The average fraction of infected nodes, in short the prevalence, of the Markovian ε-SIS (susceptible-infectedsusceptible) process with small self-infection rate ε > 0 exhibits, as a function of time, a typical "two-plateau" behavior, which was first discovered in the complete graph K N. Although the complete graph is often dismissed as an unacceptably simplistic approximation, its analytic tractability allows to unravel deeper details, that are surprisingly also observed in other graphs as demonstrated by simulations. The time-dependent mean-field approximation for K N performs only reasonably well for relatively large self-infection rates, but completely fails to mimic the typical Markovian ε-SIS process with small self-infection rates. While self-infections, particularly when their rate is small, are usually ignored, the interplay of nodal self-infection and spread over links may explain why absorbing processes are hardly observed in reality, even over long time intervals.

Network controllability and its robustness have been widely studied. However, analytical methods to calculate network controllability with respect to node in- and out-degree targeted removals are currently lacking. This paper develops methods, based on generating functions for the in- and out-degree distributions, to approximate the minimum number of driver nodes needed to control directed networks, during node in- and out-degree targeted removals. By validating the proposed methods on synthetic and real-world networks, we show that our methods work reasonably well. Moreover, when the fraction of the removed nodes is below 10% the analytical results of random removals can also be used to predict the results of targeted node removals.

Higher Education Institutions (HEIs) play an increasingly significant role in the practice of sustainability. For HEIs in their early stages of sustainability, they are still in need of sustainable assessment tools (SATs) that are suitable for their local context and also lead international sustainable development. The purpose of this paper is to develop a two-hierarchy sustainability assessment tool (THSus) for Chinese higher education institutions, including a quick analysis tool (QAT) and an in-depth benchmarking tool (IBT). The QAT provided a general overview of campus sustainability for HEIs to initiate initial actions and screen cases for the IBT. The IBT then provides more targeted analysis to plan long-term strategic changes. Based on the analysis of HEI cases, a 34-person Chinese research team was enlisted to discuss and select characteristics to formulate THSus. Indicators and weightings were developed according to the tool’s purpose and applied to 15 cases to test its effectiveness. Results showed that THSus is suitable for systematically analyzing campus issues, particularly in research areas. It offers a regional solution for Chinese campuses that is adaptable and considers the comprehensive core of sustainability.

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