In this paper, we first introduce a Lie algebra of the special orthogonal group, g = so(4, C), whose elements are 4 × 4trace-free, skew-symmetric complex matrices. As its application, we obtain a new soliton hierarchy which is reduced to AKNS hierarchy and present its bi-Hamiltonian structure and Liouville integrability. Furthermore, for one of the equations in the resulting hierarchy, we construct a Darboux matrix T depending on the spectral parameter λ.
The flowering time of Arabidopsis is sensitive to climate variability, with lighting conditions being a major determinant of the flowering time. Long-days induce early flowering, while short-days induce late flowering or even no flowers. This study investigates the intrinsic mechanisms for Arabidopsis flowering in different lighting conditions using mutual information networks and logic networks. The structure parameters of the mutual information networks show that the average degree and the average core clearly distinguish these networks. A method is then given to find the key structural genes in the mutual information networks and the logic networks respectively. Ten genes are found to possibly promote flowering with three genes that may restrain flowering. The sensitivity of this method to find the genes that promote flowering is 80%, while the sensitivity of the method to find the genes that restrain flowering is 100%.
