Some remarks on Bell non-locality and Einstein-Podolsky-Rosen steering of bipartite states

Bell nonlocality and Einstein-Podolsky-Rosen (EPR) steering are every important quantum correlations of a composite quantum system. Bell nonlocality of a bipartite state is a quantum correlation demonstrated by some local quantum measurements, while EPR steering is another form of quantum correlations, observed firstly by Schrodinger in the context of famous EPR paradox. In this paper, we give some remarks on Bell nonlocality and EPR steering of bipartite states, including mathematical definitions and characterizations of these two quantum correlations, the convexity and closedness of the set of all Bell local states and the set of all EPR unsteerable states. We also derive a EPR-steering criteria, with which the EPR steerability of the maximally entangled states are checked

The role of N∗(1535)N^{*}(1535) in η′\eta ' production

We study the near-threshold $\eta '$ production mechanism in nucleon-nucleon and $\pi N$ collisions under the assumption that sub-threshold resonance $N^{*}(1535)$ is predominant. In an effective Lagrangian approach which gives a reasonable description to the $pN \to pN \eta$ and $\pi p \to p \eta$ reactions, it is found that t-channel $\pi$ exchange make the dominate contribution to the $pN \to pN \eta '$ process, and a value of 6.5 for the ratio of $\sigma (pn \to pn \eta ')$ to $\sigma (pp \to pp \eta ')$ is predicted. A strong coupling strength of $N^{*}(1535)$ to $\eta ' N$ ($g_{\eta ' NN^*}^2 /4\pi = 1.1$) is extracted from a combined analysis to $pp \to pp \eta '$ and $\pi N \to N \eta '$, and the possible implication to the intrinsic component of $N^{*}(1535)$ is explored.Comment: 12pp + 5fig

Harnack Estimates for Conjugate Heat Kernel on Evolving Manifolds

In this article we derive Harnack estimates for conjugate heat kernel in an abstract geometric flow. Our calculation involves a correction term D. When D is nonnegative, we are able to obtain a Harnack inequality. Our abstract formulation provides a unified framework for some known results, in particular including corresponding results of Ni, Perelman, and Tran as special cases. Moreover it leads to new results in the setting of Ricci-Harmonic flow and mean curvature flow in Lorentzian manifolds with nonnegative sectional curvature.Comment: 16

Hyper-Graph Based Database Partitioning for Transactional Workloads

A common approach to scaling transactional databases in practice is horizontal partitioning, which increases system scalability, high availability and self-manageability. Usu- ally it is very challenging to choose or design an optimal partitioning scheme for a given workload and database. In this technical report, we propose a fine-grained hyper-graph based database partitioning system for transactional work- loads. The partitioning system takes a database, a workload, a node cluster and partitioning constraints as input and out- puts a lookup-table encoding the final database partitioning decision. The database partitioning problem is modeled as a multi-constraints hyper-graph partitioning problem. By deriving a min-cut of the hyper-graph, our system can min- imize the total number of distributed transactions in the workload, balance the sizes and workload accesses of the partitions and satisfy all the partition constraints imposed. Our system is highly interactive as it allows users to im- pose partition constraints, watch visualized partitioning ef- fects, and provide feedback based on human expertise and indirect domain knowledge for generating better partition- ing schemes

Approximation of Mean Field Games to N-Player Stochastic Games, with Singular Controls

This paper establishes that $N$-player stochastic games with singular controls, either of bounded velocity or of finite variation, can both be approximated by mean field games (MFGs) with singular controls of bounded velocity. More specifically, it shows i) the optimal control to an MFG with singular controls of a bounded velocity $\theta$ is shown to be an $\epsilon_N$-NE to an $N$-player game with singular controls of the bounded velocity, with $\epsilon_N = O(\frac{1}{\sqrt{N}})$, and (ii) the optimal control to this MFG is an $(\epsilon_N + \epsilon_{\theta})$-NE to an $N$-player game with singular controls of finite variation, where $\epsilon_{\theta}$ is an error term that depends on $\theta$. This work generalizes the classical result on approximation $N$-player games by MFGs, by allowing for discontinuous controls

