Blow-up criteria for Boussinesq system and MHD system and Landau-Lifshitz equations in a bounded domain

In this paper, we prove some blow-up criteria for the 3D Boussinesq system with zero heat conductivity and MHD system and Landau-Lifshitz equations in a bounded domain.Comment: 20 page

Human Pose Estimation using Global and Local Normalization

In this paper, we address the problem of estimating the positions of human joints, i.e., articulated pose estimation. Recent state-of-the-art solutions model two key issues, joint detection and spatial configuration refinement, together using convolutional neural networks. Our work mainly focuses on spatial configuration refinement by reducing variations of human poses statistically, which is motivated by the observation that the scattered distribution of the relative locations of joints e.g., the left wrist is distributed nearly uniformly in a circular area around the left shoulder) makes the learning of convolutional spatial models hard. We present a two-stage normalization scheme, human body normalization and limb normalization, to make the distribution of the relative joint locations compact, resulting in easier learning of convolutional spatial models and more accurate pose estimation. In addition, our empirical results show that incorporating multi-scale supervision and multi-scale fusion into the joint detection network is beneficial. Experiment results demonstrate that our method consistently outperforms state-of-the-art methods on the benchmarks.Comment: ICCV201

Robust and Efficient Hamiltonian Learning

With the fast development of quantum technology, the sizes of both digital and analog quantum systems increase drastically. In order to have better control and understanding of the quantum hardware, an important task is to characterize the interaction, i.e., to learn the Hamiltonian, which determines both static and dynamic properties of the system. Conventional Hamiltonian learning methods either require costly process tomography or adopt impractical assumptions, such as prior information on the Hamiltonian structure and the ground or thermal states of the system. In this work, we present a robust and efficient Hamiltonian learning method that circumvents these limitations based only on mild assumptions. The proposed method can efficiently learn any Hamiltonian that is sparse on the Pauli basis using only short-time dynamics and local operations without any information on the Hamiltonian or preparing any eigenstates or thermal states. The method has a scalable complexity and a vanishing failure probability regarding the qubit number. Meanwhile, it performs robustly given the presence of state preparation and measurement errors and resiliently against a certain amount of circuit and shot noise. We numerically test the scaling and the estimation accuracy of the method for transverse field Ising Hamiltonian with random interaction strengths and molecular Hamiltonians, both with varying sizes and manually added noise. All these results verify the robustness and efficacy of the method, paving the way for a systematic understanding of the dynamics of large quantum systems.Comment: 41 pages, 6 figures, Open source implementation available at https://github.com/zyHan2077/HamiltonianLearnin