The health benefits of the long-chain omega-3 PUFA, eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA) have been known for over 50 years and underpin the UK population recommendation to consume > 450 mg EPA+DHA per day. These recommendations, last revised in 2004, are based mainly on epidemiological evidence. Much research has been conducted in the interim. Most RCTs use doses of EPA+DHA of 840 mg per day or more. For anti-inflammatory, triglyceride lowering and anti-hypertensive effects, > 1.5 g EPA+DHA per day is needed. Cognitive benefits are also likely to require these higher intakes. Farmed salmon now contains considerably less EPA+DHA relative to wild-fish, and relative to farmed fish of 20 years ago, meaning one portion per week will no longer provide the equivalent of 450 mg EPA+DHA per day. Oily fish alone can only provide a fraction of the EPA+DHA required to meet global needs. Furthermore, there is low global oily fish consumption, with typical intakes of < 200 mg EPA+DHA per day, and limited intakes in vegans and vegetarians. Therefore, there is an urgent need for affordable, acceptable, alternative EPA+DHA sources, including vegan/vegetarian friendly options, such as bio-enriched poultry, red meat and milk products; fortified foods; enriched oilseeds e.g. genetically modified Camelina sativa; algae and algal oils; and approaches which enhance endogenous EPA/DHA synthesis. In this narrative review we suggest that current EPA+DHA intake recommendations are too low, consider EPA/DHA from a holistic health-sustainability perspective, and identify research, policy and knowledge mobilisation areas which need attention.

We show that the loop space of a moment-angle complex associated to a two-dimensional simplicial complex decomposes as a finite type product of spheres, loops on spheres and certain indecomposable spaces which appear in the loop space decomposition of Moore spaces. We also give conditions on certain subcomplexes under which, localised away from sufficiently many primes, the loop space of a moment-angle complex decomposes as a finite type product of spheres and loops on spheres.

Conjectures are given for Hilbert series related to polynomial invariants of finite general linear groups: one for invariants mod Frobenius powers of the irrelevant ideal and one for cofixed spaces of polynomials.