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Due to the conflicting reports on the antioxidant activity of cerium oxide nanoparticles, much work has been done to explore the factors influencing the antioxidant activity of nano-CeO2.

This paper examines the consensus problem on time-varying matrix-weighed undirected networks. First, we introduce the matrixweighted integral network for the analysis of such networks. Under mild assumptions on the switching pattern of the time-varying network, necessary and/or sufficient conditions for which average consensus can be achieved are then provided in terms of the null space of matrix-valued Laplacian of the corresponding integral network. In particular, for periodic matrix-weighted time-varying networks, necessary and sufficient conditions for reaching average consensus is obtained from an algebraic perspective. Moreover, we show that if the integral network with period T > 0 has a positive spanning tree over the time span [0, T ), average consensus for the node states is achieved. Simulation results are provided to demonstrate the theoretical analysis.of weight matrices are further introduced in [14], [15]. In the meantime, the notion of network connectivity can be further extended for matrix-valued networks. For instance, one can identify edges with positive/negative definite matrices as "strong" connections;whereas an edge weighted by positive/negative semi-definite matrices can be considered as a "weak" connection [16].

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