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 $L^p$ 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 $L^p$ maximum inequalities as special cases and generalize the remarkable $L^1$ 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 $\Omega$ 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 $(-\Delta)_p^s$ 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 $0<s<1$ and $p\geq 2$. 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 $f(\cdot)$ and on the domain $\Omega$. 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

nn-ary Hom-Nambu algebras

In this paper, we define $\omega$-derivations, and study some properties of $\omega$-derivations, with its properties we can structure a new $n$-ary Hom-Nambu algebra from an $n$-ary Hom-Nambu algebra. In addition, we also give derivations and representations of $n$-ary Hom-Nambu algebras.Comment: 16page

Super Congruences Involving Multiple Harmonic Sums and Bernoulli Numbers

Let $m$, $r$ and $n$ be positive integers. We denote by ${\bf k}\vdash n$ any tuple of odd positive integers ${\bf k}=(k_1,\dots,k_t)$ such that $k_1+\dots+k_t=n$ and $k_j\ge 3$ for all $j$. In this paper we prove that for every sufficiently large prime $p$ $$\sum_{\substack{l_1+l_2+\cdots+l_n=mp^r p\nmid l_1 l_2 \cdots l_n }} \frac1{l_1l_2\cdots l_n} \equiv p^{r-1} \sum_{{\bf k}\vdash n} C_{m,{\bf k}} B_{p-{\bf k}} \pmod{p^r}$$ where $B_{p-{\bf k}}=B_{p-k_1}B_{p-k_2}\cdots B_{p-k_t}$ are products of Bernoulli numbers and the coefficients $C_{m,{\bf k}}$ are polynomials of $m$ independent of $p$ and $r$. 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