Convergence to the Time Average by Stochastic Regularization

In Ergodic Theory it is natural to consider the pointwise convergence of finite time averages of functions with respect to the flow of dynamical systems. Since the pointwise convergence is too weak for applications to Hamiltonian Perturbation Theory, requiring differentiability, we first introduce regularized averages obtained through a stochastic perturbation of an integrable Hamiltonian flow, and then we provide detailed estimates. In particular, for a special vanishing limit of the stochastic perturbation, we obtain convergence even in a Sobolev norm taking into account the derivatives.     

Sparse models by iteratively reweighted feature scaling: a framework for wavelength and sample selection

In the past decade, there has been an increase in the use of sparse multivariate calibration methods in chemometrics. Sparsity describes a parsimonious state of model complexity and can be defined in terms of a subset of samples or covariates (e.g., wavelengths) that are used to define the calibration model. With respect to their classical counterparts such as principal component regression or partial least squares, sparse models are more easily interpretable and have been shown to exhibit non‐inferior prediction performance. However, sparse methods are still not as fast as the classical methods in spite of recent numerical advances. In addition, for many chemometricians, sparse methods are still “black‐box” algorithms whose internal workings are not well understood. In this paper, we describe a simple framework whereby classical multivariate calibration methods can be iteratively used to generate sparse models. Moreover, this approach allows for either wavelength or sample sparsity. We demonstrate the effectiveness of this approach on two spectroscopic data sets. Copyright © 2013 John Wiley & Sons, Ltd.     

Multi-loop zeta function regularization and spectral cutoff in curved spacetime

We emphasize the close relationship between zeta function methods and arbitrary spectral cutoff regularizations in curved spacetime. This yields, on the one hand, a physically sound and mathematically rigorous justification of the standard zeta function regularization at one loop and, on the other hand, a natural generalization of this method to higher loops. In particular, to any Feynman diagram is associated a generalized meromorphic zeta function. For the one-loop vacuum diagram, it is directly related to the usual spectral zeta function. To any loop order, the renormalized amplitudes can be read off from the pole structure of the generalized zeta functions. We focus on scalar field theories and illustrate the general formalism by explicit calculations at one-loop and two-loop orders, including a two-loop evaluation of the conformal anomaly.     

Strong Law of Large Numbers for Stationary Sequences of Random Upper Semicontinuous Functions

Abstract

The strong laws of large numbers with the convergence in the sense of the uniform Hausdorff metric for stationary sequences of random upper semicontinuous functions is established. This approach allows us to deduce many results on the convergence in uniform Hausdorff metric of random upper semicontinuous functions from the relevant results on real-valued random variables that appear as their support functions.     

循环图能量的一个上界

本文讨论循环图的能量,得到循环图能量上界的一个估计值.进一步得到整循环图能量的两个计算公式.     

On decomposition-based block preconditioned iterative methods for half-quadratic image restoration

Image restoration is a fundamental problem in image processing. Except for many different filters applied to obtain a restored image in image restoration, a degraded image can often be recovered efficiently by minimizing a cost function which consists of a data-fidelity term and a regularization term. In specific, half-quadratic regularization can effectively preserve image edges in the recovered images and a fixed-point iteration method is usually employed to solve the minimization problem. In this paper, the Newton method is applied to solve the half-quadratic regularization image restoration problem. And at each step of the Newton method, a structured linear system of a symmetric positive definite coefficient matrix arises. We design two different decomposition-based block preconditioning matrices by considering the special structure of the coefficient matrix and apply the preconditioned conjugate gradient method to solve this linear system. Theoretical analysis shows the eigenvector properties and the spectral bounds for the preconditioned matrices. The method used to analyze the spectral distribution of the preconditioned matrix and the correspondingly obtained spectral bounds are different from those in the literature. The experimental results also demonstrate that the decomposition-based block preconditioned conjugate gradient method is efficient for solving the half-quadratic regularization image restoration in terms of the numerical performance and image recovering quality.     

The Upper and Lower Solutions Method for Stochastic Inclusions with Discontinuous Multivalued Mappings

Abstract

In this article, we consider a stochastic integral inclusion driven by semimartingale with discontinuous multivalued right hand side. We discuss the existence of strong solutions using lower and upper solutions method and a fixed point theorem for ordered sets. The presented studies extend some recent results both for deterministic differential inclusions and stochastic differential equations for increasing operators.     

Comment on ‘Preconditioning of matrices partitioned in 2 Œ 2 block form: Eigenvalue estimates and Schwarz DD for mixed FEM’ by Owe Axelsson,Radim Blaheta

In this note, we discuss the inverse representations of regularized saddle point matrices and point out that some conclusions given by Axelsson and Blaheta in [Numerical Linear Algebra with Applications, 2010,17:787–810 ] are not true.Copyright © 2011 John Wiley & Sons, Ltd.     

环境温度影响下基于支持向量机与强化飞蛾扑火优化算法的结构稀疏损伤识别

结构处于自然环境中常会受到环境温度变化的影响,引起实测动力响应出现较大误差,进一步影响对结构健康状况的判定.另外,基于优化算法的损伤识别在反演损伤位置及量化损伤程度时,易出现局部最优解,且计算效率低下.针对以上难题,本文提出一种结合支持向量机与强化飞蛾扑火优化算法的损伤识别方法,用于对环境温度影响下的结构稀疏损伤进行识...     

Laplacian regularized kernel minimum squared error and its application to face recognition

Kernel minimum squared error (KMSE) has been receiving much attention in data mining and pattern recognition in recent years. Generally speaking, training a KMSE classifier, which is a kind of supervised learning, needs sufficient labeled examples. However, labeled examples are usually insufficient and unlabeled examples are abundant in real-world applications. In this paper, we introduce a semi-supervised KMSE algorithm, called Laplacian regularized KMSE (LapKMSE), which explicitly exploits the manifold structure. We construct a p nearest neighbor graph to model the manifold structure of labeled and unlabeled examples. Then, LapKMSE incorporates the structure information of labeled and unlabeled examples in the objective function of KMSE by adding a Laplacian regularization term. As a result, the labels of labeled and unlabeled examples vary smoothly along the geodesics on the manifold. Experimental results on several synthetic and real-world datasets illustrate the effectiveness of our algorithm. Finally our algorithm is applied to face recognition and achieves the comparable results compared to the other supervised and semi-supervised methods.