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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We prove sample path moderate deviation principles (MDP) for the current and the tagged particle in the symmetric simple exclusion process, which extends the results in [39], where the MDP was only proved at any fixed...
Numerous studies have shown that label noise can lead to poor generalization performance, negatively affecting classification accuracy. Therefore, understanding the effectiveness of classifiers trained using deep neur...
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Given a curve Γ and a set Λ in the plane, the concept of the Heisenberg uniqueness pair (Γ, Λ) was first introduced by Hedenmalm and Motes-Rodrígez (Ann. of Math. 173(2),1507-1527, 2011, [11]) as a variant of...
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In this article,we investigate a fractional-order singular Leslie-Gower prey-predator bioeconomic model,which describes the interaction bet ween populations of prey and predator,and takes into account the economic ***...
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In this article,we investigate a fractional-order singular Leslie-Gower prey-predator bioeconomic model,which describes the interaction bet ween populations of prey and predator,and takes into account the economic *** firstly obtain the solvability condition and the st ability of the model sys tem,and discuss the singularity induced bifurcation ***,we introduce a st ate feedback controller to elimina te the singularity induced bifurcation phenomenon,and discuss the optimal control ***,numerical solutions and their simulations are considered in order to illustrate the theoretical results and reveal the more complex dynamical behavior.
In this paper, we first develop a fourth-order multiple-relaxation-time lattice Boltzmann (MRT-LB) model for the one-dimensional convection-diffusion equation (CDE) with the constant velocity and diffusion coefficient...
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In this paper, we first develop a fourth-order multiple-relaxation-time lattice Boltzmann (MRT-LB) model for the one-dimensional convection-diffusion equation (CDE) with the constant velocity and diffusion coefficient, where the D1Q3 (three discrete velocities in one-dimensional space) lattice structure is used. We also perform the Chapman-Enskog analysis to recover the CDE from the MRT-LB model. Then an explicit four-level finite-difference (FLFD) scheme is derived from the developed MRT-LB model for the CDE. Through the Taylor expansion, the truncation error of the FLFD scheme is obtained, and at the diffusive scaling, the FLFD scheme can achieve the fourth-order accuracy in space. After that, we present a stability analysis and derive the same stability condition for the MRT-LB model and FLFD scheme. Finally, we perform some numerical experiments to test the MRT-LB model and FLFD scheme, and the numerical results show that they have a fourth-order convergence rate in space, which is consistent with our theoretical analysis.
In this work we develop an improved phase-field based lattice Boltzmann (LB) method where a hybrid Allen-Cahn equation (ACE) with a flexible weight instead of a global weight is used to suppress the numerical dispersi...
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In this work we develop an improved phase-field based lattice Boltzmann (LB) method where a hybrid Allen-Cahn equation (ACE) with a flexible weight instead of a global weight is used to suppress the numerical dispersion and eliminate the coarsening phenomenon. Then two LB models are adopted to solve the hybrid ACE and the Navier-Stokes equations, respectively. Through the Chapman-Enskog analysis, the present LB model can correctly recover the hybrid ACE, and the macroscopic order parameter used to label different phases can be calculated explicitly. Finally, the present LB method is validated by five tests, including the diagonal translation of a circular interface, two stationary bubbles with different radii, a bubble rising under the gravity, the Rayleigh-Taylor instability in two-dimensional and three-dimensional cases, and the three-dimensional Plateau-Rayleigh instability. The numerical results show that the present LB method has a superior performance in reducing the numerical dispersion and the coarsening phenomenon.
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 boundari...
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In this work, we first derive the one-point large deviations principle(LDP) for both the stochastic Cahn–Hilliard equation with small noise and its spatial finite difference method(FDM). Then, we focus on giving the ...
In this work, we first derive the one-point large deviations principle(LDP) for both the stochastic Cahn–Hilliard equation with small noise and its spatial finite difference method(FDM). Then, we focus on giving the convergence of the one-point large deviations rate function(LDRF) of the spatial FDM, which is about the asymptotical limit of a parametric variational problem. The main idea for proving the convergence of the LDRF of the spatial FDM is via the Γ-convergence of objective functions. This relies on the qualitative analysis of skeleton equations of the original equation and the numerical method. In order to overcome the difficulty that the drift coefficient is not one-sided Lipschitz continuous, we derive the equivalent characterization of the skeleton equation of the spatial FDM and the discrete interpolation inequality to obtain the uniform boundedness of the solution to the underlying skeleton equation. These play important roles in deriving the Γ-convergence of objective functions.
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