaction diffusion equation by replacing the first order time derivative with the Caputo fractional derivative, and the second order space derivatives with the fractional Laplacian. Using the matrix transfer technique proposed by Ilic, Liu, Turner and Anh [Fract. Calc. Appl. Anal., 9:333--349, 2006] and the numerical solution strategy used by Yang, Turner, Liu, and Ilic [SIAM J. Scientific Computing, 33:1159--1180, 2011], the solution of the time-space fractional reaction diffusion equations in two dimensions can be written in terms of a matrix function vector product $f(A)b$ at each time step, where $A$ is an approximate matrix representation of the standard Laplacian. We use the finite volume method over unstructured triangular meshes to generate the matrix $A$, which is therefore non-symmetric. However, the standard Lanczos method for approximating $f(A)b$ requires that $A$ is symmetric. We propose a simple and novel transformation in which the standard Lanczos method is still applicable to find $f(A)b$, despite the loss of symmetry. Numerical results are presented to verify the accuracy and efficiency of our newly proposed numerical solution strategy.

New percentage body fat prediction equations for Japanese females

Anthropometry is a simple and cost-efficient method for the assessment of body composition. However prediction equations to estimate body composition using anthropometry should be ‘population-specific’. Most popular body composition prediction equations for Japanese females were proposed more than 40 years ago and there is some concern regarding their usefulness in Japanese females living today. The aim of this study was to compare percentage body fat (%BF) estimated from anthropometry and dual energy x-ray absorptiometry (DXA) to examine the applicability of commonly used prediction equations in young Japanese females. Body composition of 139 Japanese females aged between 18 and 27 years of age (BMI range: 15.1–29.1 kg/m2) was measured using whole-body DXA (Lunar DPX-LIQ) scans. From anthropometric measurements %BF was estimated using four equations developed from Japanese females. The results showed that the traditionally employed prediction equations for anthropometry significantly (p<0.01) underestimate %BF of young Japanese females and therefore are not valid for the precise estimation of body composition. New %BF prediction equations were proposed from the DXA and anthropometry results. Application of the proposed equations may assist in more accurate assessment of body fatness in Japanese females living today.

Early local functional changes in the human diabetic retina : a global flash multifocal electroretinogram study

Purpose: To investigate early functional changes of local retinal defects in type II diabetic patients using the global flash multifocal electroretinogram (MOFO mfERG). Methods: Thirty-eight diabetic patients and 14 age-matched controls were recruited. Nine of the diabetics were free from diabetic retinopathy (DR), while the remainder had mild to moderate non-proliferative diabetic retinopathy. The MOFO mfERG was performed at high (98%) and low (46%) contrast levels. MfERG responses were grouped into 35 regions for comparison with DR classification at those locations. Z-scores of the regional mfERG responses were compared across different types of DR defects. Results: The mfERG waveform consisted of the direct component (DC) and the induced component (IC). Local reduction in DC and IC amplitudes were found in diabetic patients with and without DR. With increasing severity of retinopathy, there was a further deterioration in amplitude of both components. Under MOFO mfERG paradigm, amplitude was a useful screening parameter. Conclusion: The MOFO mfERG can help in detecting early functional anomalies before the appearance of visible signs, and may assist in monitoring further functional deterioration in diabetic patients.

Homo- and heteronuclear meso,meso-(E)-Ethene-1,2-diyl-Linked Diporphyrins : preparation, X-ray crystal structure, electronic absorption and emission spectra and density functional theory calculations

Homo-and heteronuclear meso,meso-(E)-ethene-1,2-diyl-linked diporphyrins have been prepared by the Suzuki coupling of porphyrinylboronates and iodovinylporphyrins. Combinations comprising 5,10,15-triphenylporphyrin (TriPP) on both ends of the ethene-1,2-diyl bridge M 210 (M 2=H 2/Ni, Ni 2, Ni/Zn, H 4, H 2Zn, Zn 2) and 5,15-bis(3,5-di-tert-butylphenyl)porphyrinato-nickel(II) on one end and H 2, Ni, and ZnTriPP on the other (M 211), enable the first studies of this class of compounds possessing intrinsic polarity. The compounds were characterized by electronic absorption and steady state emission spectra, 1H NMR spectra, and for the Ni 2 bis(TriPP) complex Ni 210, single crystal X-ray structure determination. The crystal structure shows ruffled distortions of the porphyrin rings, typical of Ni II porphyrins, and the (E)-C 2H 2 bridge makes a dihedral angle of 50° with the mean planes of the macrocycles. The result is a stepped parallel arrangement of the porphyrin rings. The dihedral angles in the solid state reflect the interplay of steric and electronic effects of the bridge on interporphyrin communication. The emission spectra in particular, suggest energy transfer across the bridge is fast in conformations in which the bridge is nearly coplanar with the rings. Comparisons of the fluorescence behaviour of H 410 and H 2Ni10 show strong quenching of the free base fluorescence when the complex is excited at the lower energy component of the Soret band, a feature associated in the literature with more planar conformations. TDDFT calculations on the gas-phase optimized geometry of Ni 210 reproduce the features of the experimental electronic absorption spectrum within 0.1 eV. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Should athletes return to sport after applying Ice? A systematic review of the effect of local 3 cooling on functional performance

