k-server via multiscale entropic regularization

We present an $O((\log k)^2)$-competitive randomized algorithm for the $k$-server problem on hierarchically separated trees (HSTs). This is the first $o(k)$-competitive randomized algorithm for which the competitive ratio is independent of the size of the underlying HST. Our algorithm is designed in the framework of online mirror descent where the mirror map is a multiscale entropy. When combined with Bartal's static HST embedding reduction, this leads to an $O((\log k)^2 \log n)$-competitive algorithm on any $n$-point metric space. We give a new dynamic HST embedding that yields an $O((\log k)^3 \log \Delta)$-competitive algorithm on any metric space where the ratio of the largest to smallest non-zero distance is at most $\Delta$

High Photovoltaic Quantum Efficiency in Ultrathin van der Waals Heterostructures

We report experimental measurements for ultrathin (< 15 nm) van der Waals heterostructures exhibiting external quantum efficiencies exceeding 50%, and show that these structures can achieve experimental absorbance > 90%. By coupling electromagnetic simulations and experimental measurements, we show that pn WSe2/MoS2 heterojunctions with vertical carrier collection can have internal photocarrier collection efficiencies exceeding 70%.Comment: ACS Nano, 2017. Manuscript (25 pages, 7 figures) plus supporting information (7 pages, 4 figures