Improving Penalized Least Squares through Adaptive Selection of Penalty and Shrinkage

Estimation of the mean function in nonparametric regression is usefully separated into estimating the means at the observed factor levels—a one-way layout problem—and interpolation between the estimated means at adjacent factor levels. Candidate penalized least squares (PLS) estimators for the mean vector of a one-way layout are expressed as shrinkage estimators relative to an orthogonal regression basis determined by the penalty matrix. The shrinkage representation of PLS suggests a larger class of candidate monotone shrinkage (MS) estimators. Adaptive PLS and MS estimators choose the shrinkage vector and penalty matrix to minimize estimated risk. The actual risks of shrinkage-adaptive estimators depend strongly upon the economy of the penalty basis in representing the unknown mean vector. Local annihilators of polynomials, among them difference operators, generate penalty bases that are economical in a range of examples. Diagnostic techniques for adaptive PLS or MS estimators include basis-economy plots and estimates of loss or risk.     

基于Sigmoid-iCAM色貌模型的真实影像再现算法

为了模拟人类视觉系统成像机制,真实再现人眼对外界场景的视觉感知,为机器视觉提供符合生物视觉特性的理想图像,从色度学的角度研究了彩色图像的真实影像再现技术。针对色貌模型存在图像模糊、对比度低的缺点,在iCAM色貌模型的基础上,引入了人工神经网络的非线性Sigmoid函数,提出了基于Sigmoid-iCAM色貌模型的真实影像再现算法,并给出了该模型处理不同类型图像的控制参数统计规律。与基于CIECAM02、iCAM色貌模型的真实影像再现算法相比,该算法在对色调失真图像实现颜色复原的同时,有效地提高了图像的对比度和局部细节,很好地实现了视觉系统的颜色恒定性。     

Parameter estimation in dynamic Casimir force measurements with known periodicity

It is important to have an accurate estimate of the unknown parameters such as the separation distance between interacting materials in Casimir force measurements. Current methods tend to produce large estimation errors. In this Letter, we present a novel method based on an adaptive control approach to estimate the unknown parameters using large amplitude dynamic Casimir measurements at separation distances of below 1 μm where both electrostatic force and Casimir force are significant. The estimate is proved to be accurate and the effectiveness of our method is demonstrated via a numerical example.     

Model Adaptation Enriched with an Anisotropic Mesh Spacing for Nonlinear Equations: Application to Environmental and CFD Problems

Goal of this paper is to suitably combine a model with an anisotropic mesh adaptation for the numerical simulation of nonlinear advection-diffusion-reaction systems and incompressible flows in ecological and environmental applications. Using the reduced-basis method terminology, the proposed approach leads to a noticeable computational saving of the online phase with respect to the resolution of the reference model on nonadapted grids. The search of a suitable adapted model/mesh pair is to be meant, instead, in an offline fashion.     

Balancing exploration and exploitation with adaptive variation for evolutionary multi-objective optimization

Although recent studies have shown that evolutionary algorithms are effective tools for solving multi-objective optimization problems, their performances are often bottlenecked by the suitability of the evolutionary operators with respect to the optimization problem at hand and their corresponding parametric settings. To adapt the search dynamic of evolutionary operation in multi-objective optimization, this paper proposes an adaptive variation operator that exploits the chromosomal structure of binary representation and synergizes the function of crossover and mutation. The overall search ability is deterministically tuned online to maintain a balance between extensive exploration and local fine-tuning at different stages of the evolutionary search. Also, the coordination between the two variation operators is achieved by means of an adaptive control that ensures an efficient exchange of information between the different chromosomal sub-structures throughout the evolutionary search. Extensive comparative studies with several representative variation operators are performed on different benchmark problems and significant algorithmic performance improvements in terms of proximity, uniformity and diversity are obtained with the incorporation of the proposed adaptive variation operator into the evolutionary multi-objective optimization process.     

Adaptive fuzzy synchronization for a class of fractional-order neural networks

In this paper, synchronization for a class of uncertain fractional-order neural networks with external disturbances is discussed by means of adaptive fuzzy control. Fuzzy logic systems, whose inputs are chosen as synchronization errors,are employed to approximate the unknown nonlinear functions. Based on the fractional Lyapunov stability criterion, an adaptive fuzzy synchronization controller is designed, and the stability of the closed-loop system, the convergence of the synchronization error, as well as the boundedness of all signals involved can be guaranteed. To update the fuzzy parameters,fractional-order adaptations laws are proposed. Just like the stability analysis in integer-order systems, a quadratic Lyapunov function is used in this paper. Finally, simulation examples are given to show the effectiveness of the proposed method.     