Applying ice or other forms of topical cooling is a popular method of treating sports injuries. It is commonplace for athletes to return to competitive activity, shortly or immediately after the application of a cold treatment. In this article, we examine the effect of local tissue cooling on outcomes relating to functional performance and to discuss their relevance to the sporting environment. A computerized literature search, citation tracking and hand search was performed up to April, 2011. Eligible studies were trials involving healthy human participants, describing the effects of cooling on outcomes relating to functional performance. Two reviewers independently assessed the validity of included trials and calculated effect sizes. Thirty five trials met the inclusion criteria; all had a high risk of bias. The mean sample size was 19. Meta-analyses were not undertaken due to clinical heterogeneity. The majority of studies used cooling durations >20 minutes. Strength (peak torque/force) was reported by 25 studies with approximately 75% recording a decrease in strength immediately following cooling. There was evidence from six studies that cooling adversely affected speed, power and agility-based running tasks; two studies found this was negated with a short rewarming period. There was conflicting evidence on the effect of cooling on isolated muscular endurance. A small number of studies found that cooling decreased upper limb dexterity and accuracy. The current evidence base suggests that athletes will probably be at a performance disadvantage if they return to activity immediately after cooling. This is based on cooling for longer than 20 minutes, which may exceed the durations employed in some sporting environments. In addition, some of the reported changes were clinically small and may only be relevant in elite sport. Until better evidence is available, practitioners should use short cooling applications and/or undertake a progressive warm up prior to returning to play.

Functional and advanced functional and causal relationship diagrams for remote condition monitoring

Analysing the condition of an asset is a big challenge as there can be many aspects which can contribute to the overall functional reliability of the asset that have to be considered. In this paper we propose a two-step functional and causal relationship diagram (FCRD) to address this problem. In the first step, the FCRD is designed to facilitate the analysis of the condition of an asset by evaluating the interdependence (functional and causal) relationships between different components of the asset with the help of a relationship diagram. This is followed by the advanced FCRD (AFCRD) which refines the information from the FCRD into a comprehensive and manageable format. This new two-step methodology for asset condition monitoring is tested and validated for the case of a water treatment plant. © IMechE 2012.

Efficient preconditioning of the method of lines for solving nonlinear two-sided space-fractional diffusion equations

A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Modeling ion channel dynamics through reflected stochastic differential equations

Ion channels are membrane proteins that open and close at random and play a vital role in the electrical dynamics of excitable cells. The stochastic nature of the conformational changes these proteins undergo can be significant, however current stochastic modeling methodologies limit the ability to study such systems. Discrete-state Markov chain models are seen as the "gold standard," but are computationally intensive, restricting investigation of stochastic effects to the single-cell level. Continuous stochastic methods that use stochastic differential equations (SDEs) to model the system are more efficient but can lead to simulations that have no biological meaning. In this paper we show that modeling the behavior of ion channel dynamics by a reflected SDE ensures biologically realistic simulations, and we argue that this model follows from the continuous approximation of the discrete-state Markov chain model. Open channel and action potential statistics from simulations of ion channel dynamics using the reflected SDE are compared with those of a discrete-state Markov chain method. Results show that the reflected SDE simulations are in good agreement with the discrete-state approach. The reflected SDE model therefore provides a computationally efficient method to simulate ion channel dynamics while preserving the distributional properties of the discrete-state Markov chain model and also ensuring biologically realistic solutions. This framework could easily be extended to other biochemical reaction networks. © 2012 American Physical Society.

