A Bernstein theorem for special Lagrangian graphs

We obtain a Bernstein theorem for special Lagrangian graphs in n-dimensional complex space for arbitrary n only assuming bounded slope, but no quantitative restriction.Comment: 17 page

Hydrogenated Bilayer Wurtzite SiC Nanofilms: A Two-Dimensional Bipolar Magnetic Semiconductor Material

Recently, a new kind of spintronics materials, bipolar magnetic semiconductor (BMS), has been proposed. The spin polarization of BMS can be conveniently controlled by a gate voltage, which makes it very attractive in device engineering. Now, the main challenge is finding more BMS materials. In this article, we propose that hydrogenated wurtzite SiC nanofilm is a two-dimensional BMS material. Its BMS character is very robust under the effect of strain, substrate, or even a strong electric field. The proposed two-dimensional BMS material paves the way to use this promising new material in an integrated circuit

Functional Bandits

We introduce the functional bandit problem, where the objective is to find an arm that optimises a known functional of the unknown arm-reward distributions. These problems arise in many settings such as maximum entropy methods in natural language processing, and risk-averse decision-making, but current best-arm identification techniques fail in these domains. We propose a new approach, that combines functional estimation and arm elimination, to tackle this problem. This method achieves provably efficient performance guarantees. In addition, we illustrate this method on a number of important functionals in risk management and information theory, and refine our generic theoretical results in those cases

On the Erdos-Sos Conjecture for Graphs on n=k+4 Vertices

The Erd\H{o}s-S\'{o}s Conjecture states that if $G$ is a simple graph of order $n$ with average degree more than $k-2,$ then $G$ contains every tree of order $k$. In this paper, we prove that Erd\H{o}s-S\'{o}s Conjecture is true for $n=k+4$.Comment: 18 page