Numerical solution of a multidimensional two-phase stefan problem

This paper treats a multidimensional two-phase Stefan problem with variable coefficients and mixed type boundary conditions. A numerical method for solving the problem is of fixed domain type, based on a variational inequality formulation of the problem. Numerical solutions are obtained by using piecewise linear finite elements in space and finite difference in time, and by solving a strictly convex minimization problem at each time step. Some computational results are presented.     

Multivariate calibration maintenance and transfer through robust fused LASSO

This article studies calibration maintenance and transfer to build a statistical model that is able to predict analyte concentrations by a set of spectra. Noticing that the wavelength atoms are naturally ordered in a meaningful way, we propose a novel robust fused LASSO (RFL) based on high‐dimensional sparsity techniques and a recent Θ‐IPOD technique for robustification. This new approach can attain simultaneous wavelength selection and grouping as well as outlier identification, without any human intervention. An efficient and scalable algorithm is developed on the basis of the alternating direction method of multipliers. The obtained RFL model is sparse and shows improved prediction performance over the LASSO and ridge regression. Our results reveal that wavelengths can be combined into blocks, in a smart manner, to enhance the interpretability and reliability for super‐resolution spectral analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Wavelet-Based Detection of Outliers in Time Series

This article considers the problem of detecting outliers in time series data and proposes a general detection method based on wavelets. Unlike other detection procedures found in the literature, our method does not require that a model be specified for the data. Also, use of our method is not restricted to data generated from ARIMA processes. The effectiveness of the proposed method is compared with existing outlier detection procedures. Comparisons based on various models, sample sizes, and parameter values illustrate the effectiveness of the proposed method.     

Outlier Detections in Autoregressive Models

This article proposes a new technique for detecting outliers in autoregressive models and identifying the type as either innovation or additive. This technique can be used without knowledge of the true model order, outlier location, or outlier type. Specifically, we perturb an observation to obtain the perturbation size that minimizes the resulting residual sum of squares (SSE). The reduction in the SSE yields outlier detection and identification measures. In addition, the perturbation size can be used to gauge the magnitude of the outlier. Monte Carlo studies and empirical examples are presented to illustrate the performance of the proposed method as well as the impact of outliers on model selection and parameter estimation. We also obtain robust estimators and model selection criteria, which are shown in simulation studies to perform well when large outliers occur.     

基于灰色关联度-云模型的群评价数据质量改进方法及应用研究

针对群评价中的数据质量问题, 从评价专家和评价值两个角度进行了异常数据处理, 提出了基于灰色关联度-云模型的群评价数据质量改进方法。基于改进的云距离模型测算被评价对象云和目标云之间的差距, 采用TOPSIS法进行评价排序。将数据质量改进方法和云距离模型用于区域物流竞争力群评价, 改进了群评价的数据质量, 提高了评价结果的稳定性和代表性。     

用伪同色光谱图像检测色觉正常观察者的锥细胞光谱响应

为了能够快速、准确的检测色觉正常观察者的辨色差异，从而对其红、绿、蓝三通道的锥细胞光谱响应进行研究，设计并制作了由背景层（或和明度层）以及数字层组成的伪同色光谱图像，其中背景层和数字层具有不同的光谱反射曲线，经过照明光源以及人眼锥细胞光谱响应的共同作用，使色觉正常的观察者产生不同的颜色感知差异。实验首先基于不同光谱原色的输出设备，在不同的照明光源下，制作出能够放大观察者差异的近同色异谱色样对。要求用不同颜色匹配函数计算近同色异谱色样对的CIEDE2000色差值，有的色差在人眼辨色阈值之内，有的色差人眼可明显识别。通过优化计算，将放大观察者色觉差异的近同色异谱色样对应用于伪同色光谱图像的数字层和背景层，并利用Epson Stylus Pro7908喷墨打印机和OKI C9600激光打印机分别输出伪同色光谱图像的背景层和数字层。同时组织了72名色觉正常的观察者（包含55名18～25岁的年轻观察者和17名62～74岁的老年观察者）分别在D65和LED-5000K两种光源下，对伪同色光谱图像进行识读检验。识读结果表明，伪同色光谱图像可以较为准确的判定年轻和老年观察者的视网膜锥细胞光谱响应是否老化。同种照明光源下，年轻观察者可以识读出数字的伪同色光谱图像（②/④）老年观察者不能识读，老年观察者可以识读的伪同色光谱图像（①/③）大多年轻观察者不能识读，且55名年轻观察者中有4名观察者的目视结果与老年人相同。另外，年轻观察者的锥细胞光谱响应与CIE1964和CIE2006（age=25 y）颜色匹配函数较为一致，而老年观察者的锥细胞光谱响应与CIE1931和CIE2006（age=75 y）颜色匹配函数更为一致。对比颜色匹配函数的分布，发现老年观察者的锥细胞光谱响应向长波段偏移，同时由于屈光系统光学密度增加导致其锥细胞光谱响应有所降低。     

时间序列异常值探测的Bayes方法及其GNSS数据质量控制中的应用

GNSS卫星精密定轨定位的观测量验后残差分析是数据质量控制的重要组成部分。目前的方法都是根据经验设定异常值判断的阈值,没有利用验后残差序列的时间序列特性。引入基于识别变量的AR模型异常值探测的Bayes方法对验后残差序列中的异常值进行探测;将异常值探测问题转化为识别变量后验概率值的计算问题,并给出明确的判别阈值,通过后验概率值与事先给定的阈值进行比较判别出异常值的位置;运用Gibbs抽样设计了识别变量后验概率值的计算方法和异常值的估算方法。实测数据对该算法的验证表明该算法能够准确地探测出异常值的位置,将异常值剔除之后的观测值序列应用到精密单点定位中,结果表明该算法的使用提高了精密单点定位的定位精度。     

Cluster-based outlier detection

Outlier detection has important applications in the field of data mining, such as fraud detection, customer behavior analysis, and intrusion detection. Outlier detection is the process of detecting the data objects which are grossly different from or inconsistent with the remaining set of data. Outliers are traditionally considered as single points; however, there is a key observation that many abnormal events have both temporal and spatial locality, which might form small clusters that also need to be deemed as outliers. In other words, not only a single point but also a small cluster can probably be an outlier. In this paper, we present a new definition for outliers: cluster-based outlier, which is meaningful and provides importance to the local data behavior, and how to detect outliers by the clustering algorithm LDBSCAN (Duan et al. in Inf. Syst. 32(7):978–986, 2007) which is capable of finding clusters and assigning LOF (Breunig et al. in Proceedings of the 2000 ACM SIG MOD International Conference on Manegement of Data, ACM Press, pp. 93–104, 2000) to single points.     

Heterogeneous linearly piezoelectric patches bonded on a linearly elastic body

In [1], we studied the response of a thin homogeneous piezoelectric patch perfectly bonded to an elastic body. Here we extend this study to the case of a very thin heterogeneous patch made of a periodic distribution of piezoelectric inclusions embedded in a linearly elastic matrix and perfectly bonded to an elastic body. Through a rigorous mathematical analysis, we show that various asymptotic models arise, depending on the electromechanical loading together with the relative behavior between the thickness of the patch and the size of the piezoelectric inclusions.