Perceived social support and community adaptation in schizophrenia

Prompted by the continuing transition to community care, mental health nurses are considering the role of social support in community adaptation. This article demonstrates the importance of distinguishing between kinds of social support and presents findings from the first round data of a longitudinal study of community adaptation in 156 people with schizophrenia conducted in Brisbane, Australia. All clients were interviewed using the relevant subscales of the Diagnostic Interview Schedule to confirm a primary diagnosis of schizophrenia. The study set out to investigate the relationship between community adaptation and social support. Community adaptation was measured with the Brief Psychiatric Rating Scale (BPRS), the Life Skills Profile (LSP) and measures of dissatisfaction with life and problems in daily living developed by the authors. Social support was measured with the Arizona Social Support Interview Schedule (ASSIS). The BPRS and ASSIS were incorporated into a client interview conducted by trained interviewers. The LSP was completed on each client by an informal carer (parent, relative or friend) or a professional carer (case manager or other health professional) nominated by the client. Hierarchical regression analysis was used to examine the relationship between community adaptation and four sets of social support variables. Given the order in which variables were entered in regression equations, a set of perceived social support variables was found to account for the largest unique variance of four measures of community adaptation in 96 people with schizophrenia for whom complete data are available from the first round of the three-wave longitudinal study. A set of the subjective experiences of the clients accounted for the largest unique variance in measures of symptomatology, life skills, dissatisfaction with life, and problems in daily living. Sets of community support, household support and functional variables accounted for less variance. Implications for mental health nursing practice are considered.

Exploring a functional approach to attitudinal brand loyalty

What psychological function does brand loyalty serve? Drawing on Katz’s (1960) Functional Theory of Attitudes, we propose that there are four functions (or motivational antecedents) of loyalty: utilitarian, knowledge, value-expressive and ego-defensive. We discuss how each function relates to the three dimensions of loyalty (i.e. emotional, cognitive, and behavioural loyalty). Then this conceptualisation of brand loyalty is explored using four consumer focus groups. These exploratory results demonstrate that the application of a functional approach to brand loyalty yields insights which have not been apparent in previous research. More specifically, this paper notes insights in relation to brand loyalty from a consumer’s perspective, including the notion that the ego-defensive function is an orientation around what others think and feel. This creates the possibilities for future research into brand loyalty via social network analysis, in order to better understand how the thoughts of others affect consumers’ loyalty attributes. --------------------------------------------------------------------------------

Adaptive stepsize based on control theory for stochastic differential equations

The numerical solution of stochastic differential equations (SDEs) has been focused recently on the development of numerical methods with good stability and order properties. These numerical implementations have been made with fixed stepsize, but there are many situations when a fixed stepsize is not appropriate. In the numerical solution of ordinary differential equations, much work has been carried out on developing robust implementation techniques using variable stepsize. It has been necessary, in the deterministic case, to consider the "best" choice for an initial stepsize, as well as developing effective strategies for stepsize control-the same, of course, must be carried out in the stochastic case. In this paper, proportional integral (PI) control is applied to a variable stepsize implementation of an embedded pair of stochastic Runge-Kutta methods used to obtain numerical solutions of nonstiff SDEs. For stiff SDEs, the embedded pair of the balanced Milstein and balanced implicit method is implemented in variable stepsize mode using a predictive controller for the stepsize change. The extension of these stepsize controllers from a digital filter theory point of view via PI with derivative (PID) control will also be implemented. The implementations show the improvement in efficiency that can be attained when using these control theory approaches compared with the regular stepsize change strategy.

Numerical simulation of stochastic ordinary differential equations in biomathematical modelling

In this work we discuss the effects of white and coloured noise perturbations on the parameters of a mathematical model of bacteriophage infection introduced by Beretta and Kuang in [Math. Biosc. 149 (1998) 57]. We numerically simulate the strong solutions of the resulting systems of stochastic ordinary differential equations (SDEs), with respect to the global error, by means of numerical methods of both Euler-Taylor expansion and stochastic Runge-Kutta type.

Numerical methods for strong solutions of stochastic differential equations : an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations

The pioneering work of Runge and Kutta a hundred years ago has ultimately led to suites of sophisticated numerical methods suitable for solving complex systems of deterministic ordinary differential equations. However, in many modelling situations, the appropriate representation is a stochastic differential equation and here numerical methods are much less sophisticated. In this paper a very general class of stochastic Runge-Kutta methods is presented and much more efficient classes of explicit methods than previous extant methods are constructed. In particular, a method of strong order 2 with a deterministic component based on the classical Runge-Kutta method is constructed and some numerical results are presented to demonstrate the efficacy of this approach.

Numerical solutions of stochastic differential equations – implementation and stability issues

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively.

A variable stepsize implementation for stochastic differential equations

Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge-Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this forces the stepsize to be very small. This paper presents a completely general variable stepsize implementation of an embedded Runge Kutta pair for solving SDEs numerically; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path.

Adams-Type Methods for the Numerical Solution of Stochastic Ordinary Differential Equations

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively. (C) 2000 Elsevier Science B.V. All rights reserved.

A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations

In Burrage and Burrage [1] it was shown that by introducing a very general formulation for stochastic Runge-Kutta methods, the previous strong order barrier of order one could be broken without having to use higher derivative terms. In particular, methods of strong order 1.5 were developed in which a Stratonovich integral of order one and one of order two were present in the formulation. In this present paper, general order results are proven about the maximum attainable strong order of these stochastic Runge-Kutta methods (SRKs) in terms of the order of the Stratonovich integrals appearing in the Runge-Kutta formulation. In particular, it will be shown that if an s-stage SRK contains Stratonovich integrals up to order p then the strong order of the SRK cannot exceed min{(p + 1)/2, (s - 1)/2), p greater than or equal to 2, s greater than or equal to 3 or 1 if p = 1.

Efficient solution of multiple cracks in great number using eigen COD boundary integral equations with iteration procedure

A newly developed computational approach is proposed in the paper for the analysis of multiple crack problems based on the eigen crack opening displacement (COD) boundary integral equations. The eigen COD particularly refers to a crack in an infinite domain under fictitious traction acting on the crack surface. With the concept of eigen COD, the multiple cracks in great number can be solved by using the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix to determine all the unknown CODs step by step. To deal with the interactions among cracks for multiple crack problems, all cracks in the problem are divided into two groups, namely the adjacent group and the far-field group, according to the distance to the current crack in consideration. The adjacent group contains cracks with relatively small distances but strong effects to the current crack, while the others, the cracks of far-field group are composed of those with relatively large distances. Correspondingly, the eigen COD of the current crack is computed in two parts. The first part is computed by using the fictitious tractions of adjacent cracks via the local Eshelby matrix derived from the traction boundary integral equations in discretized form, while the second part is computed by using those of far-field cracks so that the high computational efficiency can be achieved in the proposed approach. The numerical results of the proposed approach are compared not only with those using the dual boundary integral equations (D-BIE) and the BIE with numerical Green's functions (NGF) but also with those of the analytical solutions in literature. The effectiveness and the efficiency of the proposed approach is verified. Numerical examples are provided for the stress intensity factors of cracks, up to several thousands in number, in both the finite and infinite plates.

Nutritional support and functional capacity in chronic obstructive pulmonary disease: A systematic review and meta-analysis

Currently there is confusion about the value of using nutritional support to treat malnutrition and improve functional outcomes in chronic obstructive pulmonary disease (COPD). This systematic review and meta-analysis of randomised controlled trials (RCTs) aimed to clarify the effectiveness of nutritional support in improving functional outcomes in COPD. A systematic review identified 12 RCTs (n = 448) in stable COPD patients investigating the effects of nutritional support [dietary advice (1 RCT), oral nutritional supplements (ONS; 10 RCTs), enteral tube feeding (1 RCT)] versus control on functional outcomes. Meta-analysis of the changes induced by intervention found that whilst respiratory function (FEV(1,) lung capacity, blood gases) was unresponsive to nutritional support, both inspiratory and expiratory muscle strength (PI max +3.86 SE 1.89 cm H(2) O, P = 0.041; PE max +11.85 SE 5.54 cm H(2) O, P = 0.032) and handgrip strength (+1.35 SE 0.69 kg, P = 0.05) were significantly improved, and associated with weight gains of ≥ 2 kg. Nutritional support produced significant improvements in quality of life in some trials, although meta-analysis was not possible. It also led to improved exercise performance and enhancement of exercise rehabilitation programmes. This systematic review and meta-analysis demonstrates that nutritional support in COPD results in significant improvements in a number of clinically relevant functional outcomes, complementing a previous review showing improvements in nutritional intake and weight.

Assessment of neuroretinal function in a group of functional amblyopes with documented LGN deficits

Purpose In this study we examine neuroretinal function in five amblyopes, who had been shown in previous functional MRI (fMRI) studies to have compromised function of the lateral geniculate nucleus (LGN), to determine if the fMRI deficit in amblyopia may have its origin at the retinal level. Methods We used slow flash multifocal ERG (mfERG) and compared averaged five ring responses of the amblyopic and fellow eyes across a 35 deg field. Central responses were also assessed over a field which was about 6.3 deg in diameter. We measured central retinal thickness using optical coherence tomography. Central fields were measured using the MP1-Microperimeter which also assesses ocular fixation during perimetry. MfERG data were compared with fMRI results from a previous study. Results Amblyopic eyes had reduced response density amplitudes (first major negative to first positive (N1-P1) responses) for the central and paracentral retina (up to 18 deg diameter) but not for the mid-periphery (from 18 to 35 deg). Retinal thickness was within normal limits for all eyes, and not different between amblyopic and fellow eyes. Fixation was maintained within the central 4° more than 80% of the time by four of the five participants; fixation assessed using bivariate contour ellipse areas (BCEA) gave rankings similar to those of the MP-1 system. There was no significant relationship between BCEA and mfERG response for either amblyopic or fellow eye. There was no significant relationship between the central mfERG eye response difference and the selective blood oxygen level dependent (BOLD) LGN eye response difference previously seen in these participants. Conclusions Retinal responses in amblyopes can be reduced within the central field without an obvious anatomical basis. Additionally, this retinal deficit may not be the reason why the LGN BOLD (blood oxygen level dependent) responses are reduced for amblyopic eye stimulation.

Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners

We develop a fast Poisson preconditioner for the efficient numerical solution of a class of two-sided nonlinear space fractional diffusion equations in one and two dimensions using the method of lines. Using the shifted Gr¨unwald finite difference formulas to approximate the two-sided(i.e. the left and right Riemann-Liouville) fractional derivatives, the resulting semi-discrete nonlinear systems have dense Jacobian matrices owing to the non-local property of fractional derivatives. We employ a modern initial value problem solver utilising backward differentiation formulas and Jacobian-free Newton-Krylov methods to solve these systems. For efficient performance of the Jacobianfree Newton-Krylov method it is essential to apply an effective preconditioner to accelerate the convergence of the linear iterative solver. The key contribution of our work is to generalise the fast Poisson preconditioner, widely used for integer-order diffusion equations, so that it applies to the two-sided space fractional diffusion equation. A number of numerical experiments are presented to demonstrate the effectiveness of the preconditioner and the overall solution strategy.