Periodic discrete Darboux transforms

We express Darboux transformations of discrete polarised curves as parallel sections of discrete connections in the quaternionic formalism. This immediately leads to the linearisation of the monodromy of the transformation. We also consider the integrable reduction to the case of discrete bicycle correspondence. Applying our method to the case of discrete circles, we obtain closed-form discrete parametrisations of all (closed) Darboux transforms and (closed) bicycle correspondences

A Mediterranean-style dietary intervention supplemented with fish oil improves diet quality and mental health in people with depression: A randomized controlled trial (HELFIMED)

Objectives: We investigated whether a Mediterranean-style diet (MedDiet) supplemented with fish oil can improve mental health in adults suffering depression. Methods: Adults with self-reported depression were randomized to receive fortnightly food hampers and MedDiet cooking workshops for 3 months and fish oil supplements for 6 months, or attend social groups fortnightly for 3 months. Assessments at baseline, 3 and 6 months included mental health, quality of life (QoL) and dietary questionnaires, and blood samples for erythrocyte fatty acid analysis. Results: n = 152 eligible adults aged 18–65 were recruited (n = 95 completed 3-month and n = 85 completed 6-month assessments). At 3 months, the MedDiet group had a higher MedDiet score (t = 3.95, P  <  0.01), consumed more vegetables (t = 3.95, P  <  0.01), fruit (t = 2.10, P = 0.04), nuts (t = 2.29, P = 0.02), legumes (t = 2.41, P = 0.02) wholegrains (t = 2.63, P = 0.01), and vegetable diversity (t = 3.27, P  <  0.01); less unhealthy snacks (t = −2.10, P = 0.04) and red meat/chicken (t = −2.13, P = 0.04). The MedDiet group had greater reduction in depression (t = −2.24, P = 0.03) and improved mental health QoL scores (t = 2.10, P = 0.04) at 3 months. Improved diet and mental health were sustained at 6 months. Reduced depression was correlated with an increased MedDiet score (r = −0.298, P = 0.01), nuts (r = −0.264, P = 0.01), and vegetable diversity (r = −0.303, P = 0.01). Other mental health improvements had similar correlations, most notably for increased vegetable diversity and legumes. There were some correlations between increased omega-3, decreased omega-6 and improved mental health. Discussion: This is one of the first randomized controlled trials to show that healthy dietary changes are achievable and, supplemented with fish oil, can improve mental health in people with depression. © 2017 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Grou

A 6-month randomised controlled trial investigating effects of Mediterranean-style diet and fish oil supplementation on dietary behaviour change, mental and cardiometabolic health and health-related quality of life in adults with depression (HELFIMED): Study protocol

Modern diets, characterised by excess consumption of processed foods, are accompanied by an epidemic of chronic diseases. Cardiovascular disease and depression carry large burden of disease, and overlap with each other. Poor dietary patterns have been identified as an independent risk factor for depression while healthy diets are protective. Traditional Mediterranean diets have been shown to reduce risk of cardiovascular disease; however there is a need for clinical trials in people with depression. This study reports the protocol and 3-month dietary outcomes of a Mediterranean-style diet randomised controlled trial (RCT) conducted in adults with self-reported depression. Methods: HELFIMED is a parallel 6-month RCT investigating whether dietary patterns can be improved in people with depressive symptoms and whether healthier diet combined with fish oil supplementation can improve mental and cardiometabolic health and quality of life. Adults aged 18-65 with self-reported depressive symptoms (N=164) were block-randomised on age and gender between May 2014 to June 2015 to receive nutrition education, food hampers fortnightly cooking workshops based on Mediterranean-style dietary principles for 3 months and fish oil supplementation for 6 months, or to attend fortnightly social groups (control group) for 3 months. All participants completed mental health, quality of life and dietary questionnaires and provided anthropometric measurements, blood and urine samples at baseline, 3 and 6 months. Dietary changes: Compared to the control group (n=44) at 3 months the treatment group (n=60) reported a higher Mediterranean diet score (P<0.001), consumed more vegetables (P=0.002), wholegrains (P=0.040), nuts (P=0.028), legumes (p=0.029) and fish (p=0.020), greater diversity of vegetables (p=0.001) and less takeaway food (p=0.070), unhealthy snacks (p=0.061) and meat/chicken (p=0.005). Discussion: Over 3-months this intervention improved dietary patterns of adults suffering depressive symptoms and may provide a useful protocol for sustainable dietary change. Sustainability of dietary changes will be assessed at 6 months. Further analyses using linear mixed modelling and regression analysis will investigate the effects of dietary changes and fish oil supplementation on mental and cardiometabolic health and quality of life

A chemical survey of exoplanets with ARIEL

Thousands of exoplanets have now been discovered with a huge range of masses, sizes and orbits: from rocky Earth-like planets to large gas giants grazing the surface of their host star. However, the essential nature of these exoplanets remains largely mysterious: there is no known, discernible pattern linking the presence, size, or orbital parameters of a planet to the nature of its parent star. We have little idea whether the chemistry of a planet is linked to its formation environment, or whether the type of host star drives the physics and chemistry of the planet’s birth, and evolution. ARIEL was conceived to observe a large number (~1000) of transiting planets for statistical understanding, including gas giants, Neptunes, super-Earths and Earth-size planets around a range of host star types using transit spectroscopy in the 1.25–7.8 μm spectral range and multiple narrow-band photometry in the optical. ARIEL will focus on warm and hot planets to take advantage of their well-mixed atmospheres which should show minimal condensation and sequestration of high-Z materials compared to their colder Solar System siblings. Said warm and hot atmospheres are expected to be more representative of the planetary bulk composition. Observations of these warm/hot exoplanets, and in particular of their elemental composition (especially C, O, N, S, Si), will allow the understanding of the early stages of planetary and atmospheric formation during the nebular phase and the following few million years. ARIEL will thus provide a representative picture of the chemical nature of the exoplanets and relate this directly to the type and chemical environment of the host star. ARIEL is designed as a dedicated survey mission for combined-light spectroscopy, capable of observing a large and well-defined planet sample within its 4-year mission lifetime. Transit, eclipse and phase-curve spectroscopy methods, whereby the signal from the star and planet are differentiated using knowledge of the planetary ephemerides, allow us to measure atmospheric signals from the planet at levels of 10–100 part per million (ppm) relative to the star and, given the bright nature of targets, also allows more sophisticated techniques, such as eclipse mapping, to give a deeper insight into the nature of the atmosphere. These types of observations require a stable payload and satellite platform with broad, instantaneous wavelength coverage to detect many molecular species, probe the thermal structure, identify clouds and monitor the stellar activity. The wavelength range proposed covers all the expected major atmospheric gases from e.g. H2O, CO2, CH4NH3, HCN, H2S through to the more exotic metallic compounds, such as TiO, VO, and condensed species. Simulations of ARIEL performance in conducting exoplanet surveys have been performed – using conservative estimates of mission performance and a full model of all significant noise sources in the measurement – using a list of potential ARIEL targets that incorporates the latest available exoplanet statistics. The conclusion at the end of the Phase A study, is that ARIEL – in line with the stated mission objectives – will be able to observe about 1000 exoplanets depending on the details of the adopted survey strategy, thus confirming the feasibility of the main science objectives