UNKNOTTABILITY OF SPATIAL GRAPHS BY REGION CROSSING CHANGES

A region crossing change is a local transformation on spatial graph diagrams switching the over/under relation at all the crossings on the boundary of a region. In this paper, we show that a spatial graph of a planar graph is unknottable by region crossing changes if and only if the spatial graph is non-Eulerian or is Eulerian and proper

Biotin levels in blood and follicular fluid

It has been shown that biotin, a water-soluble vitamin (B7), plays roles in reproductive functions, such as oocyte maturation and embryo development, in experimental animals. On the other hand, little is known about the clinical effects of biotin on human reproduction. In this study, serum and follicular fluid biotin levels were measured in patients who underwent in vitro fertilization / intracytoplasmic sperm injection (IVF / ICSI), and their associations with reproductive outcomes were evaluated. As a result, biotin was detected in follicular fluid, as well as serum, and the biotin levels of follicular fluid were found to be positively correlated with those of serum. The biotin levels of serum were higher than those of follicular fluid, suggesting that biotin may be taken up into the follicular fluid from the blood. Although serum and follicular fluid biotin levels tended to be higher in pregnant patients than in non-pregnant patients, these data did not show the significant statistical difference. These findings indicate that biotin does not contribute to the maintenance of oocyte quality, and hence, it does not increase fertilization and pregnancy rates