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HYDRODYNAMICS FOR ASYMMETRIC SIMPLE EXCLUSION ON A FINITE SEGMENT WITH GLAUBER-TYPE SOURCE

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arXiv 2024年

作者： Xu, Lu Zhao, Linjie Gran Sasso Science Institute AQ L'Aquila67100 Italy School of Mathematics and Statistics Huazhong University of Science & Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

We consider an open interacting particle system on a finite lattice. The particles perform asymmetric simple exclusion and are randomly created or destroyed at all sites, with rates that grow rapidly near the boundaries. We study the hydrodynamic limit for the particle density at the hyperbolic space-time scale and obtain the entropy solution to a boundary-driven quasilinear conservation law with a source term. Different from the usual boundary conditions introduced in [3, 20], discontinuity (boundary layer) does not formulate at the boundaries due to the strong relaxation scheme. Copyright © 2024, The Authors. All rights reserved.

关键词： Hydrodynamics

Bridging Fairness Gaps: A (Conditional) Distance Covariance Perspective in Fairness Learning

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arXiv 2024年

作者： Huang, Ruifan Liu, Haixia School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan Hubei China School of Mathematics and Statistics Institute of Interdisciplinary Research for Mathematics and Applied Science Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan China

We bridge fairness gaps from a statistical perspective by selectively utilizing either conditional distance covariance or distance covariance statistics as measures to assess the independence between predictions and sensitive attributes. We enhance fairness by incorporating sample (conditional) distance covariance as a manageable penalty term into the machine learning process. Additionally, we present the matrix form of empirical (conditional) distance covariance for parallel calculations to enhance computational efficiency. Theoretically, we provide a proof for the convergence between empirical and population (conditional) distance covariance, establishing necessary guarantees for batch computations. Through experiments conducted on a range of real-world datasets, we have demonstrated that our method effectively bridges the fairness gap in machine learning. Copyright © 2024, The Authors. All rights reserved.

关键词： Contrastive Learning

SHOCK FORMATION FOR THE 2D ROTATING SHALLOW WATER EQUATIONS WITH NON-ZERO VORTICITY

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arXiv 2025年

作者： Chen, Zhendong Xie, Chunjing School of Mathematical Sciences Institute of Natural Sciences Shanghai Jiao Tong University Shanghai200240 China School of Mathematical Sciences Institute of Natural Sciences Ministry of Education Key Laboratory of Scientific and Engineering Computing CMA-Shanghai Shanghai Jiao Tong University Shanghai200240 China

In the paper, the shock formation for the two-dimensional rotating shallow water system is established. We construct a large class of initial data which leads to the finite-time blow-up for the solutions. Moreover, the solutions are allowed to have non-zero large vorticity (in derivative sense), even up to the shock. Our results provide the first complete geometric description of the shock formation mechanism to the two-dimensional rotating shallow water system with vorticity. The formation of shock is characterized by the collapse of the characteristic hypersurfaces, where the first-order derivatives of the velocity, the height, and the specific vorticity blow up while the potential vorticity remains Lipschitz continuous. The methods developed in this paper should also be useful in studying the shock formation for the Euler equations with various source terms and a class of quasilinear Klein-Gordon equations in multi-dimensions. Copyright © 2025, The Authors. All rights reserved.

关键词： Euler equations

CSI Sensing from Heterogeneous User Feedbacks: A Constrained Phase Retrieval Approach

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arXiv 2022年

作者： Li, Lei Zeng, Xing Liu, Ya-Feng Xu, Yanqing Chang, Tsung-Hui The School of Science and Engineering The Chinese University of Hong Kong Shenzhen China Huawei Technologies Ltd. Shanghai China The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

This paper investigates the downlink channel state information (CSI) sensing in 5G heterogeneous networks composed of user equipments (UEs) with different feedback capabilities. We aim to enhance the CSI accuracy of UEs only affording the low-resolution Type-I codebook. While existing works have demonstrated that the task can be accomplished by solving a phase retrieval (PR) formulation based on the feedback of precoding matrix indicator (PMI) and channel quality indicator (CQI), they need many feedback rounds. In this paper, we propose a novel CSI sensing scheme that can significantly reduce the feedback overhead. Our scheme involves a novel parameter dimension reduction design by exploiting the spatial consistency of wireless channels among nearby UEs, and a constrained PR (CPR) formulation that characterizes the feasible region of CSI by the PMI information. To address the computational challenge due to the non-convexity and the large number of constraints of CPR, we develop a two-stage algorithm that firstly identifies and removes inactive constraints, followed by a fast first-order algorithm. The study is further extended to multi-carrier systems. Extensive tests over DeepMIMO and QuaDriGa datasets showcase that our designs greatly outperform existing methods and achieve the high-resolution Type-II codebook performance with a few rounds of feedback. Copyright © 2022, The Authors. All rights reserved.

