Effective numerical methods for simulating diffusion on a spherical surface in three dimensions

In order to construct an algorithm for homogeneous diffusive motion that lives on a sphere, we consider the equivalent process of a randomly rotating spin vector of constant length. By introducing appropriate sets of random variables based on cross products, we construct families of methods with increasing efficacy that exactly preserve the spin modulus for every realisation. This is done by exponentiating an antisymmetric matrix whose entries are these random variables that are Gaussian in the simplest case

Almost sure stability of the Euler-Maruyama method with random variable stepsize for stochastic differential equations

In this paper, the Euler–Maruyama (EM) method with random variable stepsize is studied to reproduce the almost sure stability of the true solutions of stochastic differential equations. Since the choice of the time step is based on the current state of the solution, the time variable is proved to be a stopping time. Then the semimartingale convergence theory is employed to obtain the almost sure stability of the random variable stepsize EM solution. To our best knowledge, this is the first paper to apply the random variable stepsize (with clear proof of the stopping time) to the analysis of the almost sure stability of the EM method

The genetic basis of DOORS syndrome: an exome-sequencing study.

Deafness, onychodystrophy, osteodystrophy, mental retardation, and seizures (DOORS) syndrome is a rare autosomal recessive disorder of unknown cause. We aimed to identify the genetic basis of this syndrome by sequencing most coding exons in affected individuals

Pre- and early-postnatal nutrition modify gene and protein expressions of muscle energy metabolism markers and phospholipid fatty acid composition in a muscle type specific manner in sheep.

We previously reported that undernutrition in late fetal life reduced whole-body insulin sensitivity in adult sheep, irrespective of dietary exposure in early postnatal life. Skeletal muscle may play an important role in control of insulin action. We therefore studied a range of putative key muscle determinants of insulin signalling in two types of skeletal muscles (longissimus dorsi (LD) and biceps femoris (BF)) and in the cardiac muscle (ventriculus sinister cordis (VSC)) of sheep from the same experiment. Twin-bearing ewes were fed either 100% (NORM) or 50% (LOW) of their energy and protein requirements during the last trimester of gestation. From day-3 postpartum to 6-months of age (around puberty), twin offspring received a high-carbohydrate-high-fat (HCHF) or a moderate-conventional (CONV) diet, whereafter all males were slaughtered. Females were subsequently raised on a moderate diet and slaughtered at 2-years of age (young adults). The only long-term consequences of fetal undernutrition observed in adult offspring were lower expressions of the insulin responsive glucose transporter 4 (GLUT4) protein and peroxisome proliferator-activated receptor gamma, coactivator 1α (PGC1α) mRNA in BF, but increased PGC1α expression in VSC. Interestingly, the HCHF diet in early postnatal life was associated with somewhat paradoxically increased expressions in LD of a range of genes (but not proteins) related to glucose uptake, insulin signalling and fatty acid oxidation. Except for fatty acid oxidation genes, these changes persisted into adulthood. No persistent expression changes were observed in BF and VSC. The HCHF diet increased phospholipid ratios of n-6/n-3 polyunsaturated fatty acids in all muscles, even in adults fed identical diets for 1½ years. In conclusion, early postnatal, but not late gestation, nutrition had long-term consequences for a number of determinants of insulin action and metabolism in LD. Tissues other than muscle may account for reduced whole body insulin sensitivity in adult LOW sheep