图像的多尺度几何分析概述*

以函数的稀疏表示为主线,详细介绍了各种多尺度几何分析产生的背景、发展历程和逼近性能,并分析了它们各自存在的优缺点,最后指出了其发展方向.     

铜锌铝合金表面非线性振荡花样的研究

在Ｃｕ－Ｚｎ－Ａｌ形状记忆合金表面观察到尚未被人们认识的非线性振荡花样。这些花样经计算机图像处理得知，在空间和时间上明显呈现分形特征。这种振荡花样的产生可能与未知相变的预转变过程有关。     

SOME PROPERTIES OF THE MAXIMUM LIKELIHOOD ESTIMATOR IN THE SIMULTANEOUS SWITCHING AUTOREGRESSIVE MODEL

Abstract. The simultaneous switching autoregressive (SSAR) model proposed by Kunitomo and Sato (A non-linearity in economic time series and disequilibrium econometric models. In Theory and Application of Mathematical Statistics (ed. A. Takemura). Tokyo:University of Tokyo Press (in Japanese), 1994; Asymmetry in economic time series and simultaneous switching autoregressive model. Struct. Change Econ. Dyn. , forthcoming (1994).) is a Markovian non-linear time series model. We investigate the finite sample as well as the asymptotic properties of the least squares estimator and the maximum likelihood (ML) estimator. Due to a specific simultaneity involved in the SSAR model, the least squares estimator is badly biased. However, the ML estimator under the assumption of Gaussian disturbances gives reasonable estimates.     

基于重叠片排列的流形学习算法

针对线性数据降维算法对处理非线性结构数据的降维效果不是很好,提出一种基于重叠片排列的流形学习算法,该算法根据局部的线性贴片处在非线性流形中的特性,将流形划分为线性互相重叠的局部区域贴片,且利用主成分分析方法得到局部区域贴片的低维表示,然后排列且对齐其低维坐标,以获得整体数据的低维坐标.通过仿真结果证明,基于重叠片排列的流形学习算法在应用于人脸识别和分类问题时以及在识别准确率方面要优于其他经典的流形学习算法.     

一种交互式的岩心图像修补方法

传统的岩心图像修补方法往往无法对不同宽度的待修补域达到理想效果,并且难以对待修补区域做出选择,这在实际应用中很难满足需要。针对这些问题,提出基于联合一阶与二阶全变差（Combined TV-TV2）的交互式岩心修补方法。该方法首先进行均值漂移对图像进行预分割,然后使用基于区域合并的交互式最大相似度算法确定待修补的区域,最后以联合TV-TV2修补模型为基础,应用分裂Bregman迭代进行求解。实验结果表明,待修补的区域能够被确定,而对于不同宽度的修补区域,该算法能够获得满意的修补效果。     

牛顿迭代法在求解物料平衡式中的应用

高炉数学模型是分析炉况、指导操作的有效工具.物料平衡是高炉生产遵循的基本理论,建立高炉数学模型中常需要建立物料平衡式计算相关数据.文章提出采用Newton迭代法来求解物料平衡式,并针对炉身模拟模型建立了物料平衡式并进行了求解.结果表明,Newton迭代法能够有效的求解物料平衡方程式,并具有易于软件实现,以及高效率、高精度的优点.     

基于特征迭代的云存储数据即时确定性删除方法

传统数据删除方法易受到云存储环境中大量近似特征的影响,产生冗余数据,导致加解密时间过长、密钥可用率较低,为此提出一种基于特征迭代的云存储数据即时确定性删除方法。首先,提取云存储数据中的冗余数据特征,对云存储下冗余数据进行分类,迭代直至收敛,实现冗余数据高性能删除;其次,采用加密机制实现云存储数据在网络用户间的安全共享,将原始数据密文切分为剩余密文和采样密文;最后,把不完整的剩余数据密文上传至云端,同时引入可信任第三方对取样密文进行保存,通过销毁取样密文实现数据即时确定性删除。实验结果表明,所提方法的数据密文拆分所用时间较短,且密钥可用率较高,可达90%,说明其方法能够有效满足云存储系统中对冗余数据或过期数据的确定性删除要求。     

Stochastically resilient extended Kalman filtering for discrete-time nonlinear systems with sensor failures

Missing sensor data is a common problem, which severely influences the overall performance of modern data-intensive control and computing applications. In order to address this important issue, a novel resilient extended Kalman filter is proposed for discrete-time nonlinear stochastic systems with sensor failures and random observer gain perturbations. The failure mechanisms of multiple sensors are assumed to be independent of each other with different failure rates. The locally unbiased robust minimum mean square filter is designed for state estimation under these conditions. The performance of the proposed estimation method is verified by means of numerical Monte Carlo simulation of two different nonlinear stochastic systems, involving a sinusoidal system and a Lorenz oscillator system.     

Modelling the dynamics of the students’ academic performance in the German region of the North Rhine-Westphalia: an epidemiological approach with uncertainty

Student academic underachievement is a concern of paramount importance in Europe, where around 15% of the students in the last high school courses do not achieve the minimum knowledge academic requirement. In this paper, we propose a model based on a system of differential equations to study the dynamics of the students’ academic performance in the German region of the North Rhine-Westphalia. This approach is supported by the idea that both good and bad study habits, are a mixture of personal decisions and influence of classmates. This model allows us to forecast the student academic performance by means of confidence intervals over the next few years.     

Finite horizon optimal control of non-linear discrete-time switched systems using adaptive dynamic programming with ε-error bound

In this paper, we aim to solve the finite-horizon optimal control problem for a class of non-linear discrete-time switched systems using adaptive dynamic programming(ADP) algorithm. A new ε-optimal control scheme based on the iterative ADP algorithm is presented which makes the value function converge iteratively to the greatest lower bound of all value function indices within an error according to ε within finite time. Two neural networks are used as parametric structures to implement the iterative ADP algorithm with ε-error bound, which aim at approximating the value function and the control policy, respectively. And then, the optimal control policy is obtained. Finally, a simulation example is included to illustrate the applicability of the proposed method.