Simultaneous Embeddings with Few Bends and Crossings

A simultaneous embedding with fixed edges (SEFE) of two planar graphs $R$ and $B$ is a pair of plane drawings of $R$ and $B$ that coincide when restricted to the common vertices and edges of $R$ and $B$. We show that whenever $R$ and $B$ admit a SEFE, they also admit a SEFE in which every edge is a polygonal curve with few bends and every pair of edges has few crossings. Specifically: (1) if $R$ and $B$ are trees then one bend per edge and four crossings per edge pair suffice (and one bend per edge is sometimes necessary), (2) if $R$ is a planar graph and $B$ is a tree then six bends per edge and eight crossings per edge pair suffice, and (3) if $R$ and $B$ are planar graphs then six bends per edge and sixteen crossings per edge pair suffice. Our results improve on a paper by Grilli et al. (GD'14), which proves that nine bends per edge suffice, and on a paper by Chan et al. (GD'14), which proves that twenty-four crossings per edge pair suffice.Comment: Full version of the paper "Simultaneous Embeddings with Few Bends and Crossings" accepted at GD '1

mTICCS and its inter-rater reliability to predict the need for massive transfusion in severely injured patients

Purpose: The modified Trauma-Induced Coagulopathy Clinical Score (mTICCS) presents a new scoring system for the early detection of the need for a massive transfusion (MT). This easily applicable score was validated in a large trauma cohort and proven comparable to more established complex scoring systems. However, the inter-rater reliability of the mTICCS has not yet been investigated. Methods: Therefore, a dataset of 15 randomly selected and severely injured patients (ISS ≥ 16) derived from the database of a level I trauma centre (2010–2015) was used. Moreover, 15 severely injured subjects that received MT were chosen from the same databank. A web-based survey was sent to medical professionals working in the field of trauma care asking them to evaluate each patient using the mTICCS. Results: In total, 16 raters (9 residents and 7 specialists) completed the survey. Ratings from 15 medical professionals could be evaluated and led to an ICC of 0.7587 (95% Bootstrap confidence interval (BCI) 0.7149–0.8283). A comparison of working experience specific ICC (n = 7 specialists, ICC: 0.7558, BCI: 0.7076–0.8270; n = 8 residents, ICC: 0.7634, BCI: 0.7183–0.8335) showed no significant difference between the two groups (p = 0.67). Conclusion: In summary, reliability values need to be considered when making clinical decisions based on scoring systems. Due to its easy applicability and its almost perfect inter-rater reliability, even with non-specialists, the mTICCS might therefore be a useful tool to predict the early need for MT in multiple trauma. © 2020, The Author(s)