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 fr...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.展开更多
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 ...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.展开更多
基金supported by the National Natural Sciences Foundation of China(7137102271401193+2 种基金71671193)the Program for Innovation Research in Central University of Finance and Economicsthe Innovation Foundation of BUAA for Ph.D.Graduates
文摘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.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11575202, and 11447613)
文摘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.
