Background: Cassava is highly tolerant to stressful conditions, especially drought stress conditions; however, the mechanisms underlying this tolerance are poorly understood. The GRAS gene family is a large family of transcription factors that are involved in regulating the growth, development, and stress responses of plants. Currently, GRAS transcription factors have not been systematically studied in cassava, which is the sixth most important crop in the world.Results: Seventy-seven MeGRAS genes were identified from the cassava genome database. Phylogenetic analysis revealed that the MeGRAS proteins could be divided into 14 subfamilies. The gene structure and motif compositions of the proteins were considerably conserved within the same subfamily. Duplication events, particularly segmental duplication, were identified as the main driving force for GRAS gene expansion in cassava. Global expression analysis revealed that MeGRAS genes exhibited similar or distinct expression profiles within different tissues among different varieties. Moreover, qRT-PCR analysis revealed the expression patterns of MeGRAS genes in response to abiotic stress (drought, salt, cold, and H 2 O 2 ), and the results suggest that these genes may have multiple functions. Conclusion: This study is the first to provide comprehensive information on GRAS gene family members in cassava. The data will increase our understanding of both the molecular basis and the effects of GRAS genes. In addition, the results will contribute further to identifying the responses to various environmental conditions and provide insights into the potential functions of GRAS genes.

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This paper addresses cooperative control for a class of multi-agent networks. An interesting feature of such network is that each agent possesses the characteristic of multi-time-scale. By developing the relative states or the relative outputs based consensus protocols, some well-conditioned consensus criteria in terms of linear matrix inequalities are derived successively based on the ε-strict Lyapunov function. Compared with undirected graphs or strongly connected digraphs in existing works, a more general digraph that it contains at least a directed spanning tree is considered herein. Moreover, a fully distributed consensus protocol with time-varying coupling strength is proposed to avoid using global information. Finally, the obtained theoretical results are validated by two examples including standard and nonstandard agents.

The double grazing periodic motions and bifurcations are investigated for a two-degree-of-freedom vibroimpact system with symmetrical rigid stops in this paper. From the initial condition and periodicity, existence of the double grazing periodic motion of the system is discussed. Using the existence condition derived, a set of parameter values is found that generates a double grazing periodic motion in the considered system. By extending the discontinuity mapping of one constraint surface to that of two constraint surfaces, the Poincaré map of the vibroimpact system is constructed in the proximity of the grazing point of a double grazing periodic orbit, which has a more complex form than that of the single grazing periodic orbit. The grazing bifurcation of the system is analyzed through the Poincaré map with clearance as a bifurcation parameter. Numerical simulations show that there is a continuous transition from the chaotic band to a period-1 periodic motion, which is confirmed by the numerical simulation of the original system.

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