时变偏微分方程的贝叶斯稀疏识别方法

在数据驱动的建模中,通过测量或模拟得到时空数据,我们发现基于拉普拉斯先验的贝叶斯稀疏识别方法能有效地恢复时变偏微分方程的稀疏系数。本文将贝叶斯稀疏识别方法运用于各种时变偏微分方程模型（KdV方程、Burgers方程、Kuramoto-Sivashinsky方程、反应-扩散方程、非线性薛定谔方程和纳维-斯托克斯方程）的方程系数恢复,将贝叶斯稀疏恢复结果与PDE-FIND稀疏恢复算法进行比较,证实贝叶斯稀疏识别方法对偏微分方程具有非常强的稀疏恢复能力。同时,研究中发现贝叶斯稀疏方法对噪声更敏感,可以识别更多的附加项。此外,贝叶斯方法可以直接得到稀疏恢复解的误差方差,由此可以直接判定稀疏恢复的效果和可靠性。     

TargetATPsite: A template‐free method for ATP‐binding sites prediction with residue evolution image sparse representation and classifier ensemble

Understanding the interactions between proteins and ligands is critical for protein function annotations and drug discovery. We report a new sequence‐based template‐free predictor (TargetATPsite) to identify the Adenosine‐5′‐triphosphate (ATP) binding sites with machine‐learning approaches. Two steps are implemented in TargetATPsite: binding residues and pockets predictions, respectively. To predict the binding residues, a novel image sparse representation technique is proposed to encode residue evolution information treated as the input features. An ensemble classifier constructed based on support vector machines (SVM) from multiple random under‐samplings is used as the prediction model, which is effective for dealing with imbalance phenomenon between the positive and negative training samples. Compared with the existing ATP‐specific sequence‐based predictors, TargetATPsite is featured by the second step of possessing the capability of further identifying the binding pockets from the predicted binding residues through a spatial clustering algorithm. Experimental results on three benchmark datasets demonstrate the efficacy of TargetATPsite. © 2013 Wiley Periodicals, Inc.     

遗传算法结合正则化方法反演海洋大气波导

针对正则化方法在解决实际反演问题时既能克服问题的不适定性又可以很大程度上抑制噪声和误差的传播, 本文提出了利用遗传算法结合正则化方法的新算法, 在遗传算法适应度函数中引入正则化项来反演波导参数; 然后对算法进行仿真试验, 结果表明新算法与传统遗传算法相比具有较高的反演精度, 并指出当噪声误差小于10%时, 算法具有较强的“去噪”性能; 最后利用机载雷达在Wallops岛探测的海表面处局部回波资料进行反演试验, 将反演结果与实测大气折射率廓线进行比较, 说明该算法的有效性. 新方法为海洋大气波导反演研究提供了一种新思路.     

A light-front coupled-cluster method for the nonperturbative solution of quantum field theories

We propose a new method for the nonperturbative solution of quantum field theories and illustrate its use in the context of a light-front analog to the Greenberg–Schweber model. The method is based on light-front quantization and uses the exponential-operator technique of the many-body coupled-cluster method. The formulation produces an effective Hamiltonian eigenvalue problem in the valence Fock sector of the system of interest, combined with nonlinear integral equations to be solved for the functions that define the effective Hamiltonian. The method avoids the Fock-space truncations usually used in nonperturbative light-front Hamiltonian methods and, therefore, does not suffer from the spectator dependence, Fock-sector dependence, and uncanceled divergences caused by such truncations.     

Interpolation on Sparse Grids and Tensor Products of Nikol'skij–Besov Spaces

We investigate the order of convergence of periodic interpolation on sparse grids (blending interpolation) in the framework of tensor products of Nikol'skij–Besov spaces. To this end, we make use of the uniformity of the considered tensor norms and provide a unified approach to error estimates for the interpolation of univariate periodic functions from Nikol'skij–Besov spaces.     

A regularization of nonlinear diffusion equations in a multiresolution framework

We develop a regularization technique for Perona–Malik diffusion equations that relies on multiresolution techniques. The main result of this paper is to show that the chosen discretization overcomes the ill posedness of the nonlinear Perona–Malik model. The resulting algorithm is tested and the results are compared with pixel‐based methods. Copyright © 2007 John Wiley & Sons, Ltd.     

Sparse grids and hybrid methods for the chemical master equation

The direct numerical solution of the chemical master equation (CME) is usually impossible due to the high dimension of the computational domain. The standard method for solution of the equation is to generate realizations of the chemical system by the stochastic simulation algorithm (SSA) by Gillespie and then taking averages over the trajectories. Two alternatives are described here using sparse grids and a hybrid method. Sparse grids, implemented as a combination of aggregated grids are used to address the curse of dimensionality of the CME. The aggregated components are selected using an adaptive procedure. In the hybrid method, some of the chemical species are represented macroscopically while the remaining species are simulated with SSA. The convergence of variants of the method is investigated for a growing number of trajectories. Two signaling cascades in molecular biology are simulated with the methods and compared to SSA results. AMS subject classification (2000)  65C20, 60J25, 92C45     

A new zero-finder for Tikhonov regularization

Tikhonov regularization with the regularization parameter determined by the discrepancy principle requires the computation of a zero of a rational function. We describe a cubically convergent zero-finder for this purpose. AMS subject classification (2000)  65F22, 65H05, 65R32     

Extended Gauss–Markov Theorem for Nonparametric Mixed-Effects Models

The Gauss–Markov theorem provides a golden standard for constructing the best linear unbiased estimation for linear models. The main purpose of this article is to extend the Gauss–Markov theorem to include nonparametric mixed-effects models. The extended Gauss–Markov estimation (or prediction) is shown to be equivalent to a regularization method and its minimaxity is addressed. The resulting Gauss–Markov estimation serves as an oracle to guide the exploration for effective nonlinear estimators adaptively. Various examples are discussed. Particularly, the wavelet nonparametric regression example and its connection with a Sobolev regularization is presented.     

非正则线性增广拉格朗日乘子法的收敛速率研究CSCD

Recently,an indefinite linearized augmented Lagrangian method(IL-ALM)was proposed for the convex programming problems with linear constraints.The IL-ALM differs from the linearized augmented Lagrangian method in that the augmented Lagrangian is linearized by adding an indefinite quadratic proximal term.But,it preserves the algorithmic feature of the linearized ALM and usually has the advantage to improve the performance.The IL-ALM is proved to be convergent from contraction perspective,but its convergence rate is still missing.This is mainly because that the indefinite setting destroys the structures when we directly employ the contraction frameworks.In this paper,we derive the convergence rate for this algorithm by using a different analysis.We prove that a worst-case O(1/t)convergence rate is still hold for this algorithm,where t is the number of iterations.Additionally we show that the customized proximal point algorithm can employ larger step sizes by proving its equivalence to the linearized ALM.