The relationship between chronic disease self-efficacy and nutritional status, functional ability and quality of life in older adults at risk of hospital readmission

Background and significance: Older adults with chronic diseases are at increasing risk of hospital admission and readmission. Approximately 75% of adults have at least one chronic condition, and the odds of developing a chronic condition increases with age. Chronic diseases consume about 70% of the total Australian health expenditure, and about 59% of hospital events for chronic conditions are potentially preventable. These figures have brought to light the importance of the management of chronic disease among the growing older population. Many studies have endeavoured to develop effective chronic disease management programs by applying social cognitive theory. However, limited studies have focused on chronic disease self-management in older adults at high risk of hospital readmission. Moreover, although the majority of studies have covered wide and valuable outcome measures, there is scant evidence on examining the fundamental health outcomes such as nutritional status, functional status and health-related quality of life. Aim: The aim of this research was to test social cognitive theory in relation to self-efficacy in managing chronic disease and three health outcomes, namely nutritional status, functional status, and health-related quality of life, in older adults at high risk of hospital readmission. Methods: A cross-sectional study design was employed for this research. Three studies were undertaken. Study One examined the nutritional status and validation of a nutritional screening tool; Study Two explored the relationships between participants. characteristics, self-efficacy beliefs, and health outcomes based on the study.s hypothesized model; Study Three tested a theoretical model based on social cognitive theory, which examines potential mechanisms of the mediation effects of social support and self-efficacy beliefs. One hundred and fifty-seven patients aged 65 years and older with a medical admission and at least one risk factor for readmission were recruited. Data were collected from medical records on demographics, medical history, and from self-report questionnaires. The nutrition data were collected by two registered nurses. For Study One, a contingency table and the kappa statistic was used to determine the validity of the Malnutrition Screening Tool. In Study Two, standard multiple regression, hierarchical multiple regression and logistic regression were undertaken to determine the significant influential predictors for the three health outcome measures. For Study Three, a structural equation modelling approach was taken to test the hypothesized self-efficacy model. Results: The findings of Study One suggested that a high prevalence of malnutrition continues to be a concern in older adults as the prevalence of malnutrition was 20.6% according to the Subjective Global Assessment. Additionally, the findings confirmed that the Malnutrition Screening Tool is a valid nutritional screening tool for hospitalized older adults at risk of readmission when compared to the Subjective Global Assessment with high sensitivity (94%), and specificity (89%) and substantial agreement between these two methods (k = .74, p < .001; 95% CI .62-.86). Analysis data for Study Two found that depressive symptoms and perceived social support were the two strongest influential factors for self-efficacy in managing chronic disease in a hierarchical multiple regression. Results of multivariable regression models suggested advancing age, depressive symptoms and less tangible support were three important predictors for malnutrition. In terms of functional status, a standard regression model found that social support was the strongest predictor for the Instrumental Activities of Daily Living, followed by self-efficacy in managing chronic disease. The results of standard multiple regression revealed that the number of hospital readmission risk factors adversely affected the physical component score, while depressive symptoms and self-efficacy beliefs were two significant predictors for the mental component score. In Study Three, the results of the structural equation modelling found that self-efficacy partially mediated the effect of health characteristics and depression on health-related quality of life. The health characteristics had strong direct effects on functional status and body mass index. The results also indicated that social support partially mediated the relationship between health characteristics and functional status. With regard to the joint effects of social support and self-efficacy, social support fully mediated the effect of health characteristics on self-efficacy, and self-efficacy partially mediated the effect of social support on functional status and health-related quality of life. The results also demonstrated that the models fitted the data well with relative high variance explained by the models, implying the hypothesized constructs under discussion were highly relevant, and hence the application for social cognitive theory in this context was supported. Conclusion: This thesis highlights the applicability of social cognitive theory on chronic disease self-management in older adults at risk of hospital readmission. Further studies are recommended to validate and continue to extend the development of social cognitive theory on chronic disease self-management in older adults to improve their nutritional and functional status, and health-related quality of life.

Anomalous subdiffusion equations by the meshless collocation method

This paper aims to develop an implicit meshless collocation technique based on the moving least squares approximation for numerical simulation of the anomalous subdiffusion equation(ASDE). The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach related to the time discretization are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling of ASDEs.

Analytical solutions of the multi-term modified power law wave equations in a finite domain

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n) (n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko’s Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi term time-space fractional models including fractional Laplacian.