Trees with Given Stability Number and Minimum Number of Stable Sets

We study the structure of trees minimizing their number of stable sets for given order $n$ and stability number $\alpha$. Our main result is that the edges of a non-trivial extremal tree can be partitioned into $n-\alpha$ stars, each of size $\lceil \frac{n-1}{n-\alpha} \rceil$ or $\lfloor \frac{n-1}{n-\alpha}\rfloor$, so that every vertex is included in at most two distinct stars, and the centers of these stars form a stable set of the tree.Comment: v2: Referees' comments incorporate

Efficacy, safety, and tolerability of oral semaglutide versus placebo added to insulin with or without metformin in patients with type 2 diabetes: The PioNEER 8 trial

OBJECTIVE To investigate the efficacy, safety, and tolerability of oral semaglutide added to insulin with or without metformin. RESEARCH DESIGN AND METHODS Patients with type 2 diabetes uncontrolled on insulin with or without metformin were randomized to oral semaglutide 3 mg (N 5 184), 7 mg (N 5 182), or 14 mg (N 5 181) or to placebo (N 5 184) in a 52-week, double-blind trial. End points were change from baseline to week 26 in HbA1c (primary) and body weight (confirmatory secondary). Two estimands were defined: treatment policy (effect regardless of trial product discontinuation or rescue medication) and trial product (effect assuming trial product continuation without rescue medication) in randomized patients. RESULTS Oral semaglutide was superior to placebo in reducing HbA1c (estimated treatment difference [ETD] –0.5% [95% CI –0.7, –0.3], –0.9% [–1.1, –0.7], and –1.2% [–1.4, –1.0] for 3, 7, and 14 mg, respectively; P < 0.001) and body weight (ETD 20.9 kg [95% CI 21.8, 20.0], 22.0 kg [23.0, 21.0], and 23.3 kg [24.2, 22.3]; P 5 0.0392 for 3 mg, P £ 0.0001 for 7 and 14 mg) at week 26 (treatment policy estimand). Significantly greater dose-dependent HbA1c and body weight reductions versus placebo were achieved with oral semaglutide at weeks 26 and 52 (both estimands). The most frequent adverse event with oral semaglutide was nausea (11.4–23.2% of patients vs. 7.1% with placebo; mostly mild to moderate). CONCLUSIONS Oral semaglutide was superior to placebo in reducing HbA1c and body weight when added to insulin with or without metformin in patients with type 2 diabetes. The safety profile was consistent with other glucagon-like peptide 1 receptor agonists

Global estimates of the extent and production of macroalgal forests

Aim Macroalgal habitats are believed to be the most extensive and productive of all coastal vegetated ecosystems. In stark contrast to the growing attention on their contribution to carbon export and sequestration, understanding of their global extent and production is limited and these have remained poorly assessed for decades. Here we report a first data-driven assessment of the global extent and production of macroalgal habitats based on modelled and observed distributions and net primary production (NPP) across habitat types. Location Global coastal ocean. Time period Contemporary. Major taxa studied Macroalgae. Methods Here we apply a comprehensive niche model to generate an improved global map of potential macroalgal distribution, constrained by incident light on the seafloor and substrate type. We compiled areal net primary production (NPP) rates across macroalgal habitats from the literature and combined this with our estimates of the global extent of these habitats to calculate global macroalgal NPP. Results We show that macroalgal forests are a major biome with a global area of 6.06–7.22 million km2, dominated by red algae, and NPP of 1.32 Pg C/year, dominated by brown algae. Main conclusions The global macroalgal biome is comparable, in area and NPP, to the Amazon forest, but is globally distributed as a thin strip around shorelines. Macroalgae are expanding in polar, subpolar and tropical areas, where their potential extent is also largest, likely increasing the overall contribution of algal forests to global carbon sequestration

Anthropogenic Space Weather

Anthropogenic effects on the space environment started in the late 19th century and reached their peak in the 1960s when high-altitude nuclear explosions were carried out by the USA and the Soviet Union. These explosions created artificial radiation belts near Earth that resulted in major damages to several satellites. Another, unexpected impact of the high-altitude nuclear tests was the electromagnetic pulse (EMP) that can have devastating effects over a large geographic area (as large as the continental United States). Other anthropogenic impacts on the space environment include chemical release ex- periments, high-frequency wave heating of the ionosphere and the interaction of VLF waves with the radiation belts. This paper reviews the fundamental physical process behind these phenomena and discusses the observations of their impacts.Comment: 71 pages, 35 figure

Grain Surface Models and Data for Astrochemistry

AbstractThe cross-disciplinary field of astrochemistry exists to understand the formation, destruction, and survival of molecules in astrophysical environments. Molecules in space are synthesized via a large variety of gas-phase reactions, and reactions on dust-grain surfaces, where the surface acts as a catalyst. A broad consensus has been reached in the astrochemistry community on how to suitably treat gas-phase processes in models, and also on how to present the necessary reaction data in databases; however, no such consensus has yet been reached for grain-surface processes. A team of ∼25 experts covering observational, laboratory and theoretical (astro)chemistry met in summer of 2014 at the Lorentz Center in Leiden with the aim to provide solutions for this problem and to review the current state-of-the-art of grain surface models, both in terms of technical implementation into models as well as the most up-to-date information available from experiments and chemical computations. This review builds on the results of this workshop and gives an outlook for future directions