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Convergence analysis of accelerated first-order methods for convex optimization problems are developed from the point of view of ordinary differential equation solvers. A new dynamical system, called Nesterov accelerated gradient (NAG) flow, is derived from the connection between acceleration mechanism andA-stability of ODE solvers, and the exponential decay of a tailored Lyapunov function along with the solution trajectory is proved. Numerical discretizations of NAG flow are then considered and convergence rates are established via a discrete Lyapunov function. The proposed differential equation solver approach can not only cover existing accelerated methods, such as FISTA, Güler’s proximal algorithm and Nesterov’s accelerated gradient method, but also produce new algorithms for composite convex optimization that possess accelerated convergence rates. Both the convex and the strongly convex cases are handled in a unified way in our approach.

 

Memory allocation is increasingly important to parallel performance, yet it is challenging because a program has data of many sizes, and the demand differs from thread to thread. Modern allocators use highly tuned heuristics but do not provide uniformly good performance when the level of concurrency increases from a few threads to hundreds of threads. This paper presents a new timescale theory to model the memory demand in real time. Using the new theory, an allocator can ad- just its synchronization frequency using a single parameter called allocations per fetch (apf ). The paper presents the timescale the- ory, the design and implementation of APF tuning in an existing allocator, and evaluation of the effect on program speed and mem- ory efficiency. APF tuning improves the throughput of MongoDB by 55%, reduces the tail latency of a Web server by over 60%, and increases the speed of a selection of synthetic benchmarks by up to 24× while using the same amount of memory. 

The recent trend of global warming has exerted a disproportionately strong influence on the Eurasian land surface, causing a steady decline in snow cover extent over the Himalayan-Tibetan Plateau region. Here we show that this loss of snow is undermining winter convective mixing and causing stratification of the upper layer of the Arabian Sea at a much faster rate than predicted by global climate models. Over the past four decades, the Arabian Sea has also experienced a profound loss of inorganic nitrate. In all probability, this is due to increased denitrification caused by the expansion of the permanent oxygen minimum zone and consequent changes in nutrient stoichiometries. These exceptional changes appear to be creating a niche particularly favorable to the mixotroph,Noctiluca scintillanswhich has recently replaced diatoms as the dominant winter, bloom forming organism. AlthoughNoctilucablooms are non-toxic, they can cause fish mortality by exacerbating oxygen deficiency and ammonification of seawater. As a consequence, their continued range expansion represents a significant and growing threat for regional fisheries and the welfare of coastal populations dependent on the Arabian Sea for sustenance.

 

Coastal waters in the Labrador Sea are influenced by the seasonal input of meltwater from the Greenland ice sheet, which is predicted to more than double by the end of the century. Mechanisms controlling the offshore export of meltwater can have a significant effect on stratification and vertical stability in the Labrador Sea, being particularly important if the meltwater is transported toward the interior of the basin where winter convection occurs. Here we use a high‐resolution ocean model to show that coastal upwelling winds play a critical role transporting the meltwater offshore to about 150 km from the coast, where increased eddy activity and mean circulation can then transport the meltwater farther offshore. While meltwater discharged from West Greenland is either transported to Baffin Bay or circumnavigates the basin flowing mostly along isobaths, meltwater from East Greenland can reach the interior of the basin where it may influence stratification and winter convection whenever winds are anomalously upwelling favorable in late summer and early fall.