SPH核函数光滑长度最优选取和自适应准则研究

基于小波分析理论和RKPM再生核函数研究无网格方法SPH中多尺度诊断工具,多尺度再生核函数使得数值计算在不同尺度上的响应分离,并通过动态伸缩窗函数给出计算域不同位置的时频特性,实现在无网格体系下构造网格计算方法的“自适应网格”,从而达到对不同流场位置多分辨率分析的目的.利用多尺度诊断工具中的小波分解算法给出SPH核函数在频域内能量残差估计,发展一种核函数光滑长度最优选取准则.最后,基于可压缩流场激波稀疏波共存的现象,针对传统的光滑长度自适应的缺陷,构造一种避免数值计算“拖尾”现象的自适应准则.     

A stochastic approximation algorithm with multiplicative step size modification

An algorithm of searching a zero of an unknown function ϕ: ℝ → ℝ is considered: x _t = x _t−1 − γ _t−1 y _t , t = 1, 2, ..., where y _t = ϕ(x _t−1) + ξ _t is the value of ϕ measured at x _t−1 and ξ _t is the measurement error. The step sizes γ _t > 0 are modified in the course of the algorithm according to the rule: γ _t = min{uγ _t−1, } if y _t−1 y _t > 0, and γ _t = dγ _t−1, otherwise, where 0 < d < 1 < u, > 0. That is, at each iteration γ _t is multiplied either by u or by d, provided that the resulting value does not exceed the predetermined value . The function ϕ may have one or several zeros; the random values ξ _t are independent and identically distributed, with zero mean and finite variance. Under some additional assumptions on ϕ, ξ _t , and , the conditions on u and d guaranteeing a.s. convergence of the sequence {x _t }, as well as a.s. divergence, are determined. In particular, if P(ξ ₁ > 0) = P (ξ ₁ < 0) = 1/2 and P(ξ ₁ = x) = 0 for any x ∈ ℝ, one has convergence for ud < 1 and divergence for ud > 1. Due to the multiplicative updating rule for γ _t , the sequence {x _t } converges rapidly: like a geometric progression (if convergence takes place), but the limit value may not coincide with, but instead, approximate one of the zeros of ϕ. By adjusting the parameters u and d, one can reach arbitrarily high precision of the approximation; higher accuracy is obtained at the expense of lower convergence rate.      

Yeast adaptation on softwood prehydrolysate

Several strains and genera of yeast, includingSaccharomyces cerevisiae D₅A,Pachysolen tannophilus, S. cerevisiae K-l,Brettanomyces custersii, Candida shehatae, andCandida acidothermophilum, are screened for growth on dilute acid-pretreated softwood prehydrolysate. Selected softwood species found in forest underbrush of the western United States, which contain predominantly hexosan hemicellulose, were studied. This phase of the work emphasized debarked Douglas fir. The two best initial isolates were gradually selected for improved growth by adaptation to increasing prehydrolysate concentrations in batch culture, with due consideration of nutrient requirements. Microaerophilic conditions were evaluated to encourage tolerance of pretreatment hydrolysate, as well as ethanol product. Adaptation and simultaneous saccharification and fermentation (SSF) results are used to illustrate improved performance with an adapted strain, compared to the wild type.     

A local pseudo arc-length method for hyperbolic conservation laws

A local pseudo arc-length method（LPALM）for solving hyperbolic conservation laws is presented in this paper.The key idea of this method comes from the original arc-length method,through which the critical points are bypassed by transforming the computational space.The method is based on local changes of physical variables to choose the discontinuous stencil and introduce the pseudo arc-length parameter,and then transform the governing equations from physical space to arc-length space.In order to solve these equations in arc-length coordinate,it is necessary to combine the velocity of mesh points in the moving mesh method,and then convert the physical variable in arclength space back to physical space.Numerical examples have proved the effectiveness and generality of the new approach for linear equation,nonlinear equation and system of equations with discontinuous initial values.Non-oscillation solution can be obtained by adjusting the parameter and the mesh refinement number for problems containing both shock and rarefaction waves.