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arXiv 2021年

作者： Wang, Yun Xie, Chunjing School of Mathematical Sciences Center for dynamical systems and differential equations Soochow University Suzhou China School of mathematical Sciences Institute of Natural Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing IMA-Shanghai Shanghai Jiao Tong University 800 Dongchuan Road Shanghai China

In this paper, uniqueness and uniform structural stability of Poiseuille flows in an infinitely long pipe with Navier boundary conditions are established for axisymmetric solutions of steady Navier-Stokes system. The crucial point is that the estimate is uniform with respect both the flux of flows and slip coefficient which appeared in Navier boundary conditions. With the aid of special structure of Navier-Stokes system and the refined estimate for some quantities such as radial velocity, the uniqueness and existence of steady solutions of Navier-Stokes system can be obtained even when the external forces are large as long as the fluxes of flows are large. The delicate decomposition in the two dimensional plane for slip coefficient and frequency corresponding to Fourier variable in the axial direction plays a key role to achieve these estimates. Copyright © 2021, The Authors. All rights reserved.

关键词： Stability

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Multi-label Classification with High-rank and High-order Label Correlations

arXiv

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arXiv 2022年

作者： Si, Chongjie Jia, Yuheng Wang, Ran Zhang, Min-Ling Feng, Yanghe Qu, Chongxiao The Chien-Shiung Wu College Southeast University Nanjing210096 China The MoE Key Lab of Artificial Intelligence AI Institute Shanghai Jiao Tong University Shanghai200240 China The School of Computer Science and Engineering Southeast University Nanjing210096 China Ministry of Education China School of Computing & Information Sciences Caritas Institute of Higher Education Hong Kong The Key Laboratory of Computer Network and Information Integration Southeast University Ministry of Education China The School of Mathematical Science Shenzhen University Shenzhen518060 China Shenzhen Key Laboratory of Advanced Machine Learning and Applications Shenzhen University Shenzhen518060 China The College of Systems Engineering National University of Defense Technology China The 52nd Research Institute of China Electronics Technology Group China

Exploiting label correlations is important to multi-label classification. Previous methods capture the high-order label correlations mainly by transforming the label matrix to a latent label space with low-rank matrix factorization. However, the label matrix is generally a full-rank or approximate full-rank matrix, making the low-rank factorization inappropriate. Besides, in the latent space, the label correlations will become implicit. To this end, we propose a simple yet effective method to depict the high-order label correlations explicitly, and at the same time maintain the high-rank of the label matrix. Moreover, we estimate the label correlations and infer model parameters simultaneously via the local geometric structure of the input to achieve mutual enhancement. Comparative studies over twelve benchmark data sets validate the effectiveness of the proposed algorithm in multi-label classification. The exploited high-order label correlations are consistent with common sense empirically. Our code is publicly available at https://***/Chongjie-Si/HOMI. Copyright © 2022, The Authors. All rights reserved.

关键词： Matrix algebra

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THE GLOBAL ATTRACTOR FOR A VISCOUS WEAKLY DISSIPATIVE GENERALIZED TWO-COMPONENT μ-HUNTER-SAXTON SYSTEM

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Acta Mathematica Scientia 2018年第2期38卷 651-672页

作者：张磊刘斌 School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology

This article is concerned with the existence of global attractor of a weakly dissipative generalized two-component μ-Hunter-Saxton （gμHS2） system with viscous terms. Under the period boundary conditions and with the help of the Galerkin procedure and compactness method, we first investigate the existence of global solution for the viscous weakly dissipative （gμHS2） system. On the basis of some uniformly prior estimates of the solution to the viscous weakly dissipative （gμHS2） system, we show that the semi-group of the solution operator {S（t）}t≥0 has a bounded absorbing set. Moreover, we prove that the dynamical system {S（t）}t≥0 possesses a global attractor in the Sobolev space H2（S） × H2（S）.

关键词： Generalized two-component μ-Hunter-Saxton system viscous weakly dissipative existence global attractor period boundary conditions

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A diffuse-interface lattice Boltzmann method for the dissolution through nonlinear heterogeneous reaction

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Physics of Fluids 2025年第5期37卷

作者： Yang, Xiaofeng Zhan, Chengjie Liu, Xi Chai, Zhenhua School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China The State Key Laboratory of Intelligent Manufacturing Equipment and Technology Huazhong University of Science and Technology Wuhan430074 China

In this work, a diffuse-interface lattice Boltzmann method (DI-LBM) is proposed for the dissolution through nonlinear heterogeneous reaction. In this method, the sharp boundary between the fluid and solid phases is replaced by a diffuse interface with a nonzero thickness. To describe the changes of physical variables from the fluid region to the solid region, a smooth function is introduced, and simultaneously, the nonlinear Robin boundary condition imposed on the fluid-solid interface is reformulated as a source term into the modified convection-diffusion equation. We then test the DI-LBM through several benchmark problems, and find that the numerical results are in agreement with the analytical solutions and available data. Finally, the present DI-LBM is adopted to study the dissolution in a two-dimensional porous medium, and the results show that with the decrease in reaction order, the reactant in the central region with a large fluid velocity reacts faster and forms a conical pathway. © 2025 Author(s).

