276,587 research outputs found
Beating Effects of Vector Solitons in Bose-Einstein Condensate
We study the beating effects of solitons in multi-component coupled
Bose-Einstein condensate systems. Our analysis indicate that the period of
beating behavior is determined by the energy eigenvalue difference in the
effective quantum well induced by solitons, and the beating pattern is
determined by the eigen-states of quantum well which are involved in the
beating behavior. We show that the beating solitons correspond to linear
superpositions of eigen-states in some quantum wells, and the correspondence
relations are identical for solitons in both attractive interaction and
repulsive interaction condensate. This provides a possible way to understand
the beating effects of solitons for attractive and repulsive interaction cases
in a unified way, based on the knowledge of quantum eigen-states. Moreover, our
results demonstrate many different beating patterns for solitons in
three-component coupled condensate, in sharp contrast to the beating dark
soliton reported before. The beating behavior can be used to test the
eigenvalue differences of some certain quantum wells, and more abundant beating
patterns are expected to exist in more components coupled systems.Comment: 7 papes, 3 figure
Multi-modal Aggregation for Video Classification
In this paper, we present a solution to Large-Scale Video Classification
Challenge (LSVC2017) [1] that ranked the 1st place. We focused on a variety of
modalities that cover visual, motion and audio. Also, we visualized the
aggregation process to better understand how each modality takes effect. Among
the extracted modalities, we found Temporal-Spatial features calculated by 3D
convolution quite promising that greatly improved the performance. We attained
the official metric mAP 0.8741 on the testing set with the ensemble model
Moderate maximal inequalities for the Ornstein-Uhlenbeck process
The maximal inequalities for diffusion processes have drawn increasing
attention in recent years. However, the existing proof of the maximum
inequalities for the Ornstein-Uhlenbeck process was dubious. Here we give a
rigorous proof of the moderate maximum inequalities for the Ornstein-Uhlenbeck
process, which include the maximum inequalities as special cases and
generalize the remarkable maximum inequalities obtained by Graversen and
Peskir [P. Am. Math. Soc., 128(10):3035-3041, 2000]. As a corollary, we also
obtain a new moderate maximal inequality for continuous local martingales,
which can be viewed as a supplement of the classical Burkholder-Davis-Gundy
inequality
Maximum principles and monotonicity of solutions for fractional p-equations in unbounded domains
In this paper, we consider the following non-linear equations in unbounded
domains with exterior Dirichlet condition:
\begin{equation*}\begin{cases} (-\Delta)_p^s u(x)=f(u(x)), & x\in\Omega,\\
u(x)>0, &x\in\Omega,\\ u(x)\leq0, &x\in \mathbb{R}^n\setminus \Omega,
\end{cases}\end{equation*} where is the fractional p-Laplacian
defined as \begin{equation} (-\Delta)_p^s
u(x)=C_{n,s,p}P.V.\int_{\mathbb{R}^n}\frac{|u(x)-u(y)|^{p-2}[u(x)-u(y)]}{|x-y|^{n+s
p}}dy \label{0} \end{equation} with and . We first establish a
maximum principle in unbounded domains involving the fractional p-Laplacian by
estimating the singular integral in (\ref{0}) along a sequence of approximate
maximum points. Then, we obtain the asymptotic behavior of solutions far away
from the boundary. Finally, we develop a sliding method for the fractional
p-Laplacians and apply it to derive the monotonicity and uniqueness of
solutions. There have been similar results for the regular Laplacian
\cite{BCN1} and for the fractional Laplacian \cite{DSV}, which are linear
operators. Unfortunately, many approaches there no longer work for the fully
non-linear fractional p-Laplacian here. To circumvent these difficulties, we
introduce several new ideas, which enable us not only to deal with non-linear
non-local equations, but also to remarkably weaken the conditions on
and on the domain . We believe that the new methods developed in our
paper can be widely applied to many problems in unbounded domains involving
non-linear non-local operators.Comment: 29 page
On the topological pressure of the saturated set with non-uniform structure
We derive a conditional variational principle of the saturated set for
systems with the non-uniform structure. Our result applies to a broad class of
systems including beta-shifts, S-gap shifts and their factors.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1605.07283; text
overlap with arXiv:1304.5497 by other author
A Comprehensive Method to Measure Solar Meridional Circulation and Center-to-Limb Effect Using Time-Distance Helioseismology
Meridional circulation is a crucial component of the Sun's internal dynamics,
but its inference in the deep interior is complicated by a systematic
center-to-limb effect in helioseismic measurement techniques. Previously, an
empirical method, removing travel-time shifts measured for east-west traveling
waves in the equatorial area from those measured for north-south traveling
waves in the central meridian area, was used, but its validity and accuracy
need to be assessed. Here we develop a new method to separate the
center-to-limb effect, \delta\tau_CtoL, and meridional-flow-induced travel-time
shifts, \delta\tau_MF, in a more robust way. Using 7-yr observations of the
SDO/HMI, we exhaustively measure travel-time shifts between two surface
locations along the solar disk's radial direction for all azimuthal angles and
all skip distances. The measured travel-time shifts are a linear combination of
\delta\tau_CtoL and \delta\tau_MF, which can be disentangled through solving
the linear equation set. The \delta\tau_CtoL is found isotropic relative to the
azimuthal angle, and the \delta\tau_MF are then inverted for the meridional
circulation. Our inversion results show a three-layer flow structure, with
equatorward flow found between about 0.82 and 0.91 R_sun for low latitude areas
and between about 0.85 and 0.91 R_sun for higher latitude areas. Poleward flows
are found below and above the equatorward flow zones, indicating a double-cell
circulation in each hemisphere.Comment: Accepted for publication in Ap
-ary Hom-Nambu algebras
In this paper, we define -derivations, and study some properties of
-derivations, with its properties we can structure a new -ary
Hom-Nambu algebra from an -ary Hom-Nambu algebra. In addition, we also give
derivations and representations of -ary Hom-Nambu algebras.Comment: 16page
Super Congruences Involving Multiple Harmonic Sums and Bernoulli Numbers
Let , and be positive integers. We denote by any
tuple of odd positive integers such that
and for all . In this paper we prove that for
every sufficiently large prime where are products of Bernoulli numbers and
the coefficients are polynomials of independent of and
. This generalizes previous results by many different authors and confirms a
conjecture by the authors and their collaborators.Comment: 19 pages. We updated the proof of Lemma 5.1 and corrected some
misprint
New Construction of Authentication Codes with Arbitration from Pseudo-Symplectic Geometry over Finite Fields
A new construction of authentication codes with arbitration from
pseudo-symplectic geometry over finite fields is given. The parameters and the
probabilities of deceptions of the codes are also computed.Comment: arXiv admin note: text overlap with arXiv:1302.3160 by other author
Boosted Attention: Leveraging Human Attention for Image Captioning
Visual attention has shown usefulness in image captioning, with the goal of
enabling a caption model to selectively focus on regions of interest. Existing
models typically rely on top-down language information and learn attention
implicitly by optimizing the captioning objectives. While somewhat effective,
the learned top-down attention can fail to focus on correct regions of interest
without direct supervision of attention. Inspired by the human visual system
which is driven by not only the task-specific top-down signals but also the
visual stimuli, we in this work propose to use both types of attention for
image captioning. In particular, we highlight the complementary nature of the
two types of attention and develop a model (Boosted Attention) to integrate
them for image captioning. We validate the proposed approach with
state-of-the-art performance across various evaluation metrics.Comment: Published in ECCV 201
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