Topological textures and their bifurcation processes in 2D ferromagnetic thin films

In this paper, by the use of the topological current theory, the topological structures and the dynamic processes in thin-film ferromagnetic systems are investigated directly from viewpoint of topology. It is found that the topological charge of a thin-film ferromagnetic system can be changed by annihilation or creation processes of opposite polarized vortex-antivortex pairs taking place at space-time singularities of the normalized magnetization vector field of the system, the variation of the topological charge is integer and can further be expressed in terms of the Hopf indices and Brouwer degrees of the magnetization vector field around the singularities. Moreover, the change of the topological charge of the system is crucial to vortex core reversal processes in ferromagnetic thin films. With the help of the topological current theory and implicit function theorem, the processes of vortex merging, splitting as well as vortex coreComment: 10 pages, 8 figure

New approach for fabrication germanene with Dirac electrons preserved: A first principle study

How to obtain germanene with Dirac electrons preserved is still an open challenge. Here we report a sandwich-dehydrogenation approach, i.e., to fabricate germanene through dehydrogenating germanane in a sandwiched structure. The dehydrogenation can spontaneously occur for the sandwiched structure, which overcomes the problem of amorphization in the heating dehydrogenation approach. The obtained germanene preserve the Dirac electronic properties very well. Moreover, the Fermi velocity of germanene can be efficiently manipulated through controlling the interlayer spacing between germanane and the sandwiching surfaces. Our results indicate a guideline for fabrication of prefect two-dimensional materials.Comment: 23 pages,6 figure

Generalization Bounds for Metric and Similarity Learning

Recently, metric learning and similarity learning have attracted a large amount of interest. Many models and optimisation algorithms have been proposed. However, there is relatively little work on the generalization analysis of such methods. In this paper, we derive novel generalization bounds of metric and similarity learning. In particular, we first show that the generalization analysis reduces to the estimation of the Rademacher average over "sums-of-i.i.d." sample-blocks related to the specific matrix norm. Then, we derive generalization bounds for metric/similarity learning with different matrix-norm regularisers by estimating their specific Rademacher complexities. Our analysis indicates that sparse metric/similarity learning with $L^1$-norm regularisation could lead to significantly better bounds than those with Frobenius-norm regularisation. Our novel generalization analysis develops and refines the techniques of U-statistics and Rademacher complexity analysis.Comment: 20 page

Ultrafast Manipulation of a Double Quantum Dot via Lyapunov Control Method

For a double quantum dot (DQD) system, here we propose alternative ultrafast manipulate approach: Lyapunov control method, to transfer the state from R to L on the picosecond scale, orders of magnitude faster and transfer probability higher than the previously measured electrically controlled charge- or spin-based quits. The control laws are composed of two-direction components, one is used to eliminate the dissipation in the system, another is used to transfer the state. The control theory's stability ensures the system can be transferred to the target state in high probability, and the coefficients in control laws leads very fast convergence. The role of eliminating the dissipation plays the suppression of decoherence effect. Numerical simulation results show that under the realistic implementation conditions, the transfer probability and fidelity can be increased up to 98.79% and 98.97%, respectively. This is the first result directly applicable to a DQD system's state transferring using the Lyapunov control method. We also give specific experimental realization scheme.Comment: 8 pages, 4 figure

Uniqueness of planar vortex patch in incompressible steady flow

We investigate a steady planar flow of an ideal fluid in a bounded simple connected domain and focus on the vortex patch problem with prescribed vorticity strength. There are two methods to deal with the existence of solutions for this problem: the vorticity method and the stream function method. A long standing open problem is whether these two entirely different methods result in the same solution. In this paper, we will give a positive answer to this problem by studying the local uniqueness of the solutions. Another result obtained in this paper is that if the domain is convex, then the vortex patch problem has a unique solution.Comment: 36 page