9,508 research outputs found
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 -dimensional
() hypersurface in the Euclidean space and any Riemannian
manifold , when the sectional curvature of satisfies
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
-dimensional () complete hypersurface in the Euclidean space, if
the sectional curvature of satisfies , then we conclude that there exist no stable compact minimal
submanifolds in .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
In this article we study surfaces in for
which the -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 in lattice QCD
We investigate the coupling constant for the hadronic
decay 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 MILC
gauge configuration with flavor of the "Asqtad" improved staggered
dynamical sea quarks at the lattice spacing fm. Our estimated
value for this given MILC fine lattice gauge ensemble
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
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