Hexagonal Smoothness-Increasing Accuracy-Conserving Filtering

Discontinuous Galerkin (DG) methods are a popular class of numerical techniques to solve partial differential equations due to their higher order of accuracy. However, the inter-element discontinuity of a DG solution hinders its utility in various applications, including visualization and feature extraction. This shortcoming can be alleviated by postprocessing of DG solutions to increase the inter-element smoothness. A class of postprocessing techniques proposed to increase the inter-element smoothness is SIAC filtering. In addition to increasing the inter-element continuity, SIAC filtering also raises the convergence rate from order k+1k+1 to order 2k+12k+1 . Since the introduction of SIAC filtering for univariate hyperbolic equations by Cockburn et al. (Math Comput 72(242):577–606, 2003), many generalizations of SIAC filtering have been proposed. Recently, the idea of dimensionality reduction through rotation has been the focus of studies in which a univariate SIAC kernel has been used to postprocess a two-dimensional DG solution (Docampo-Sánchez et al. in Multi-dimensional filtering: reducing the dimension through rotation, 2016. arXiv preprint arXiv:1610.02317). However, the scope of theoretical development of multidimensional SIAC filters has never gone beyond the usage of tensor product multidimensional B-splines or the reduction of the filter dimension. In this paper, we define a new SIAC filter called hexagonal SIAC (HSIAC) that uses a nonseparable class of two-dimensional spline functions called hex splines. In addition to relaxing the separability assumption, the proposed HSIAC filter provides more symmetry to its tensor-product counterpart. We prove that the superconvergence property holds for a specific class of structured triangular meshes using HSIAC filtering and provide numerical results to demonstrate and validate our theoretical results

Late weaning and maternal closeness, associated with advanced motor and visual maturation, reinforce autonomy in healthy, 2-year-old children.

We studied neurodevelopmental outcomes and behaviours in healthy 2-year old children (N = 1306) from Brazil, India, Italy, Kenya and the UK participating in the INTERGROWTH-21st Project. There was a positive independent relationship of duration of exclusive breastfeeding (EBF) and age at weaning with gross motor development, vision and autonomic physical activities, most evident if children were exclusively breastfed for ≥7 months or weaned at ≥7 months. There was no association with cognition, language or behaviour. Children exclusively breastfed from birth to 6 months had, in a dose-effect pattern, adjusting for confounding factors, higher scores for "emotional reactivity". The positive effect of EBF and age at weaning on gross motor, running and climbing scores was strongest among children with the highest scores in maternal closeness proxy indicators. EBF, late weaning and maternal closeness, associated with advanced motor and vision maturation, independently influence autonomous behaviours in healthy children

Nutrition and the ageing brain: moving towards clinical applications

The global increases in life expectancy and population have resulted in a growing ageing population and with it a growing number of people living with age-related neurodegenerative conditions and dementia, shifting focus towards methods of prevention, with lifestyle approaches such as nutrition representing a promising avenue for further development. This overview summarises the main themes discussed during the 3 Symposium on "Nutrition for the Ageing Brain: Moving Towards Clinical Applications" held in Madrid in August 2018, enlarged with the current state of knowledge on how nutrition influences healthy ageing and gives recommendations regarding how the critical field of nutrition and neurodegeneration research should move forward into the future. Specific nutrients are discussed as well as the impact of multi-nutrient and whole diet approaches, showing particular promise to combatting the growing burden of age-related cognitive decline. The emergence of new avenues for exploring the role of diet in healthy ageing, such as the impact of the gut microbiome and development of new techniques (imaging measures of brain metabolism, metabolomics, biomarkers) are enabling researchers to approach finding answers to these questions. But the translation of these findings into clinical and public health contexts remains an obstacle due to significant shortcomings in nutrition research or pressure on the scientific community to communicate recommendations to the general public in a convincing and accessible way. Some promising programs exist but further investigation to improve our understanding of the mechanisms by which nutrition can improve brain health across the human lifespan is still required