On stable compact minimal submanifolds of Riemannian product manifolds

In this paper, we prove a classification theorem for the stable compact minimal submanifolds of the Riemannian product of an $m_1$-dimensional ($m_1\geq3$) hypersurface $M_1$ in the Euclidean space and any Riemannian manifold $M_2$, when the sectional curvature $K_{M_1}$ of $M_1$ satisfies $\frac{1}{\sqrt{m_1-1}}\leq K_{M_1}\leq 1.$ This gives a generalization to the results of F. Torralbo and F. Urbano [9], where they obtained a classification theorem for the stable minimal submanifolds of the Riemannian product of a sphere and any Riemannian manifold. In particular, when the ambient space is an $m$-dimensional ($m\geq3$) complete hypersurface $M$ in the Euclidean space, if the sectional curvature $K_{M}$ of $M$ satisfies $\frac{1}{\sqrt{m+1}}\leq K_{M}\leq 1$, then we conclude that there exist no stable compact minimal submanifolds in $M$.Comment: 11 page

Experiments on Parallel Training of Deep Neural Network using Model Averaging

In this work we apply model averaging to parallel training of deep neural network (DNN). Parallelization is done in a model averaging manner. Data is partitioned and distributed to different nodes for local model updates, and model averaging across nodes is done every few minibatches. We use multiple GPUs for data parallelization, and Message Passing Interface (MPI) for communication between nodes, which allows us to perform model averaging frequently without losing much time on communication. We investigate the effectiveness of Natural Gradient Stochastic Gradient Descent (NG-SGD) and Restricted Boltzmann Machine (RBM) pretraining for parallel training in model-averaging framework, and explore the best setups in term of different learning rate schedules, averaging frequencies and minibatch sizes. It is shown that NG-SGD and RBM pretraining benefits parameter-averaging based model training. On the 300h Switchboard dataset, a 9.3 times speedup is achieved using 16 GPUs and 17 times speedup using 32 GPUs with limited decoding accuracy loss

Constant Angle Surfaces in S3(1)×R\mathbb{S}^3(1) \times \mathbb{R}

In this article we study surfaces in $\mathbb{S}^3(1) \times \mathbb{R}$ for which the $\mathbb{R}$-direction makes a constant angle with the normal plane. We give a complete classification for such surfaces with parallel mean curvature vector.Comment: 16 page

Variational Approach to the Spin-boson Model With a Sub-Ohmic Bath

The influence of dissipation on quantum tunneling in the spin-boson model with a sub-Ohmic bath is studied by a variational calculation. By examining the evolution of solutions of the variational equation with the coupling strength near the phase boundary, we are able to present a scenario of discontinuous transition in sub-Ohmic dissipation case in accord with Ginzburg-Landau theory. Based on the constructed picture, it is shown that the critical point found in the general way is not thermodynamically the critical point, but the point where the second energy minimum begins to develop. The true cross-over point is calculated and the obtained phase diagram is in agreement with the result of numerical renormalization group calculation.Comment: 6 pgaes, 8 figure

Effects of temperature and strain rate on mechanical behaviors of Stone-Wales defective monolayer black phosphorene

The mechanical behaviors of monolayer black phosphorene (MBP) are explored by molecular dynamics (MD) simulations using reactive force field. It is revealed that the temperature and strain rate have significant influence on mechanical behaviors of MBP, and they are further weakened by SW (Stone-Wales) defects. In general, the tensile strength for both of the pristine and SW defective MBP decreases with the increase of temperature or decreasing of strain rate. Surprisingly, for relatively high temperature and low strain rate, phase transition from the black phosphorene to a mixture of {\beta}-phase ({\beta}-P) and {\gamma}-phase ({\gamma}-P) is observed for the SW-2 defective MBP under armchair tension, while self-healing of the SW-2 defect is observed under zigzag tension. A deformation map of SW-2 defective MBP under armchair tension at different temperature and strain rate is established, which is useful for the design of phosphorene allotropes by strain. The results presented herein yield useful insights for designing and tuning the structure, and the mechanical and physical properties of phosphorene

