Background: The expectation maximization (EM) algorithm is a common tool for estimating the parameters of Gaussian mixture models (GMM). However, it is highly sensitive to initial value and easily gets trapped in a local optimum.Method: To address these problems, a new iterative method of EM initialization (MRIPEM) is proposed in this paper. It incorporates the ideas of multiple restarts, iterations and clustering. In particular, the mean vector and covariance matrix of sample are calculated as the initial values of the iteration. Then, the optimal feature vector is selected from the candidate feature vectors by the maximum Mahalanobis distance as a new partition vector for clustering. The parameter values are renewed continuously according to the clustering results.Results: To verify the applicability of the MRIPEM, we compared it with other two popular initialization methods on simulated and real datasets, respectively. The comparison results of the three stochastic algorithms indicate that MRIPEM algorithm is comparable in relatively high dimensions and high overlaps and significantly better in low dimensions and low overlaps.

One-to-multiple path analysis model describes the regulation mechanism of multiple independent variables to one dependent variable by dividing the correlation coefficient and the determination coefficient. How to analyse more complex regulation mechanisms of multiple independent variables to multiple dependent variables? Similarly, according to multiple-to-multiple linear regression analysis, multiple-to-multiple path analysis model was proposed in this paper and it demonstrated more complex regulation mechanisms among multiple independent variables and multiple dependent variables by dividing the generalized determination coefficient. Differently, three other types of paths were generated in multiple-to-multiple path analysis model in that the correlation among multiple dependent variables was considered. Then, the decision coefficient of each independent variable was constructed for dependent variables system, and its hypothesis testing statistics were given. Finally, the research example of the wheat breeding rules in arid area demonstrated that the multiple-to-multiple path analysis considering more correlation information can get better results.

Insect Taiman (Tai) binds to methoprene-tolerant to form a heterodimeric complex, mediating juvenile hormone (JH) signaling to regulate larval development and to prevent premature metamorphosis. Tai also acts as a steroid receptor coactivator of 20-hydroxyecdysone (20E) receptor heterodimer, ecdysone receptor (EcR) and Ultraspiracle (USP), to control the differentiation of early germline cells and the migration of specific follicle cells and border cells in ovaries in several insect species. In holometabolous insects, however, whether Tai functions as the coactivator of EcR/USP to transduce 20E message during larval-pupal transition is unknown. In the present paper, we found that the LdTai mRNA levels were positively correlated with circulating JH and 20E titers in Leptinotarsa decemlineata; and ingestion of either JH or 20E stimulated the transcription of LdTai. Moreover, RNA interference (RNAi)-aided knockdown of LdTai at the fourth (final) instar stage repressed both JH and 20E signals, inhibited larval growth and shortened larval developing period. The knockdown caused 100% larval lethality due to failure of larval-pupal ecdysis. Under the apolysed larval cuticle, the LdTai RNAi prepupae possessed pupal thorax. In contrast, the process of tracheal ecdysis was uncompleted. Neither JH nor 20E rescued the aforementioned defectives in LdTai RNAi larvae. It appears that Tai mediates both JH and 20E signaling. Our results uncover a link between JH and 20E pathways during metamorphosis in L. decemlineata.

To fully explore the influence mechanism of interactions between different monomer units of proanthocyanidins (PAs) on biological activity, a path analysis model of the PA structure-activity relationship was proposed. This model subdivides the total correlation between each monomer unit and activity into direct and indirect effects by taking into account not only each monomer unit but also the correlation with its related monomer units. In addition, this method can determine the action mode of each monomer unit affecting the activity by comparing the direct and total indirect effects. Finally, the advantage of this model is demonstrated through an influence mechanism analysis of Rhodiola crenulata PA monomer units on antioxidant and anti-diabetes activities.