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In this paper, we firstly design a chaotic complex system and study its dynamical properties including invariance, dissipativity, equilibria, Lyapunov exponents, chaotic behavior, as well as chaotic attractors. What is more, the scaling matrices are always chosen as real matrices in previous combination synchronization schemes within two drive real systems and one response real system evolving in the same or inverse directions simultaneously. However, in many real-life applications, the drive-response systems may evolve in different directions with a constant intersection angle. Therefore, combination synchronization with regard to the complex scaling matrices, referred as combination complex synchronization, will be made the further research about three chaotic complex systems. Based on Lyapunov stability theory, three identical chaotic complex systems are considered and the corresponding controllers are designed to achieve the complex combination synchronization. The corresponding theoretical proofs and numerical simulations are given to demonstrate the validity and feasibility of the presented control technique.

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DNA tile based self-assembly provides a bottom-up approach to construct desired nanostructures. DNA tiles have been directly constructed from ssDNA and readily self-assembled into 2D lattices and 3D superstructures. However, for more complex lattice designs including algorithmic assemblies requiring larger tile sets, a more modular approach could prove useful. This paper reports a new DNA 'sub-tile' strategy to easily create whole families of programmable tiles. Here, we demonstrate the stability and flexibility of our sub-tile structures by constructing 3-, 4- and 6-arm DNA tiles that are subsequently assembled into 2D lattices and 3D nanotubes according to a hierarchical design. Assembly of sub-tiles, tiles, and superstructures was analyzed using polyacrylamide gel electrophoresis and atomic force microscopy. DNA tile self-assembly methods provide a bottom-up approach to create desired nanostructures; the sub-tile strategy adds a useful new layer to this technique. Complex units can be made from simple parts. The sub-tile approach enables the rapid redesign and prototyping of complex DNA tile sets and tiles with asymmetric designs.

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