Poisson Structures for Dispersionless Integrable Systems and Associated W-Algebras

In analogy to the KP theory, the second Poisson structure for the dispersionless KP hierarchy can be defined on the space of commutative pseudodifferential operators $L=p^n+\sum_{j=-\infty}^{n-1}u_j p^j$. The reduction of the Poisson structure to the symplectic submanifold $u_{n -1}=0$ gives rise to the w-algebras. In this paper, we discuss properties of this Poisson structure, its Miura transformation and reductions. We are particularly interested in the following two cases: a) L is pure polynomial in p with multiple roots and b) L has multiple poles at finite distance. The w-algebra corresponding to the case a) is defined as $w_ {[m_1,m_2, ... ,m_r]}$, where m_i means the multiplicity of roots and to the case b) is defined by $w(n,[m_1,m_2, ... ,m_r])$ where m_i is the multiplicity of poles. We prove that w(n,[m_1, m_2, ... , m_r])$-algebra is isomorphic via a transformation to$w_{[m_1,m_2, ... ,m_r]} \bigoplus w_{n+m} \bigoplus U(1) with $m=\sum m_i$. We also give the explicit free fields representations for these w-algebras.Comment: Latex, 11 pages, no figures; Lett. Math. Phy

Virasoro type algebraic structure hidden in the constrained discrete KP hierarchy

In this paper, we construct the additional symmetries of one-component constrained discrete KP (cdKP) hierarchy, and then prove that the algebraic structure of the symmetry flows is the positive half of Virasoro algebra.Comment: 13 page

Hyperbolic Structure and Stickiness Effect: A case of a 2D Area-Preserving Twist Mapping

The stickiness effect suffered by chaotic orbits diffusing in the phase space of a dynamical system is studied in this paper. Previous works have shown that the hyperbolic structures in the phase space play an essential role in causing the stickiness effect. We present in this paper the relationship between the stickiness effect and the geometric property of hyperbolic structures. Using a two-dimensional area-preserving twist mapping as the model, we develop the numerical algorithms for computing the positions of the hyperbolic periodic orbits and for calculating the angle between the stable and unstable manifolds of the hyperbolic periodic orbit. We show how the stickiness effect and the orbital diffusion speed are related to the angle.Comment: 12 pages, 14 figures. accepted by SCIENCE CHINA Physics, Mechanics & Astronom

The recursion operator for a constrained CKP hierarchy

This paper gives a recursion operator for a 1-constrained CKP hierarchy, and by the recursion operator it proves that the 1-constrained CKP hierarchy can be reduced to the mKdV hierarchy under condition $q=r$.Comment: To appear in "Acta Matematica Scientia

Zero-shot Chinese Discourse Dependency Parsing via Cross-lingual Mapping

Due to the absence of labeled data, discourse parsing still remains challenging in some languages. In this paper, we present a simple and efficient method to conduct zero-shot Chinese text-level dependency parsing by leveraging English discourse labeled data and parsing techniques. We first construct the Chinese-English mapping from the level of sentence and elementary discourse unit (EDU), and then exploit the parsing results of the corresponding English translations to obtain the discourse trees for the Chinese text. This method can automatically conduct Chinese discourse parsing, with no need of a large scale of Chinese labeled data

Research on the influence of Internet technology popularization on the green development of agriculture in the Yangtze River Economic Belt

Based on the panel data from 2000 To 2018, the super efficiency sbm-dea model is used to calculate the agricultural green development efficiency of 11 Provinces and cities in the Yangtze River economic belt, and then the Tobit econometric model is used to empirically test the impact of Internet technology popularization on the agricultural green development of the Yangtze River economic belt. The results show that: (1) on the whole, the efficiency of agricultural green development in the Yangtze River Economic Belt showed a downward trend in fluctuations from 2000 To 2018; in terms of regions, the efficiency of agricultural green development in various regions of the Yangtze River Economic Belt varies greatly, showing a spatial pattern of "downstream > upstream > midstream". (2) The popularization of Internet technology has significantly promoted the green development of agriculture in the Yangtze River economic belt; at the same time, there is a significant positive correlation between rural human capital and the green development of agriculture in the Yangtze River economic belt, while the level of agricultural mechanization, the degree of capital deepening, the level of urbanization and agricultural economic growth inhibit the improvement of the green development of agriculture in the Yangtze River Economic Belt to a certain extent. Therefore, the local governments of the Yangtze River Economic Belt should actively promote the popularization of Internet technology, enhance the Internet awareness of farmers, and give better play to the enabling role of Internet technology in the green development of agriculture in the Yangtze River economic belt

