arXiv subjects
Publications and source records attributed to Mu Zhao.
We introduce a variant of the classic poker game blackjack -- the continuous blackjack. We study the Nash Equilibrium as well as the case where players deviate from it. We then pivot to the study of a large class of adaptive strategies and obtain a model-free strategy. Finally, we apply reinforcement learning techniques to the game and address several associated engineering challenges.
We introduce a new invariant, the \textit{positive idempotent group}, for strongly asymptotically dynamically convex contact manifolds. This invariant can be used to distinguish different contact structures. As an application, for any complex dimension $n>8$ and any positive integer $k$, we can construct $n-$dimensional Stein manifolds $V_0,V_1,\cdots,V_k$ such that $\tilde{H}_j(V_i)=0, j\neq n-1,n$, $V_i's$ are almost symplectomorphic, their boundaries are in the same almost contact class but not contactomorphic.
Modifying material properties at the nanoscale is crucially important for devices in nanoelectronics, nanophotonics and quantum information. Optically active defects in wide band gap materials, for instance, are vital constituents for the realisation of quantum technologies. Yet, the introduction of atomic defects through direct ion implantation remains a fundamental challenge. Herein, we establish a universal method for material doping by exploiting one of the most fundamental principles of physics - momentum transfer. As a proof of concept, we direct-write arrays of emitters into diamond via momentum transfer from a Xe+ focused ion beam (FIB) to thin films of the group IV dopants pre-deposited onto a diamond surface. We conclusively show that the technique, which we term knock-on doping, can yield ultra-shallow dopant profiles localized to the top 5 nm of the target surface, and use it to achieve sub-50 nm lateral resolution. The knock-on doping method is cost-effective, yet very versatile, powerful and universally suitable for applications such as electronic and magnetic doping of atomically thin materials and engineering of near-surface states of semiconductor devices.