关键词： Kinetic theory of gases

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Stabilized multiple-relaxation implicit-explicit Runge-Kutta methods for nonlinear Gross-Pitaevskii equations

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Journal of Computational Physics 2025年 538卷

作者： Dongfang Li Xiaoxi Li Jiwei Zhang Zhimin Zhang School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan 430074 China School of Mathematics and Statistics Wuhan University Wuhan 430072 China Hubei Key Laboratory of Computational Science Wuhan University Wuhan 430072 China Department of Mathematics Wayne State University Detroit 48202 MI USA

A novel class of stabilized multiple-relaxation implicit-explicit Runge-Kutta methods is proposed for solving nonlinear Gross-Pitaevskii equations. The methods conserve the mass and the energy simultaneously in the discrete sense, and achieve arbitrarily high-order accuracy in the temporal direction. Additionally, there are several highlights in this study. Firstly, this is the first attempt to apply the stabilization approach to develop relaxation-type schemes, which effectively avoids the blow-up of the relaxation parameters due to the nonlinearity and stiffness of the problems. Secondly, the governing equations that determine the relaxation parameters are newly designed to conserve the original invariants, which can be extended to conserve more invariants of other physical models. Thirdly, the schemes are linearly implicit after obtaining the relaxation parameters, and thus are easy to implement. Several numerical experiments are carried out to confirm the effectiveness and theoretical results of the proposed methods.

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When Brain-inspired AI Meets AGI

arXiv

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arXiv 2023年

作者： Zhao, Lin Zhang, Lu Wu, Zihao Chen, Yuzhong Dai, Haixing Yu, Xiaowei Liu, Zhengliang Zhang, Tuo Hu, Xintao Jiang, Xi Li, Xiang Zhu, Dajiang Shen, Dinggang Liu, Tianming School of Computing The University of Georgia Athens30602 United States Department of Computer Science and Engineering The University of Texas at Arlington Arlington76019 United States MOE Key Laboratory for Neuroinformation School of Life Science and Technology University of Electronic Science and Technology of China Chengdu611731 China School of Automation Northwestern Polytechnical University Xi’an710072 China Department of Radiology Massachusetts General Hospital Harvard Medical School Boston02115 United States School of Biomedical Engineering ShanghaiTech University Shanghai201210 China Shanghai United Imaging Intelligence Co. Ltd. Shanghai200230 China Shanghai Clinical Research and Trial Center Shanghai201210 China

Artificial General Intelligence (AGI) has been a long-standing goal of humanity, with the aim of creating machines capable of performing any intellectual task that humans can do. To achieve this, AGI researchers draw inspiration from the human brain and seek to replicate its principles in intelligent machines. Brain-inspired artificial intelligence is a field that has emerged from this endeavor, combining insights from neuroscience, psychology, and computer science to develop more efficient and powerful AI systems. In this article, we provide a comprehensive overview of brain-inspired AI from the perspective of AGI. We begin with the current progress in brain-inspired AI and its extensive connection with AGI. We then cover the important characteristics for both human intelligence and AGI (e.g., scaling, multimodality, and reasoning). We discuss important technologies toward achieving AGI in current AI systems, such as in-context learning and prompt tuning. We also investigate the evolution of AGI systems from both algorithmic and infrastructural perspectives. Finally, we explore the limitations and future of AGI. © 2023, CC BY.

关键词： Brain

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Complexity Analysis and Algorithm Design of Pooling Problem

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Journal of the Operations Research Society of China 2018年第2期6卷 249-266页

作者： Yu-Hong Dai Rui Diao Kai Fu State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

The pooling problem,also called the blending problem,is fundamental in production planning of *** can be formulated as an optimization problem similar with the minimum-cost flow ***,Alfaki and Haugland(J Glob Optim 56:897–916,2013)proved the strong NP-hardness of the pooling problem in general *** also pointed out that it was an open problem to determine the computational complexity of the pooling problem with a fixed number of *** this paper,we prove that the pooling problem is still strongly NP-hard even with only one *** means the quality is an essential difference between minimum-cost flow problem and the pooling *** solving large-scale pooling problems in real applications,we adopt the non-monotone strategy to improve the traditional successive linear programming *** convergence of the algorithm is *** numerical experiments show that the non-monotone strategy is effective to push the algorithm to explore the global minimizer or provide a good local *** results for real problems from factories show that the proposed algorithm is competitive to the one embedded in the famous commercial software Aspen PIMS.

