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Chinese Medical Journal 2024年第8期137卷 883-886页

作者： Xiaoshuang Wang Jing Wang Tao Cheng institute of Basic Medical sciences Chinese Academy of Medical Sciences&Peking Union Medical CollegeBeijing 100005China State Key Laboratory of Experimental Hematology National Clinical Research Center for Blood DiseasesHaihe Laboratory of Cell EcosystemInstitute of Hematology&Blood Diseases HospitalChinese Academy of Medical Sciences&Peking Union Medical CollegeTianjin 300020China

The institute of Basic Medical sciences(IBMS)is a global leader in biomedical research and advanced medical *** year(2023)marks the 65^(th)anniversary of its foundation at the Chinese Academy of Medical sciences(CAMS)and School of Basic Medicine(SBM)of the Peking Union Medical College(PUMC).In the beginning,the IBMS and SBM incorporated the premedical departments of the PUMC,which was established by the Rockefeller Foundation in *** then,these departments have been committed to undertakingrstrate medical science research in China.

关键词： Basic IBMS foundation

NSNO:Neumann Series Neural Operator for Solving Helmholtz Equations in Inhomogeneous Medium

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Journal of Systems Science & Complexity 2024年第2期37卷 413-440页

作者： CHEN Fukai LIU Ziyang LIN Guochang CHEN Junqing SHI Zuoqiang Department of mathematical sciences Tsinghua UniversityBeijing 100084China Yau mathematical sciences Center Tsinghua UniversityBeijing 100084China Yanqi Lake Beijing institute of mathematical sciences and Applications Beijing 101408China

In this paper,the authors propose Neumann series neural operator(NSNO)to learn the solution operator of Helmholtz equation from inhomogeneity coefficients and source terms to *** equation is a crucial partial differential equation(PDE)with applications in various scientific and engineering ***,efficient solver of Helmholtz equation is still a big challenge especially in the case of high ***,deep learning has shown great potential in solving PDEs especially in learning solution *** by Neumann series in Helmholtz equation,the authors design a novel network architecture in which U-Net is embedded inside to capture the multiscale *** experiments show that the proposed NSNO significantly outperforms the state-of-the-art FNO with at least 60%lower relative L^(2)-error,especially in the large wavenumber case,and has 50%lower computational cost and less data ***,NSNO can be used as the surrogate model in inverse scattering *** tests show that NSNO is able to give comparable results with traditional finite difference forward solver while the computational cost is reduced tremendously.

关键词： Helmholtz equation inverse problem neumann series neural network solution operator

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Pseudo-Differential Operators of Homogeneous Symbol Class Associated with the Weinstein Transform

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Acta Mathematica Sinica,English Series 2024年第6期40卷 1533-1562页

作者： Santosh Kumar UPADHYAY Mohd SARTAJ Department of mathematical sciences Indian Institute of Technology(BHU)VaranasiIndia

In this paper,pseudo-differential operators with homogeneous symbol classes associated with the Weinstein transform are *** boundedness of pseudo-differential operators and commutator between two pseudo-differential o... 详细信息

关键词： Pseudo-Differential Operators Homogeneous Symbol Class Weinstein Operator Sobolev space Weinstein transform

Optimization of Random Feature Method in the High-Precision Regime

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Communications on Applied Mathematics and Computation 2024年第2期6卷 1490-1517页

作者： Jingrun Chen Weinan E Yifei Sun School of mathematical sciences and Suzhou institute for Advanced research Suzhou 215006JiangsuChina University of Science and Technology of China Hefei 230026AnhuiChina Center for Machine Learning research and School of mathematical sciences Peking UniversityBeijing 100871China AI for Science institute Beijing 100084China School of mathematical sciences Soochow UniversitySuzhou 215006JiangsuChina

