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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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This letter examines the controllability of consensus dynamics on matrix-weighed networks from a graph-theoretic perspective. Unlike the scalar-weighted networks, the rank of weight matrix introduces additional intricacies into characterizing the dimension of controllable subspace for such networks. Specifically, we investigate how the definiteness of weight matrices influences the dimension of the controllable subspace. In this direction, graph-theoretic characterizations of the lower and upper bounds on the dimension of the controllable subspace are provided by employing, respectively, distance partition and almost equitable partition of matrix-weighted networks. Furthermore, the structure of an uncontrollable input for such networks is examined. Examples are then provided to demonstrate the theoretical results.