A moment-based criterion for determining the number of components in a normal mixture model

Determining the number of components is a crucial issue in a mixture model. A moment-based criterion is considered to estimate the number of components arising from a normal mixture model. This criterion is derived from an omnibus statistic involving the skewness and kurtosis of each component. The proposed criterion additionally provides a measurement for the model fit in an absolute sense. The performances of our criterion are satisfactory compared with other classical criteria through Monte-Carlo experiments.

Feature Extraction of Fabric Defects Based on Complex Contourlet Transform and Principal Component Analysis

To extract features of fabric defects effectively and reduce dimension of feature space,a feature extraction method of fabric defects based on complex contourlet transform （CCT） and principal component analysis （PCA） is proposed.Firstly,training samples of fabric defect images are decomposed by CCT.Secondly,PCA is applied in the obtained low-frequency component and part of highfrequency components to get a lower dimensional feature space.Finally,components of testing samples obtained by CCT are projected onto the feature space where different types of fabric defects are distinguished by the minimum Euclidean distance method.A large number of experimental results show that,compared with PCA,the method combining wavdet low-frequency component with PCA （WLPCA）,the method combining contourlet transform with PCA （CPCA）,and the method combining wavelet low-frequency and highfrequency components with PCA （WPCA）,the proposed method can extract features of common fabric defect types effectively.The recognition rate is greatly improved while the dimension is reduced.

Notes on integrable boundary interactions of open SU(4) alternating spin chains

Ref. [J. High Energy Phys. 1708, 001(2017)] showed that the planar flavored Ahanory-Bergman-Jafferis-Maldacena(ABJM)theory is integrable in the scalar sector at two-loop order using coordinate Bethe ansatz. A salient feature of this case is that the boundary reflection matrices are anti-diagonal with respect to the chosen basis. In this paper, we relax the coefficients of the boundary terms to be general constants to search for integrable systems among this class. We found that the only integrable boundary interaction at each end of the spin chain aside from the one in ref. [J. High Energy Phys. 1708, 001(2017)] is the one with vanishing boundary interactions leading to diagonal reflection matrices. We also construct non-supersymmetric planar flavored ABJM theory which leads to trivial boundary interactions at both ends of the open chain from the two-loop anomalous dimension matrix in the scalar sector.