Machine learning has been widely used for solving partial differential equations(PDEs)in recent years,among which the random feature method(RFM)exhibits spectral accuracy and can compete with traditional solvers in terms of both accuracy and ***,the optimization problem in the RFM is more difficult to solve than those that arise in traditional *** the broader machine-learning research,which frequently targets tasks within the low-precision regime,our study focuses on the high-precision regime crucial for solving *** this work,we study this problem from the following aspects:(i)we analyze the coeffcient matrix that arises in the RFM by studying the distribution of singular values;(ii)we investigate whether the continuous training causes the overfitting issue;(ii)we test direct and iterative methods as well as randomized methods for solving the optimization *** on these results,we find that direct methods are superior to other methods if memory is not an issue,while iterative methods typically have low accuracy and can be improved by preconditioning to some extent.

关键词： Random feature method(RFM) Partial differential equation(PDE) Least-squares problem Direct method Iterative method

Competitive Resource Allocation Among Urban Congestion Areas in a Modern Big City

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Journal of the Operations research Society of China 2024年第1期12卷 133-153页

作者： Alexander Krylatov Anastasiya Raevskaya institute of Applied mathematical research of the Karelian research Centre of the Russian Academy of sciences Petrozavodsk185910Russia Saint Petersburg State University Saint Petersburg199034Russia

The continuing growth of modern big cities leads to their spatial expansion and the emergence of new road connections and urban *** where large transportation flows of pedestrians,passengers,and drivers come together create demand points,which attract business companies that strive to allocate their resources in the most sought-after ***,the law of supply and demand restrains companies from allocating all their resources solely in the most popular congestion areas since the more valuable an urban area,the higher the cost to be paid for a resource unit allocation *** a result,companies act in a non-cooperative manner and try to minimize their own overall costs when allocating resources across available commercial areas in a big ***-cooperative behavior of companies leads to the problem of Nash equilibrium search in the game of competing *** this paper,we study the corresponding resource allocation game under affine cost functions and obtain Nash equilibrium strategies in explicit *** findings allow us to develop a simple procedure for computing Nash equilibria in the game of companies allocating their resources among urban congestion *** computational study demonstrates the dependence of the average price for resource allocation on the number of players and their resource *** outcome of the paper contributes to flow theory and seems to be fresh and useful for managers.

关键词： Resource allocation Nash equilibrium Affine costs

An oscillation-free Hermite WENO scheme for hyperbolic conservation laws

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Science China Mathematics 2024年第2期67卷 431-454页

作者： Zhuang Zhao Jianxian Qiu School of mathematical sciences and institute of Natural sciences Shanghai Jiao Tong UniversityShanghai 200240China School of mathematical sciences and Fujian Provincial Key Laboratory of mathematical Modeling and High-Performance Scientific Computing Xiamen UniversityXiamen 361005China

In this paper, the sixth-order oscillation-free Hermite weighted essentially non-oscillatory (OFHWENO) scheme is proposed for hyperbolic conservation laws on structured meshes, where the zeroth- andfirst-order moments are the variables for the governing equations. The main difference from other HWENOschemes existing in the literature is that we add high-order numerical damping terms in the first-order momentequations to control spurious oscillations for the OF-HWENO scheme. The OF-HWENO scheme not only canachieve the designed optimal numerical order, but also can be easily implemented as we use only one set ofstencils in the reconstruction procedure and the same reconstructed polynomials are applied for the zeroth- andfirst-order moment equations. In order to obtain the adaptive order resolution when facing discontinuities, atransition polynomial is added in the reconstruction, where the associated linear weights can also be any positivenumbers as long as their summation equals one. In addition, the OF-HWENO scheme still keeps compactnessas only immediate neighbor values are needed in the space discretization. Some benchmark numerical tests areperformed to illustrate the high-order accuracy, high resolution and robustness of the proposed scheme.