CSRS: Code Search with Relevance Matching and Semantic Matching

Developers often search and reuse existing code snippets in the process of software development. Code search aims to retrieve relevant code snippets from a codebase according to natural language queries entered by the developer. Up to now, researchers have already proposed information retrieval (IR) based methods and deep learning (DL) based methods. The IR-based methods focus on keyword matching, that is to rank codes by relevance between queries and code snippets, while DL-based methods focus on capturing the semantic correlations. However, the existing methods do not consider capturing two matching signals simultaneously. Therefore, in this paper, we propose CSRS, a code search model with relevance matching and semantic matching. CSRS comprises (1) an embedding module containing convolution kernels of different sizes which can extract n-gram embeddings of queries and codes, (2) a relevance matching module that measures lexical matching signals, and (3) a co-attention based semantic matching module to capture the semantic correlation. We train and evaluate CSRS on a dataset with 18.22M and 10k code snippets. The experimental results demonstrate that CSRS achieves an MRR of 0.614, which outperforms two state-of-the-art models DeepCS and CARLCS-CNN by 33.77% and 18.53% respectively. In addition, we also conducted several experiments to prove the effectiveness of each component of CSRS

Scalable one-way quantum computer using on-chip resonator qubits

We propose a scalable and robust architecture for one-way quantum computation using coupled networks of superconducting transmission line resonators. In our protocol, quantum information is encoded into the long-lived photon states of the resonators, which have a much longer coherence time than the usual superconducting qubits. Each resonator contains a charge qubit used for the state initialization and local projective measurement of the photonic qubit. Any pair of neighboring photonic qubits are coupled via a mediator charge qubit, and large photonic cluster states can be created by applying Stark-shifted Rabi pulses to these mediator qubits. The distinct advantage of our architecture is that it combines both the excellent scalability of the solid-state systems and the long coherence time of the photonic qubits. Furthermore, this architecture is very robust against the parameter variations.Comment: 6 pages, 3 figure

Implementing Quantum Search Algorithm with Metamaterials

Metamaterials, artificially structured electromagnetic (EM) materials, have enabled the realization of many unconventional electromagnetic properties not found in nature, such as negative refractive index, magnetic response, invisibility cloaking and so on. Based on these man-made materials with novel EM properties, various devices have been designed and realized. However, quantum analog devices based on metamaterials have not been achieved so far. Here we designed and printed metamaterials to perform quantum search algorithm. The structures, comprising of an array of two-dimensional (2D) sub-wavelength air holes with different radii perforated on the dielectric layer, have been fabricated by using 3D printing technique. When an incident wave enters in the designed metamaterials, the profile of beam wavefront is processed iteratively as it propagates through the metamaterial periodically. After roundtrips, precisely the same as the efficiency of quantum search algorithm, searched items will be found with the incident wave all focusing on the marked positions. Such a metamaterial-based quantum searching simulator may lead to remarkable achievements in wave-based signal processors.Comment: 22 pages,6 figure

HMS-Net: Hierarchical Multi-scale Sparsity-invariant Network for Sparse Depth Completion

Dense depth cues are important and have wide applications in various computer vision tasks. In autonomous driving, LIDAR sensors are adopted to acquire depth measurements around the vehicle to perceive the surrounding environments. However, depth maps obtained by LIDAR are generally sparse because of its hardware limitation. The task of depth completion attracts increasing attention, which aims at generating a dense depth map from an input sparse depth map. To effectively utilize multi-scale features, we propose three novel sparsity-invariant operations, based on which, a sparsity-invariant multi-scale encoder-decoder network (HMS-Net) for handling sparse inputs and sparse feature maps is also proposed. Additional RGB features could be incorporated to further improve the depth completion performance. Our extensive experiments and component analysis on two public benchmarks, KITTI depth completion benchmark and NYU-depth-v2 dataset, demonstrate the effectiveness of the proposed approach. As of Aug. 12th, 2018, on KITTI depth completion leaderboard, our proposed model without RGB guidance ranks first among all peer-reviewed methods without using RGB information, and our model with RGB guidance ranks second among all RGB-guided methods.Comment: IEEE Trans. on Image Processin