Traffic accidents pose a significant risk to human health and property safety. To address this issue, predicting their risks has garnered growing interest. We argue that a desired prediction solution should demonstrat...
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In existing deep learning-based semantic communication systems, centralized training of semantic models brings a risk of privacy leakage, whereas distributed training imposes a huge computational burden on user equipm...
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An extended semi-definite programming, the SDP with an additional quadratic term in the objective function, is studied. Our generalization is similar to the generalization from linear programming to quadratic programm...
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An extended semi-definite programming, the SDP with an additional quadratic term in the objective function, is studied. Our generalization is similar to the generalization from linear programming to quadratic programming. Optimal conditions for this new class of problems are discussed and a potential reduction algorithm for solving QSDP problems is presented. The convergence properties of this algorithm are also given.
This paper discusses how to develop a high-order multiple-relaxation-time lattice Boltzmann (MRT-LB) model for the general d(≥ 1)-dimensional diagonal-anisotropic diffusion equation. Such an MRT-LB model considers th...
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This paper discusses how to develop a high-order multiple-relaxation-time lattice Boltzmann (MRT-LB) model for the general d(≥ 1)-dimensional diagonal-anisotropic diffusion equation. Such an MRT-LB model considers the transformation matrix constructed in a natural way and the DdQ(2d2 + 1) [(2d2 + 1) discrete velocities in d-dimensional space] lattice structure. A key step in developing the high-order MRT-LB model is to determine the additional adjustable relaxation parameters and weight coefficients, which are used to eliminate the truncation errors at some certain orders of the MRT-LB model, while ensuring the stability of the MRT-LB model. In this work, we first present a unified MRT-LB model for the d-dimensional diagonal-anisotropic diffusion equation. Then, through the direct Taylor expansion, we analyze the macroscopic modified equations of the MRT-LB model up to fourth-order at the diffusive scaling, and further derive the conditions that ensure the MRT-LB model to be fourth-order consistent with the diagonal-anisotropic diffusion equation. In particular, when the diagonal-anisotropic diffusion equation is reduced to the isotropic type, we propose another MRT-LB model with the DdQ(2d+ 1) lattice structure [fewer discrete velocities than the DdQ(2d2 + 1) lattice structure], and the fourth-order conditions are similarly derived. Additionally, we also construct the fourth-order initialization scheme for the present LB method. After that, the condition which guarantees that the MRT-LB model can satisfy the stability structure is explicitly given, and we would like to point out that from a numerical perspective, once the stability structure is satisfied, the MRT-LB model must be L2 stable. In combination with the fourth-order consistent and L2 stability conditions, the relaxation parameters and weight coefficients of the MRT-LB model can be automatically given by a simple computer code. Finally, we perform numerical simulations of several benchmark problems, and f
作者:
Peng, JMAssistant Professor
State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific Engineering Computing Academia Sinica Beijing China
The implicit Lagrangian has attracted much attention recently because of its utility in reformulating complementarity and variational inequality problems as unconstrained minimization problems, II was first proposed b...
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The implicit Lagrangian has attracted much attention recently because of its utility in reformulating complementarity and variational inequality problems as unconstrained minimization problems, II was first proposed by Mangasarian and Solodov as a merit function for the nonlinear complementarity problem (Ref. 1). Three open problems were also raised in the same paper, This paper addresses, among other issues, one of these problems by giving the properties of the implicit Lagrangian and establishing its convexity under appropriate assumptions.
A recent research work pointed out that the reversible data hiding algorithms proposed for gray-scale images can be implemented on the reconstructed palette images to improve embedding capacity and visual quality by r...
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We propose a clustering-based generalized low rank approximation method, which takes advantage of appealing features from both the generalized low rank approximation of matrices (GLRAM) and cluster analysis. It exploi...
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Magnetic Resonance Imaging (MRI), including diffusion MRI (dMRI), serves as a "microscope" for anatomical structures and routinely mitigates the influence of low signal-to-noise ratio scans by compromising t...
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Meandering rivers sculpt landscapes and foster diverse ecosystems, with secondary flows in bends exerting a pivotal influence on sediment transport and channel morphology. Although the Froude number typically remains ...
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