关键词： Pooling problem Complexity analysis Successive linear programming Non-monotone

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A semi-adaptive finite difference method for simulating two-sided fractional convection–diffusion quenching problems

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Journal of Computational and Applied Mathematics 2026年 472卷

作者： Rumin Dong Lin Zhu Qin Sheng Bingxin Zhao School of Mathematics and Statistics Ningxia Key Laboratory of Interdisciplinary Mechanics and Scientific Computing Ningxia Basic Science Research Center of Mathematics Ningxia University Yinchuan 750021 China Department of Mathematics and Center for Astrophysics Space Physics and Engineering Research Baylor University Waco TX 76798-7328 USA

This paper investigates quenching solutions of an one-dimensional, two-sided Riemann–Liouville fractional order convection–diffusion problem. Fractional order spatial derivatives are discretized using weighted averaging approximations in conjunction with standard and shifted Grünwald formulas. The advective term is handled utilizing a straightforward Euler formula, resulting in a semi-discretized system of nonlinear ordinary differential equations. The conservativeness of the proposed scheme is rigorously proved and validated through simulation experiments. The study is further advanced to a fully discretized, semi-adaptive finite difference method. Detailed analysis is implemented for the monotonicity, positivity and stability of the scheme. Investigations are carried out to assess the potential impacts of the fractional order on quenching location, quenching time, and critical length. The computational results are thoroughly discussed and analyzed, providing a more comprehensive understanding of the quenching phenomena modeled through two-sided fractional order convection–diffusion problems.

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Upper capacity entropy and packing entropy of saturated sets for amenable group actions

arXiv

引用

arXiv 2021年

作者： Ren, Xiankun Zhang, Wenda Zhang, Yiwei College of Mathematics and Statistics Chongqing University Chongqing 401331 China College of Mathematics and Statistics Chongqing Jiaotong University Chongqing 400074 China School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Sciences and Technology Wuhan430074 China

Let (X, G) be a G-action topological system, where G is a countable infinite discrete amenable group and X a compact metric space. In this paper we study the upper capacity entropy and packing entropy for systems with weaker version of specification. We prove that the upper capacity always carries full entropy while there is a variational principle for packing entropy of saturated sets. © 2021, CC BY-NC-ND.

关键词： Specifications

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Quantum noise protects quantum classifiers against adversaries

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Physical Review Research 2021年第2期3卷 023153-023153页

作者： Yuxuan Du Min-Hsiu Hsieh Tongliang Liu Dacheng Tao Nana Liu UBTECH Sydney AI Centre School of Computer Science Faculty of Engineering University of Sydney Australia Hon Hai Quantum Computing Research Center No. 32 Jihu Road Neihu District Taipei 114 Taiwan Institute of Natural Sciences Shanghai Jiao Tong University Shanghai 200240 China Ministry of Education Key Laboratory in Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai 200240 China University of Michigan-Shanghai Jiao Tong University Joint Institute Shanghai 200240 China

Noise in quantum information processing is often viewed as a disruptive and difficult-to-avoid feature, especially in near-term quantum technologies. However, noise has often played beneficial roles, from enhancing weak signals in stochastic resonance to protecting the privacy of data in differential privacy. It is then natural to ask: Can we harness the power of quantum noise that is beneficial to quantum computing? An important current direction for quantum computing is its application to machine learning, such as classification problems. One outstanding problem in machine learning for classification is its sensitivity to adversarial examples. These are small, undetectable perturbations from the original data where the perturbed data is completely misclassified in otherwise extremely accurate classifiers. They can also be considered as worst-case perturbations by unknown noise sources. We show that by taking advantage of depolarization noise in quantum circuits for classification, a robustness bound against adversaries can be derived where the robustness improves with increasing noise. This robustness property is intimately connected with an important security concept called differential privacy, which can be extended to quantum differential privacy. For the protection of quantum data, this quantum protocol can be used against the most general adversaries. Furthermore, we show how the robustness in the classical case can be sensitive to the details of the classification model, but in the quantum case the details of the classification model are absent, thus also providing a potential quantum advantage for classical data. This opens the opportunity to explore other ways in which quantum noise can be used in our favor, as well as identifying other ways quantum algorithms can be helpful in a way which is distinct from quantum speedups.

关键词： Machine learning Quantum algorithms Quantum information processing Quantum protocols

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