关键词： Channel state information

Taking Myopic Best Response Against The Hedge Algorithm

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Taking Myopic Best Response Against The Hedge Algorithm

Chinese Control Conference (CCC)

作者： Xinxiang Guo Yifen Mu School of Mathematical Sciences University of Chinese Academy of Sciences Beijing China The State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China The Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

With the rapid development of artificial intelligence (AI), the game between the human and machine/AI becomes more and more common. The related theoretical analysis becomes significant and necessary, which however is still rare. This problem involves evolution analysis and optimal control of dynamic game systems driven by learning algorithms. In this paper, we consider a finitely repeated two-player zero-sum game. We study the dynamic evolution process of the game system, in which one player employs the Hedge algorithm and the other player takes the myopic best response. By the updating formula of the Hedge algorithm, we define a quantity called the state and construct the State Transition Triangle Graph (STTG). Then, we prove that the game system is periodic after o(T) stages.

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Randomness-Enhanced Expressivity of Quantum Neural Networks

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Physical Review Letters 2024年第1期132卷 010602-010602页

作者： Yadong Wu Juan Yao Pengfei Zhang Xiaopeng Li Department of Physics Fudan University Shanghai 200438 China State Key Laboratory of Surface Physics Key Laboratory of Micro and Nano Photonic Structures (MOE) Institute for Nanoelectronic Devices and Quantum Computing Fudan University Shanghai 200438 China Shanghai Qi Zhi Institute AI Tower Xuhui District Shanghai 200232 China Shenzhen Institute for Quantum Science and Engineering Southern University of Science and Technology Shenzhen 518055 Guangdong China International Quantum Academy Shenzhen 518048 Guangdong China Guangdong Provincial Key Laboratory of Quantum Science and Engineering Southern University of Science and Technology Shenzhen 518055 Guangdong China Shanghai Artificial Intelligence Laboratory Shanghai 200232 China Shanghai Research Center for Quantum Sciences Shanghai 201315 China

As a hybrid of artificial intelligence and quantum computing, quantum neural networks (QNNs) have gained significant attention as a promising application on near-term, noisy intermediate-scale quantum devices. Conventional QNNs are described by parametrized quantum circuits, which perform unitary operations and measurements on quantum states. In this Letter, we propose a novel approach to enhance the expressivity of QNNs by incorporating randomness into quantum circuits. Specifically, we introduce a random layer, which contains single-qubit gates sampled from a trainable ensemble pooling. The prediction of QNN is then represented by an ensemble average over a classical function of measurement outcomes. We prove that our approach can accurately approximate arbitrary target operators using Uhlmann’s theorem for majorization, which enables observable learning. Our proposal is demonstrated with extensive numerical experiments, including observable learning, Rényi entropy measurement, and image recognition. We find the expressivity of QNNs is enhanced by introducing randomness for multiple learning tasks, which could have broad application in quantum machine learning.

关键词： Machine learning Quantum algorithms & computation Quantum channels Quantum circuits Quantum simulation Artificial neural networks

Multi-granularity Information Flow Enhanced Skeleton-based Infant Seizure Detection

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Multi-granularity Information Flow Enhanced Skeleton-based I...

