Symplectic Bregman Divergences.

We present a generalization of Bregman divergences in finite-dimensional symplectic vector spaces that we term symplectic Bregman divergences. Symplectic Bregman divergences are derived from a symplectic generalization of the Fenchel-Young inequality which relies on the notion of symplectic subdifferentials. The symplectic Fenchel-Young inequality is obtained using the symplectic Fenchel transform which is defined with respect to the symplectic form.

Fast Proxy Centers for the Jeffreys Centroid: The Jeffreys-Fisher-Rao Center and the Gauss-Bregman Inductive Center.

The symmetric Kullback-Leibler centroid, also called the Jeffreys centroid, of a set of mutually absolutely continuous probability distributions on a measure space provides a notion of centrality which has proven useful in many tasks, including information retrieval, information fusion, and clustering. However, the Jeffreys centroid is not available in closed form for sets of categorical or multivariate normal distributions, two widely used statistical models, and thus needs to be approximated numerically in practice. In this paper, we first propose the new Jeffreys-Fisher-Rao center defined as the Fisher-Rao midpoint of the sided Kullback-Leibler centroids as a plug-in replacement of the Jeffreys centroid.

An Environmentally Compatible and Less Costly (Greener) Microwave Digestion Method of Bone Samples Using Dilute Nitric Acid for Analysis by ICP-MS.

An environmentally compatible and less costly (greener) analytical method for the digestion of bone meal samples using microwave-assisted dilute nitric acid (HNO) was developed and optimized. The method, employing a mixture of 1 mL concentrated HNO and 4 mL of deionized water, offered a comparable performance to the conventional method using 5 mL of concentrated HNO. The accuracy of the method was validated by using certified reference material NIST 1486 (Bone Meal); percentage recoveries were within ±15% for all eight certified elements.

The Role of Dietary Magnesium in Cardiovascular Disease.

In the past 20 years, a large number of epidemiological studies, randomized controlled trials, and meta-analyses have found an inverse relationship between magnesium intake or serum magnesium and cardiovascular disease, indicating that low magnesium status is associated with hypertension, coronary artery calcification, stroke, ischemic heart disease, atrial fibrillation, heart failure, and cardiac mortality. Controlled metabolic unit human depletion-repletion experiments found that a mild or moderate magnesium deficiency can cause physiological and metabolic changes that respond to magnesium supplementation, which indicates that these types of deficiencies or chronic latent magnesium deficiency are contributing factors to the occurrence and severity of cardiovascular disease. Mechanisms through which a mild or moderate magnesium deficiency can contribute to this risk include inflammatory stress, oxidative stress, dyslipidemia and deranged lipid metabolism, endothelial dysfunction, and dysregulation of cellular ion channels, transporters, and signaling.

Dietary Intake of Chromista Oil Alters Hepatic Metabolomic Profile of Mice With Excess Fat Mass.

Increasing dietary intake of fish oil is frequently recommended for decreasing the risk for cardiovascular diseases and improving metabolic health. We hypothesised that dietary intake of chromista oil (a marine food product and a rich source of long-chain n-3 polyunsaturated fatty acids) ameliorates metabolic impairments in mice with established excess adiposity. Three-to 4-week-old mice (male) were fed a control (n = 12) or a high-fat diet (HFD, n = 24) for 12 weeks to establish body fat mass.