Hadronic coupling constants of gσππg_{\sigma\pi\pi} in lattice QCD

We investigate the coupling constant $g_{\sigma\pi\pi}$ for the hadronic decay $\sigma\to\pi\pi$ only using the relevant three-point function, which is evaluated by the moving-wall source technique with a pretty good noise-to-signal ratio. This simulation is carried out on a $40^3\times96$ MILC gauge configuration with $N_f=2+1$ flavor of the "Asqtad" improved staggered dynamical sea quarks at the lattice spacing $a \approx 0.09$ fm. Our estimated value for this given MILC fine lattice gauge ensemble $g_{\sigma\pi\pi}=2.71(42)$ GeV.Comment: Submitted to Chinese Physics

Thermal conductivity of armchair black phosphorus nanotubes: a molecular dynamics study

The effects of size, strain, and vacancies on thermal properties of armchair black phosphorus nanotubes are investigated based on qualitative analysis from molecular dynamics simulations. It is found that the thermal conductivity has a remarkable size effect because of the restricted paths for phonon transport, strongly depending on the diameter and length of nanotube. Owing to the intensified low-frequency phonons, axial tensile strain can facilitate thermal transport. On the contrary, compressive strain weakens thermal transport due to the enhanced phonon scattering around the buckling of nanotube. In addition, the thermal conductivity is dramatically reduced by single vacancies, especially upon high defect concentrations

Generalized coherent-squeezed-state expansion for the quantum Rabi model

We develop a systematic variational coherent-squeezed-state expansion for the ground state of the quantum Rabi model, which includes an additional squeezing effect with comparisons to previous coherent-state approach. For finite large ratio between the atomic and field frequency, the essential feature of the ground-state wave function in the super-radiant phase appears, which has a structure of two delocalized wake packets. The single-peaked wave function with one coherent-squeezed state works well even around the critical regime, exhibiting the advantage over the coherent-state method. As the coupling increases to form strong correlations physics in the vicinity of phase transition, we develop an improved wave function with a structure of two Gaussian wave packets, which is a linear superposition of two coherent-squeezed state. The ground-state energy and the average photon number agree well with numerical ones even in the strong-correlated regimes, exhibiting a substantial improvement over the coherent-state expansion. The advantage of the coherent-squeezed-state expansion lies in the inclusion of the second coherent-squeezed state and the additional squeezed deformation of the wave function, providing a useful tool for multi-modes spin-boson coupling systems of greater complexity.Comment: 6pages,4 figure

Divisible Load Scheduling in Mobile Grid based on Stackelberg Pricing Game

Nowadays, it has become feasible to use mobile nodes as contributing entities in computing systems. In this paper, we consider a computational grid in which the mobile devices can share their idle resources to realize parallel processing. The overall computing task can be arbitrarily partitioned into multiple subtasks to be distributed to mobile resource providers (RPs). In this process, the computation load scheduling problem is highlighted. Based on the optimization objective, i.e., minimizing the task makespan, a buyer-seller model in which the task sponsor can inspire the SPs to share their computing resources by paying certain profits, is proposed. The Stackelberg Pricing Game (SPG) is employed to obtain the optimal price and shared resource amount of each SP. Finally, we evaluate the performance of the proposed algorithm by system simulation and the results indicate that the SPG-based load scheduling algorithm can significantly improve the time gain in mobile grid systems.Comment: 5 pages, 3 figures, conferenc

Two-stage Best-scored Random Forest for Large-scale Regression

We propose a novel method designed for large-scale regression problems, namely the two-stage best-scored random forest (TBRF). "Best-scored" means to select one regression tree with the best empirical performance out of a certain number of purely random regression tree candidates, and "two-stage" means to divide the original random tree splitting procedure into two: In stage one, the feature space is partitioned into non-overlapping cells; in stage two, child trees grow separately on these cells. The strengths of this algorithm can be summarized as follows: First of all, the pure randomness in TBRF leads to the almost optimal learning rates, and also makes ensemble learning possible, which resolves the boundary discontinuities long plaguing the existing algorithms. Secondly, the two-stage procedure paves the way for parallel computing, leading to computational efficiency. Last but not least, TBRF can serve as an inclusive framework where different mainstream regression strategies such as linear predictor and least squares support vector machines (LS-SVMs) can also be incorporated as value assignment approaches on leaves of the child trees, depending on the characteristics of the underlying data sets. Numerical assessments on comparisons with other state-of-the-art methods on several large-scale real data sets validate the promising prediction accuracy and high computational efficiency of our algorithm