Maternal concern about her toddler undereating and becoming underweight and use of feeding practices - analysis of the NOURISH and SAIDI cohorts using structural equation modeling

The chubby baby who eats well is desirable in our culture. Perceived low weight gains and feeding concerns are common reasons mothers seek advice in the early years. In contrast, childhood obesity is a global public health concern. Use of coercive feeding practices, prompted by maternal concern about weight, may disrupt a child’s innate self regulation of energy intake, promoting overeating and overweight. This study describes predictors of maternal concern about her child undereating/becoming underweight and feeding practices. Mothers in the control group of the NOURISH and South Australian Infants Dietary Intake studies (n = 332) completed a self-administered questionnaire when the child was aged 12–16 months. Weight-for-age z-score (WAZ)was derived from weight measured by study staff. Mean age (SD) was 13.8 (1.3) months, mean WAZ (SD), 0.58 (0.86) and 49% were male. WAZ and two questions describing food refusal were combined in a structural equation model with four items from the Infant feeding Questionnaire (IFQ) to form the factor ‘Concern about undereating/weight’. Structural relationships were drawn between concern and IFQ factors ‘awareness of infant’s hunger and satiety cues’, ‘use of food to calm infant’s fussiness’ and ‘feeding infant on a schedule’, resulting in a model of acceptable fit. Lower WAZ and higher frequency of food refusal predicted higher maternal concern. Higher maternal concern was associated with lower awareness of infant cues (r = −.17, p = .01) and greater use of food to calm (r = .13, p = .03). In a cohort of healthy children, maternal concern about undereating and underweight was associated with practices that have the potential to disrupt self-regulation.

A critical review of structural equation modeling applications in construction research

Structural equation modeling (SEM) is a versatile multivariate statistical technique, and applications have been increasing since its introduction in the 1980s. This paper provides a critical review of 84 articles involving the use of SEM to address construction related problems over the period 1998–2012 including, but not limited to, seven top construction research journals. After conducting a yearly publication trend analysis, it is found that SEM applications have been accelerating over time. However, there are inconsistencies in the various recorded applications and several recurring problems exist. The important issues that need to be considered are examined in research design, model development and model evaluation and are discussed in detail with reference to current applications. A particularly important issue concerns the construct validity. Relevant topics for efficient research design also include longitudinal or cross-sectional studies, mediation and moderation effects, sample size issues and software selection. A guideline framework is provided to help future researchers in construction SEM applications.

A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation

This paper aims to develop a meshless approach based on the Point Interpolation Method (PIM) for numerical simulation of a space fractional diffusion equation. Two fully-discrete schemes for the one-dimensional space fractional diffusion equation are obtained by using the PIM and the strong-forms of the space diffusion equation. Numerical examples with different nodal distributions are studied to validate and investigate the accuracy and efficiency of the newly developed meshless approach.

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.

High order unconditionally stable difference schemes for the Riesz space-fractional telegraph equation

In this paper, a class of unconditionally stable difference schemes based on the Pad´e approximation is presented for the Riesz space-fractional telegraph equation. Firstly, we introduce a new variable to transform the original dfferential equation to an equivalent differential equation system. Then, we apply a second order fractional central difference scheme to discretise the Riesz space-fractional operator. Finally, we use (1, 1), (2, 2) and (3, 3) Pad´e approximations to give a fully discrete difference scheme for the resulting linear system of ordinary differential equations. Matrix analysis is used to show the unconditional stability of the proposed algorithms. Two examples with known exact solutions are chosen to assess the proposed difference schemes. Numerical results demonstrate that these schemes provide accurate and efficient methods for solving a space-fractional hyperbolic equation.

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.