The ocean moderates the world’s climate through absorption of heat and carbon, but how much carbon the ocean will continue to absorb remains unknown. The North Atlantic Ocean west (Baffin Bay/Labrador Sea) and east (Fram Strait/Greenland Sea) of Greenland features the most intense absorption of anthropogenic carbon globally; the biological carbon pump (BCP) contributes substantially. As Arctic sea-ice melts, the BCP changes, impacting global climate and other critical ocean attributes (e.g. biodiversity). Full understanding requires year-round observations across a range of ice conditions. Here we present such observations: autonomously collected Eulerian continuous 24-month time-series in Fram Strait. We show that, compared to ice-unaffected conditions, sea-ice derived meltwater stratification slows the BCP by 4 months, a shift from an export to a retention system, with measurable impacts on benthic communities. This has implications for ecosystem dynamics in the future warmer Arctic where the seasonal ice zone is expected to expand.

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Geometric branch-and-bound solution methods, in particular the big square small square technique and its many generalizations, are popular solution approaches for non-convex global optimization problems. Most of these approaches differ in the lower bounds they use which have been compared empirically in a few studies. The aim of this paper is to introduce a general convergence theory which allows theoretical results about the different bounds used. To this end we introduce the concept of a bounding operation and propose a new definition of the rate of convergence for geometric branch-and-bound methods. We discuss the rate of convergence for some well-known bounding operations as well as for a new general bounding operation with an arbitrary rate of convergence. This comparison is done from a theoretical point of view. The results we present are justified by some numerical experiments using the Weber problem on the plane with some negative weights.

We provide a simple method for the calculation of the terms c_n in the Zassenhaus product $e^{a+b}=e^a e^b \prod_{n=2}^{\infty} e^{c_n}$ for non-commuting a and b. This method has been implemented in a computer program. Furthermore, we formulate a conjecture on how to translate these results into nested commutators. This conjecture was checked up to order n=17 using a computer