关键词： Hermite WENO scheme hyperbolic conservation laws oscillation-free adaptive order discontinuous Galerkin method

Trace inequalities, isocapacitary inequalities, and regularity of the complex Hessian equations

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Science China Mathematics 2024年第3期67卷 557-576页

作者： Jiaxiang Wang Bin Zhou Beijing International Center for mathematical research Peking UniversityBeijing 100871China School of mathematical sciences Peking UniversityBeijing 100871China

In this paper, we study the relations between trace inequalities(Sobolev and Moser-Trudinger types), isocapacitary inequalities, and the regularity of the complex Hessian and Monge-Amp`ere equations with respect to a general nonnegative Borel measure. We obtain a quantitative characterization for these relations through the properties of the capacity-minimizing functions.

关键词： complex Monge-Ampère equations plurisubharmonic functions Sobolev inequality Moser-Trudinger inequality

The Rate of Convergence of Augmented Lagrangian Method for Minimax Optimization Problems with Equality Constraints

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Journal of the Operations research Society of China 2024年第2期12卷 265-297页

作者： Yu-Hong Dai Li-Wei Zhang LSEC ICMSECAMSSChinese Academy of SciencesBeijing 100190China institute of Operations research and Control Theory School of Mathematical SciencesDalian University of TechnologyDalian 116024China

The augmented Lagrangian function and the corresponding augmented Lagrangian method are constructed for solving a class of minimax optimization problems with equality *** prove that,under the linear independence constraint qualification and the second-order sufficiency optimality condition for the lower level problem and the second-order sufficiency optimality condition for the minimax problem,for a given multiplier vectorμ,the rate of convergence of the augmented Lagrangian method is linear with respect to||μu-μ^(*)||and the ratio constant is proportional to 1/c when the ratio|μ-μ^(*)||/c is small enough,where c is the penalty parameter that exceeds a threshold c_(*)>O andμ^(*)is the multiplier corresponding to a local ***,we prove that the sequence of multiplier vectors generated by the augmented Lagrangian method has at least Q-linear convergence if the sequence of penalty parameters(ck)is bounded and the convergence rate is superlinear if(ck)is increasing to ***,we use a direct way to establish the rate of convergence of the augmented Lagrangian method for the minimax problem with a quadratic objective function and linear equality constraints.

关键词： Minimax optimization Augmented Lagrangian method.Rate of convergence Second-order sufficiency optimality

Dilation,discrimination and Uhlmann's theorem of link products of quantum channels

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Chinese Physics B 2024年第3期33卷 201-206页

作者：雷强操刘桁 Asutosh Kumar 武俊德 School of mathematical sciences Harbin Institute of TechnologyHarbin 150001China Department of Physics Gaya CollegeMagadh UniversityRampurGaya 823001India School of mathematical sciences Zhejiang UniversityHangzhou 310027China

We establish the Stinespring dilation theorem of the link product of quantum channels in two different ways,discuss the discrimination of quantum channels,and show that the distinguishability can be improved by self-linking each quantum channel n times as n *** also find that the maximum value of Uhlmann's theorem can be achieved for diagonal channels.

关键词： quantum channels link products Stinespring dilation theorem Uhlmann's theorem

Rational Solutions of First Order Algebraic Ordinary Differential Equations

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Journal of Systems Science & Complexity 2024年第2期37卷 567-580页

作者： FENG Shuang SHEN Liyong School of Physical and mathematical sciences Nanjing Tech UniversityNanjing 211816China School of mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

Let f(t,y,y')=∑ _(i=0)^(n )a_(i)(t,y)y'^(i)=0 be an irreducible first order ordinary differential equation with polynomial *** in 1998 proved that there exists a constant C such that every rational solution of f(t,y,y')=0 is of degree not greater than *** show that this degree bound C depends not only on the degrees of f in t,y,y' but also on the coefficients of f viewed as the polynomial in t,y,y'.In this paper,the authors show that if f satisfies deg(f,y)0,then the degree bound C only depends on the degrees of f in t,y,y',and furthermore we present an explicit expression for C in terms of the degrees of f in t,y,y'.

关键词： Degree bound first order AODE height rational solution

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