Edge Partitions of Optimal 22-plane and 33-plane Graphs

A topological graph is a graph drawn in the plane. A topological graph is $k$-plane, $k>0$, if each edge is crossed at most $k$ times. We study the problem of partitioning the edges of a $k$-plane graph such that each partite set forms a graph with a simpler structure. While this problem has been studied for $k=1$, we focus on optimal $2$-plane and $3$-plane graphs, which are $2$-plane and $3$-plane graphs with maximum density. We prove the following results. (i) It is not possible to partition the edges of a simple optimal $2$-plane graph into a $1$-plane graph and a forest, while (ii) an edge partition formed by a $1$-plane graph and two plane forests always exists and can be computed in linear time. (iii) We describe efficient algorithms to partition the edges of a simple optimal $2$-plane graph into a $1$-plane graph and a plane graph with maximum vertex degree $12$, or with maximum vertex degree $8$ if the optimal $2$-plane graph is such that its crossing-free edges form a graph with no separating triangles. (iv) We exhibit an infinite family of simple optimal $2$-plane graphs such that in any edge partition composed of a $1$-plane graph and a plane graph, the plane graph has maximum vertex degree at least $6$ and the $1$-plane graph has maximum vertex degree at least $12$. (v) We show that every optimal $3$-plane graph whose crossing-free edges form a biconnected graph can be decomposed, in linear time, into a $2$-plane graph and two plane forests

Boreal forest floor greenhouse gas emissions across a Pleurozium schreberi-dominated, wildfire-disturbed chronosequence

The boreal forest is a globally critical biome for carbon cycling. Its forests are shaped by wildfire events that affect ecosystem properties and climate feedbacks including greenhouse gas (GHG) emissions. Improved understanding of boreal forest floor processes is needed to predict the impacts of anticipated increases in fire frequency, severity, and extent. In this study, we examined relationships between time since last wildfire (TSF), forest floor soil properties, and GHG emissions (CO2, CH4, N2O) along a Pleurozium schreberi-dominated chronosequence in mid- to late succession located in northern Sweden. Over three growing seasons in 2012–2014, GHG flux measurements were made in situ and samples were collected for laboratory analyses. We predicted that P. schreberi-covered forest floor GHG fluxes would be related to distinct trends in the soil properties and microbial community along the wildfire chronosequence. Although we found no overall effect of TSF on GHG emissions, there was evidence that soil C/N, one of the few properties to show a trend with time, was inversely linked to ecosystem respiration. We also found that local microclimatic conditions and site-dependent properties were better predictors of GHG fluxes than TSF. This shows that site-dependent co-variables (that is, forest floor climate and plant-soil properties) need to be considered as well as TSF to predict GHG emissions as wildfires become more frequent, extensive and severe

Global patient outcomes after elective surgery: prospective cohort study in 27 low-, middle- and high-income countries.

BACKGROUND: As global initiatives increase patient access to surgical treatments, there remains a need to understand the adverse effects of surgery and define appropriate levels of perioperative care. METHODS: We designed a prospective international 7-day cohort study of outcomes following elective adult inpatient surgery in 27 countries. The primary outcome was in-hospital complications. Secondary outcomes were death following a complication (failure to rescue) and death in hospital. Process measures were admission to critical care immediately after surgery or to treat a complication and duration of hospital stay. A single definition of critical care was used for all countries. RESULTS: A total of 474 hospitals in 19 high-, 7 middle- and 1 low-income country were included in the primary analysis. Data included 44 814 patients with a median hospital stay of 4 (range 2-7) days. A total of 7508 patients (16.8%) developed one or more postoperative complication and 207 died (0.5%). The overall mortality among patients who developed complications was 2.8%. Mortality following complications ranged from 2.4% for pulmonary embolism to 43.9% for cardiac arrest. A total of 4360 (9.7%) patients were admitted to a critical care unit as routine immediately after surgery, of whom 2198 (50.4%) developed a complication, with 105 (2.4%) deaths. A total of 1233 patients (16.4%) were admitted to a critical care unit to treat complications, with 119 (9.7%) deaths. Despite lower baseline risk, outcomes were similar in low- and middle-income compared with high-income countries. CONCLUSIONS: Poor patient outcomes are common after inpatient surgery. Global initiatives to increase access to surgical treatments should also address the need for safe perioperative care. STUDY REGISTRATION: ISRCTN5181700

Cost-effectiveness of edoxaban versus rivaroxaban for stroke prevention in patients with nonvalvular atrial fibrillation (NVAF) in the US

Jeffrey D Miller,1 Xin Ye,2 Gregory M Lenhart,1 Amanda M Farr,1 Oth V Tran,1 W Jackie Kwong,2 Elizabeth A Magnuson,3 William S Weintraub41Truven Health Analytics Inc, Cambridge, MA, 2Daiichi Sankyo Inc, Parsippany, NJ, 3St Luke Mid-America Heart Institute, Kansas City, MO, 4Center for Heart and Vascular Health, Christiana Care Health System, Newark, DE, USABackground: Understanding the value of new anticoagulation therapies compared with existing therapies is of paramount importance in today&rsquo;s cost-conscious and efficiency-driven health care environment. Edoxaban and rivaroxaban for stroke prevention in nonvalvular atrial fibrillation (NVAF) patients with CHADS2 scores &ge;2 have been evaluated in pivotal trials versus warfarin. The relative value of edoxaban versus rivaroxaban would be of interest to health care stakeholders and patients who prefer a once-daily treatment option for long-term stroke prevention in NVAF.Objective: To evaluate the relative cost-effectiveness of two once-daily regimens of novel oral anticoagulation therapy &ndash; edoxaban (60 mg/30 mg dose-reduced) versus rivaroxaban (20 mg/15 mg dose-reduced) &ndash; for stroke prevention in NVAF patients from a US health-plan perspective.Materials and methods: A Markov model simulated lifetime risk and treatment of stroke, systemic embolism, major bleeding, clinically relevant nonmajor bleeding, myocardial infarction, and death in NVAF patients treated with edoxaban or rivaroxaban. Efficacy and safety data were derived from a network meta-analysis that utilized data from patients enrolled in ENGAGE AF-TIMI 48 and ROCKET-AF. Health care cost and utility data were obtained from published sources. Incremental cost-effectiveness ratios of 150,000 per quality-adjusted life year (QALY) gained were used as thresholds for “highly cost-effective”, “cost-effective”, and “not cost-effective” treatment options, respectively, as per American Heart Association/American College of Cardiology guidelines.Results: Edoxaban was dominant relative to rivaroxaban, such that it was associated with lower total health care costs and better effectiveness in terms of QALYs in the base-case analysis. Results were supported by probabilistic sensitivity analyses that showed edoxaban as either dominant or a highly cost-effective alternative (incremental cost-effectiveness ratio <50,000) to rivaroxaban in 88.4% of 10,000 simulations.Conclusion: Results of this study showed that the once-daily edoxaban (60 mg/30 mg dose-reduced) regimen is a cost-saving or highly cost-effective treatment relative to rivaroxaban (20 mg/15 mg dose-reduced) for stroke prevention in NVAF patients with CHADS2 &ge;2.Keywords: edoxaban, rivaroxaban, cost-effectiveness, nonvalvular atrial fibrillation, oral anticoagulation, stroke, NOAC, SPAF, economic model, economic analysi