So You Want to Teach For the Environment ...

This article contends that the most effective way to move forward in the realm of environmental education may be to do so outside the sanction of official policy. When all the rhetoric is removed, teaching for the environment is a radical activity which governments will almost certainly attempt to neutralise and control. Thus, attempting to reconcile market‐driven government policy with environmental educational goals is likely to be a waste of effort.     

The impact of graph symmetry on the number of driver nodes in complex networks

This study investigates on a strong correlation between complex network (CN) controllability (characterized by the number of required driver nodes) and graph symmetry (described by automorphism groups) in undirected and unweighted networks. Based on the properties of permutation products of elementary automorphisms, novel necessary conditions for CN controllability are presented which are computationally more effective than previous method. In addition, a novel index of symmetry is proposed upon which a more meaningful understanding of symmetry impact on CN controllability can be comprehended. Based on this new index, a modification strategy is suggested aiming to satisfy CN controllability with a lower number of driver nodes. The study shows that the proposed modification approach can result in a minimal set of driver nodes with a reasonable computational complexity. Further, the critical components of complex networks, in terms of their impact on the number of required driver nodes, are identified. The results of the proposed methodologies have been verified for several synthetic and real test systems including small, medium, and large power networks.