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For each odd integer r greater than one and not divisible by three we give explicit examples of infinite families of simply and tangentially homotopy equivalent but pairwise non-homeomorphic closed homogeneous spaces with fundamental group isomorphic to Z/r. As an application we construct the first examples of manifolds which possess infinitely many metrics of nonnegative sectional curvature with pairwise non-homeomorphic homogeneous souls of codimension three with trivial normal bundle, such that their curvatures and the diameters of the souls are uniformly bounded. These manifolds are the first examples of manifolds fulfilling such geometric conditions and they serve as solutions to a problem posed by I. Belegradek, S. Kwasik and R. Schultz.

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The generation and supply of electricity is currently about to undergo a fundamental transition that includes extensive development of smart grids. Smart grids are huge and complex networks consisting of a vast number of devices and entities which are connected with each other. This opens new variations of disruption scenarios which can increase the vulnerability of a power distribution network. However, the network topology of a smart grid has significant effects on urban resilience particularly referring to the adequate provision of infrastructures. Thus, topology massively codetermines the degree of urban resilience, i.e. different topologies enable different strategies of power distribution. Therefore, this article introduces a concept of criticality adapted to a power system relying on an advanced metering infrastructure. The authors propose a two-stage operationalization of this concept that refers to the design phase of a smart grid and its operation mode, targeting at an urban resilient power flow during power shortage.