A generalisation of the fractional Brownian field based on non-Euclidean norms

We explore a generalisation of the L´evy fractional Brownian field on the Euclidean space based on replacing the Euclidean norm with another norm. A characterisation result for admissible norms yields a complete description of all self-similar Gaussian random fields with stationary increments. Several integral representations of the introduced random fields are derived. In a similar vein, several non-Euclidean variants of the fractional Poisson field are introduced and it is shown that they share the covariance structure with the fractional Brownian field and converge to it. The shape parameters of the Poisson and Brownian variants are related by convex geometry transforms, namely the radial pth mean body and the polar projection transforms.

Imaging emotional brain functions: conceptual and methodological issues

This article reviews the psychophysiological and brain imaging literature on emotional brain function from a methodological point of view. The difficulties in defining, operationalising and measuring emotional activation and, in particular, aversive learning will be considered. Emotion is a response of the organism during an episode of major significance and involves physiological activation, motivational, perceptual, evaluative and learning processes, motor expression, action tendencies and monitoring/subjective feelings. Despite the advances in assessing the physiological correlates of emotional perception and learning processes, a critical appraisal shows that functional neuroimaging approaches encounter methodological difficulties regarding measurement precision (e.g., response scaling and reproducibility) and validity (e.g., response specificity, generalisation to other paradigms, subjects or settings). Since emotional processes are not only the result of localised but also of widely distributed activation, a more representative model of assessment is needed that systematically relates the hierarchy of high- and low-level emotion constructs with the corresponding patterns of activity and functional connectivity of the brain.

Children's performance estimation in mathematics and science tests over a school year: A pilot study

The metacognitve ability to accurately estimate ones performance in a test, is assumed to be of central importance for initializing task-oriented effort. In addition activating adequate problem-solving strategies, and engaging in efficient error detection and correction. Although school children's' ability to estimate their own performance has been widely investigated, this was mostly done under highly-controlled, experimental set-ups including only one single test occasion. Method: The aim of this study was to investigate this metacognitive ability in the context of real achievement tests in mathematics. Developed and applied by a teacher of a 5th grade class over the course of a school year these tests allowed the exploration of the variability of performance estimation accuracy as a function of test difficulty. Results: Mean performance estimations were generally close to actual performance with somewhat less variability compared to test performance. When grouping the children into three achievement levels, results revealed higher accuracy of performance estimations in the high achievers compared to the low and average achievers. In order to explore the generalization of these findings, analyses were also conducted for the same children's tests in their science classes revealing a very similar pattern of results compared to the domain of mathematics. Discussion and Conclusion: By and large, the present study, in a natural environment, confirmed previous laboratory findings but also offered additional insights into the generalisation and the test dependency of students' performances estimations.

New geometries for black hole horizons

We construct several classes of worldvolume effective actions for black holes by integrating out spatial sections of the worldvolume geometry of asymptotically flat black branes. This provides a generalisation of the blackfold approach for higher-dimensional black holes and yields a map between different effective theories, which we exploit by obtaining new hydrodynamic and elastic transport coefficients via simple integrations. Using Euclidean minimal surfaces in order to decouple the fluid dynamics on different sections of the worldvolume, we obtain local effective theories for ultraspinning Myers-Perry branes and helicoidal black branes, described in terms of a stress-energy tensor, particle currents and non-trivial boost vectors. We then study in detail and present novel compact and non-compact geometries for black hole horizons in higher-dimensional asymptotically flat space-time. These include doubly-spinning black rings, black helicoids and helicoidal p-branes as well as helicoidal black rings and helicoidal black tori in D ≥ 6.

Continued fractions built from convex sets and convex functions

In a partially ordered semigroup with the duality (or polarity) transform, it is pos- sible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

Strengthening the food systems governance evidence base: Supporting commensurability of research through a systematic review of methods

Governance of food systems is a poorly understood determinant of food security. Much scholarship on food systems governance is non-empirical, while existing research is often case study-based and theoretically and methodologically incommensurable. This frustrates aggregation of evidence and generalisation. We undertook a systematic review of methods used in food systems governance research with a view to identifying a core set of indicators for future research. We gathered literature through a structured consultation and sampling from recent reviews. Indicators were identified and classified according to the levels and sectors they investigate. We found a concentration of indicators in food production at local to national levels and a sparseness in distribution and consumption. Unsurprisingly, many indicators of institutional structure were found, while agency-related indicators are moderately represented. We call for piloting and validation of these indicators and for methodological development to fill gaps identified. These efforts are expected to support a more consolidated future evidence base and eventual meta-analysis.