Googling the brain: discovering hierarchical and asymmetric network structures, with applications in neuroscience

Hierarchical organisation is a common feature of many directed networks arising in nature and technology. For example, a well-defined message-passing framework based on managerial status typically exists in a business organisation. However, in many real-world networks such patterns of hierarchy are unlikely to be quite so transparent. Due to the nature in which empirical data is collated the nodes will often be ordered so as to obscure any underlying structure. In addition, the possibility of even a small number of links violating any overall “chain of command” makes the determination of such structures extremely challenging. Here we address the issue of how to reorder a directed network in order to reveal this type of hierarchy. In doing so we also look at the task of quantifying the level of hierarchy, given a particular node ordering. We look at a variety of approaches. Using ideas from the graph Laplacian literature, we show that a relevant discrete optimization problem leads to a natural hierarchical node ranking. We also show that this ranking arises via a maximum likelihood problem associated with a new range-dependent hierarchical random graph model. This random graph insight allows us to compute a likelihood ratio that quantifies the overall tendency for a given network to be hierarchical. We also develop a generalization of this node ordering algorithm based on the combinatorics of directed walks. In passing, we note that Google’s PageRank algorithm tackles a closely related problem, and may also be motivated from a combinatoric, walk-counting viewpoint. We illustrate the performance of the resulting algorithms on synthetic network data, and on a real-world network from neuroscience where results may be validated biologically

Connectivity of Soft Random Geometric Graphs Over Annuli

Nodes are randomly distributed within an annulus (and then a shell) to form a point pattern of communication terminals which are linked stochastically according to the Rayleigh fading of radio-frequency data signals. We then present analytic formulas for the connection probability of these spatially embedded graphs, describing the connectivity behaviour as a dense-network limit is approached. This extends recent work modelling ad hoc networks in non-convex domains.Comment: 12 pages, 6 figure

Positive psychology of Malaysian students: impacts of engagement, motivation, self-compassion and wellbeing on mental health

Malaysia plays a key role in education of the Asia Pacific, expanding its scholarly output rapidly. However, mental health of Malaysian students is challenging, and their help-seeking is low because of stigma. This study explored the relationships between mental health and positive psychological constructs (academic engagement, motivation, self-compassion, and wellbeing), and evaluated the relative contribution of each positive psychological construct to mental health in Malaysian students. An opportunity sample of 153 students completed the measures regarding these constructs. Correlation, regression, and mediation analyses were conducted. Engagement, amotivation, self-compassion, and wellbeing were associated with, and predicted large variance in mental health. Self-compassion was the strongest independent predictor of mental health among all the positive psychological constructs. Findings can imply the strong links between mental health and positive psychology, especially selfcompassion. Moreover, intervention studies to examine the effects of self-compassion training on mental health of Malaysian students appear to be warranted.N/

Compassionate pedagogy: the ethics of care in early childhood professionalism

This paper builds upon an earlier attempt (Taggart, 2011) to articulate a rationale for professional training in early childhood education and care (ECEC) which is ethical as opposed to one which is purely instrumental or rooted in a patriarchal notion of women’s supposed unique suitability. The argument proposes that a feminist approach to ethics, as both socially critical and psychologically affective or flexible, has a particular relevance to professional identity in ECEC. In particular, compassion, as a concept which has both sociological and psychological connotations, foregrounds the ethical dimension of the work whilst overcoming false dichotomies between discourses of ‘children’s rights’ and ‘care’. The implications for the training and professional identity of practitioners are discussed