Fourier spectral methods for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains ofRn. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.

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.

Impact of online privacy concerns and brand reputation on consumer willingness to provide personal information

The aim of this research was to identify the role of brand reputation in encouraging consumer willingness to provide personal data online, for the benefits of personalisation. This study extends on Malhotra, Kim and Agarwal’s (2004) Internet Users Information Privacy Concerns Model, and uses the theoretical underpinning of Social Contract Theory to assess how brand reputation moderates the relationship between trusting beliefs and perceived value (Privacy Calculus framework) with willingness to give personal information. The research is highly relevant as most privacy research undertaken to date focuses on consumer related concerns. Very little research exists examining the role of brand reputation and online privacy. Practical implications of this research include gaining knowledge as to how to minimise online privacy concerns; improve brand reputation; and provide insight on how to reduce consumer resistance to the collection of personal information and encourage consumer opt-in.

Enterprise system investments for competitive advantage: An empirical study of Swiss SMEs

Previous research identifies various reasons companies invest in information technology (IT), often as a means to generate value. To add to the discussion of IT value generation, this study investigates investments in enterprise software systems that support business processes. Managers of more than 500 Swiss small and medium-sized enterprises (SMEs) responded to a survey regarding the levels of their IT investment in enterprise software systems and the perceived utility of those investments. The authors use logistic and ordinary least squares regression to examine whether IT investments in two business processes affect SMEs' performance and competitive advantage. Using cluster analysis, they also develop a firm typology with four distinct groups that differ in their investments in enterprise software systems. These findings offer key implications for both research and managerial practice.

A multi-centre open-label randomised non-inferiority trial comparing watchful waiting to antibiotic treatment for acute otitis media without perforation in low-risk urban Aboriginal and Torres Strait Islander children (the WATCH trial): study protocol for a randomised controlled trial

Background Treatment guidelines recommend watchful waiting for children older than 2 years with acute otitis media (AOM) without perforation, unless they are at high risk of complications. The high prevalence of chronic suppurative otitis media (CSOM) in remote Aboriginal and Torres Strait Islander communities leads these children to be classified as high risk. Urban Aboriginal and Torres Strait Islander children are at lower risk of complications, but evidence to support the subsequent recommendation for watchful waiting in this population is lacking. Methods/Design This non-inferiority multi-centre randomised controlled trial will determine whether watchful waiting is non-inferior to immediate antibiotics for urban Aboriginal and Torres Strait Islander children with AOM without perforation. Children aged 2 − 16 years with AOM who are considered at low risk for complications will be recruited from six participating urban primary health care services across Australia. We will obtain informed consent from each participant or their guardian. The primary outcome is clinical resolution on day 7 (no pain, no fever of at least 38 °C, no bulging eardrum and no complications of AOM such as perforation or mastoiditis) as assessed by general practitioners or nurse practitioners. Participants and outcome assessors will not be blinded to treatment. With a sample size of 198 children in each arm, we have 80 % power to detect a non-inferiority margin of up to 10 % at a significance level of 5 %, assuming clinical improvement of at least 80 % in both groups. Allowing for a 20 % dropout rate, we aim to recruit 495 children. We will analyse both by intention-to-treat and per protocol. We will assess the cost- effectiveness of watchful waiting compared to immediate antibiotic prescription. We will also report on the implementation of the trial from the perspectives of parents/carers, health professionals and researchers. Discussion The trial will provide evidence for the safety and effectiveness of watchful waiting for the management of AOM in Aboriginal and Torres Strait Islander children living in urban settings who are considered to be at low risk of complications.

Characterization of anomalous relaxation using the time-fractional Bloch equation and multiple echo T2 *-weighted magnetic resonance imaging at 7T

PURPOSE To study the utility of fractional calculus in modeling gradient-recalled echo MRI signal decay in the normal human brain. METHODS We solved analytically the extended time-fractional Bloch equations resulting in five model parameters, namely, the amplitude, relaxation rate, order of the time-fractional derivative, frequency shift, and constant offset. Voxel-level temporal fitting of the MRI signal was performed using the classical monoexponential model, a previously developed anomalous relaxation model, and using our extended time-fractional relaxation model. Nine brain regions segmented from multiple echo gradient-recalled echo 7 Tesla MRI data acquired from five participants were then used to investigate the characteristics of the extended time-fractional model parameters. RESULTS We found that the extended time-fractional model is able to fit the experimental data with smaller mean squared error than the classical monoexponential relaxation model and the anomalous relaxation model, which do not account for frequency shift. CONCLUSIONS We were able to fit multiple echo time MRI data with high accuracy using the developed model. Parameters of the model likely capture information on microstructural and susceptibility-induced changes in the human brain.