No abstract

Many link prediction algorithms require the computation of a similarity metric on each vertex pair, which is quadratic in the number of vertices and infeasible for large networks. We develop a class of link prediction algorithms based on a spectral embedding and the k closest pairs algorithm that are scalable to very large networks. We compare the prediction accuracy and runtime of these methods to existing algorithms on several large link prediction tasks. Our methods achieve comparable accuracy to standard algorithms but are significantly faster.

We establish rigorous upper bounds on the time-averaged heat transport for a model of rotating Rayleigh-Bénard convection between no-slip boundaries at infinite Prandtl number and with Ekman pumping. The analysis is based on the asymptotically reduced equations derived for rotationally constrained dynamics with no-slip boundaries, and hence includes a lower order correction that accounts for the Ekman layer and corresponding Ekman pumping into the bulk. Using the auxiliary functional method we find that, to leading order, the temporally averaged heat transport is bounded above as a function of the Rayleigh and Ekman numbers Ra and Ek according to Nu ≤ 0.3704Ra 2 Ek 2 . Dependent on the relative values of the thermal forcing represented by Ra and the effects of rotation represented by Ek, this bound is both an improvement on earlier rigorous upper bounds, and provides a partial explanation of recent numerical and experimental results that were consistent yet surprising relative to the previously derived upper bound of Nu Ra 3 Ek 4 . * whitehead@mathematics.byu.edu.

No abstract

No abstract