Recognizing and Drawing IC-planar Graphs

IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph $G$ with $n$ vertices, we present an $O(n)$-time algorithm that computes a straight-line drawing of $G$ in quadratic area, and an $O(n^3)$-time algorithm that computes a straight-line drawing of $G$ with right-angle crossings in exponential area. Both these area requirements are worst-case optimal. We also show that it is NP-complete to test IC-planarity both in the general case and in the case in which a rotation system is fixed for the input graph. Furthermore, we describe a polynomial-time algorithm to test whether a set of matching edges can be added to a triangulated planar graph such that the resulting graph is IC-planar

Greenhouse gas emissions of realistic dietary choices in Denmark: the carbon footprint and nutritional value of dairy products

Background: Dairy products are important in a healthy diet due to their high nutritional value; they are, however, associated with relatively large greenhouse gas emissions (GHGE) per kg product. When discussing the need to reduce the GHGE caused by the food system, it is crucial to consider the nutritional value of alternative food choices. Objective: The objective of this study was to elucidate the role of dairy products in overall nutrition and to clarify the effects of dietary choices on GHGE, and to combine nutritional value and GHGE data. Methods: We created eight dietary scenarios with different quantity of dairy products using data from the Danish National Dietary Survey (1995–2006). Nutrient composition and GHGE data for 71 highly consumed foods were used to estimate GHGE and nutritional status for each dietary scenario. An index was used to estimate nutrient density in relation to nutritional recommendation and climate impact for solid food items; high index values were those with the highest nutrient density scores in relation to the GHGE. Results: The high-dairy scenario resulted in 27% higher protein, 13% higher vitamin D; 55% higher calcium; 48% higher riboflavin; and 18% higher selenium than the non-dairy scenario. There was a significant correlation between changes in calcium and changes in vitamin D, selenium, and riboflavin content (P=0.0001) throughout all of the diets. The estimated GHGE for the dietary scenario with average-dairy consumption was 4,631 g CO2e/day. Conclusions: When optimizing a diet with regard to sustainability, it is crucial to account for the nutritional value and not solely focus on impact per kg product. Excluding dairy products from the diet does not necessarily mitigate climate change but in contrast may have nutritional consequences

Genomic rearrangements in BRCA1 and BRCA2: A literature review

Women with mutations in the breast cancer genes BRCA1 or BRCA2 have an increased lifetime risk of developing breast, ovarian and other BRCA-associated cancers. However, the number of detected germline mutations in families with hereditary breast and ovarian cancer (HBOC) syndrome is lower than expected based upon genetic linkage data. Undetected deleterious mutations in the BRCA genes in some high-risk families are due to the presence of intragenic rearrangements such as deletions, duplications or insertions that span whole exons. This article reviews the molecular aspects of BRCA1 and BRCA2 rearrangements and their frequency among different populations. An overview of the techniques used to screen for large rearrangements in BRCA1 and BRCA2 is also presented. The detection of rearrangements in BRCA genes, especially BRCA1, offers a promising outlook for mutation screening in clinical practice, particularly in HBOC families that test negative for a germline mutation assessed by traditional methods