IEEE International Conference on Bioinformatics and Biomedicine (BIBM)

作者： Huiyuan Chen Weiting Chen Yiqing Zhang Na Li MOE Research Center of Software/Hardware Co-Design Engineering Shanghai Key Laboratory of Trustworthy Computing East China Normal University Shanghai China Children’s Hospital Shanghai Jiao Tong University School of Medicine Shanghai China

Automatic video seizure detection can assist in the diagnosis of seizures. Existing works usually rely on the information of single granularity for learning seizure patterns and the performance of these works is often constrained by the limited annotated data. To overcome these problems, we introduce a multi-granularity information flow method to enhance skeleton-based infant seizure detection from different perspectives. A forward-backward consistency constraint is proposed to use the reverse temporal sequences as augmented data, helping make better predictions. Besides, an importance-aware module is proposed to adaptively pay more attention to important frames. Experimental results indicate that our method can improve the performance of seizure detection and achieve high performance with a relatively low amount of parameters.

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High-Order Discontinuous Galerkin Schemes for Radiation Hydrodynamics Equations in the Equilibrium-Diffusion Limit

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SSRN

SSRN 2023年

作者： Peng, Gang Luo, Dongmi Qiu, Jianxian Chen, Yibing Command and Control Engineering College Army Engineering University of PLA Nanjing210007 China Institute of Applied Physics and Computational Mathematics National Key Laboratory of Computational Physics Beijing100088 China School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University Fujian Xiamen361005 China

In this paper, the high-order discontinuous Galerkin (DG) schemes are presented for radiation hydrodynamics equations in the equilibrium-diffusion limit. The governor equations contain two parts, one part is a hyperbolic system of conservation laws and another part is a radiative heat transfer term. The discrete schemes are constructed in three parts and possess characteristics of the high-order, oscillation-free and efficient. Firstly, the DG method and local DG (LDG) method are respectively used to discretize the hyperbolic system and radiative heat transfer term to achieve high-order spatial accuracy. Secondly, the combination of the KXRCF shock detector, Hermite WENO limiter, and positivity-preserving limiter is utilized to enhance the robustness of the discretization schemes. Finally, the implicit-explicit schemes are employed for time discretization to enable the schemes suitable for larger time steps. Numerical experiments have verified that the new schemes are high-order accuracy, oscillation-free and efficiency. © 2023, The Authors. All rights reserved.

关键词： Hydrodynamics

ON SCHRÖDINGERIZATION BASED QUANTUM ALGORITHMS FOR LINEAR DYNAMICAL SYSTEMS WITH INHOMOGENEOUS TERMS

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arXiv 2024年

作者： Jin, Shi Liu, Nana Ma, Chuwen School of Mathematical Sciences Shanghai Jiao Tong University Institute of Natural Sciences Shanghai Jiao Tong University Ministry of Education Key Laboratory in Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China Institute of Natural Sciences Shanghai Jiao Tong University Ministry of Education Key Laboratory in Scientific and Engineering Computing Shanghai Jiao Tong University University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China School of Mathematical Sciences Shanghai Jiao Tong University Institute of Natural Sciences Shanghai Jiao Tong University Shanghai200240 China

We analyze the Schrödingerization method for quantum simulation of a general class of non-unitary dynamics with inhomogeneous source terms. The Schrödingerization technique, introduced in [S. Jin, N. Liu and Y. Yu, Phys. Rev. Lett., 133 (2024), 230602], transforms any linear ordinary and partial differential equations with non-unitary dynamics into a system under unitary dynamics via a warped phase transition that maps the equations into a higher dimension, making them suitable for quantum simulation. This technique can also be applied to these equations with inhomogeneous terms modeling source or forcing terms, or boundary and interface conditions, and discrete dynamical systems such as iterative methods in numerical linear algebra, through extra equations in the system. Difficulty arises with the presence of inhomogeneous terms since they can change the stability of the original system. In this paper, we systematically study—both theoretically and numerically—the important issue of recovering the original variables from the Schrödingerized equations, even when the evolution operator contains unstable modes. We show that, even with unstable modes, one can still construct a stable scheme;however, to recover the original variable, one needs to use suitable data in the extended space. We analyze and compare both the discrete and continuous Fourier transforms used in the extended dimension and derive corresponding error estimates, which allow one to use the more appropriate transform for specific equations. We also provide a smoother initialization for the Schrödingerized system to gain higher-order accuracy in the extended space. We homogenize the inhomogeneous terms with a stretch transformation, making it easier to recover the original variable. Our recovery technique also provides a simple and generic framework to solve general ill-posed problems in a computationally stable way. Copyright © 2024, The Authors. All rights reserved.

关键词： Iterative methods