Nucleation in scale-free networks

We have studied nucleation dynamics of the Ising model in scale-free networks with degree distribution $P(k)\sim k^{-\gamma}$ by using forward flux sampling method, focusing on how the network topology would influence the nucleation rate and pathway. For homogeneous nucleation, the new phase clusters grow from those nodes with smaller degree, while the cluster sizes follow a power-law distribution. Interestingly, we find that the nucleation rate $R_{Hom}$ decays exponentially with the network size $N$, and accordingly the critical nucleus size increases linearly with $N$, implying that homogeneous nucleation is not relevant in the thermodynamic limit. These observations are robust to the change of $\gamma$ and also present in random networks. In addition, we have also studied the dynamics of heterogeneous nucleation, wherein $w$ impurities are initially added, either to randomly selected nodes or to targeted ones with largest degrees. We find that targeted impurities can enhance the nucleation rate $R_{Het}$ much more sharply than random ones. Moreover, $\ln (R_{Het}/R_{Hom})$ scales as $w^{\gamma-2/\gamma-1}$ and $w$ for targeted and random impurities, respectively. A simple mean field analysis is also present to qualitatively illustrate above simulation results.Comment: 7 pages, 5 figure

Sensory processing in young children with visual impairments:Use and extension of the Sensory Profile

Background: Children with visual impairments (VI) are at risk for sensory processing difficulties. A widely used measure for sensory processing is the Sensory Profile (SP). However, the SP requires adaptation to accommodate for how children with VI experience sensory information. Aims: (1) To examine sensory processing patterns in young children with VI, (2) to develop VI-specific items to use in conjunction with the SP and to determine internal consistency and construct validity of these newly developed items, and (3) to examine the association between sensory processing and and emotional and behavioral problems. Methods: Twenty-six VI-specific items were added to the SP. The SP and these items were completed by caregivers of 90 children with VI between 3 and 8 years old. The Child Behavior Checklist (CBCL) was used to assess emotional and behavioral problems. Results: Three- to five-year-old children with VI have significantly more difficulties in three quadrants of the SP as compared to the norm group. Six- to eight-year-old children with VI have more difficulties in all quadrants. A reliable and valid VI-specific set of 15 items was established following psychometric evaluation. Age-related differences were found in the associations between the SP and CBCL. Conclusion: Although further validation is recommended, this evaluation of the VI-specific item set suggests it has the potential to be a useful measure for children with VI

Explanations for medically unexplained symptoms:a qualitative study on GPs in daily practice consultations

BACKGROUND: General practice is the centre of care for patients with medically unexplained symptoms (MUS). Providing explanations for MUS, i.e. making sense of symptoms, is considered to be an important part of care for MUS patients. However, little is known how general practitioners (GPs) do this in daily practice. OBJECTIVE: This study aimed to explore how GPs explain MUS to their patients during daily general practice consultations. METHODS: A thematic content analysis was performed of how GPs explained MUS to their patients based on 39 general practice consultations involving patients with MUS. RESULTS: GP provided explanations in nearly all consultations with MUS patients. Seven categories of explanation components emerged from the data: defining symptoms, stating causality, mentioning contributing factors, describing mechanisms, excluding explanations, discussing the severity of symptoms and normalizing symptoms. No pattern of how GPs constructed explanations with the various categories was observed. In general, explanations were communicated as a possibility and in a patient-specific way; however, they were not very detailed. CONCLUSION: Although explanations for MUS are provided in most MUS consultations, there seems room for improving the explanations given in these consultations. Further studies on the effectiveness of explanations and on the interaction between patients and GP in constructing these explanations are required in order to make MUS explanations more suitable in daily primary care practice

ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation