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[en] We investigate the expected time to extinction in the susceptible-infectious-susceptible model of disease spreading. Rather than using stochastic simulations, or asymptotic calculations in network models, we solve the extinction time exactly for all connected graphs with three to eight vertices. This approach enables us to discover descriptive relations that would be impossible with stochastic simulations. It also helps us discovering graphs and configurations of S and I with anomalous behaviors with respect to disease spreading. We find that for large transmission rates the extinction time is independent of the configuration, just dependent on the graph. In this limit, the number of vertices and edges determine the extinction time very accurately (deviations primarily coming from the fluctuations in degrees). We find that the rankings of configurations with respect to extinction times at low and high transmission rates are correlated at low prevalences and negatively correlated for high prevalences. The most important structural factor determining this ranking is the degrees of the infectious vertices. (paper)
[en] To what extent do the characteristic features of a chemical reaction network reflect its purpose and function? In general, one argues that correlations between specific features and specific functions are key to understanding a complex structure. However, specific features may sometimes be neutral and uncorrelated with any system-specific purpose, function or causal chain. Such neutral features are caused by chance and randomness. Here we compare two classes of chemical networks: one that has been subjected to biological evolution (the chemical reaction network of metabolism in living cells) and one that has not (the atmospheric planetary chemical reaction networks). Their degree distributions are shown to share the very same neutral system-independent features. The shape of the broad distributions is to a large extent controlled by a single parameter, the network size. From this perspective, there is little difference between atmospheric and metabolic networks; they are just different sizes of the same random assembling network. In other words, the shape of the degree distribution is a neutral characteristic feature and has no functional or evolutionary implications in itself; it is not a matter of life and death. (paper)
[en] Highlights: • We propose a topology control model for resource allocation in ad hoc networks. • We design two mobility models to simulate move patterns in search and rescue. • We design ad hoc networks with small world feature. • Our repeated game strategy well controls the interactions between neighbor nodes. - Abstract: Due to their self-organized, multi-hop and distributed characteristics, ad hoc networks are useful in search and rescue. Topology control models need to be designed for energy-efficient, robust and fast communication in ad hoc networks. This paper proposes a topology control model which specializes for search and rescue—Compensation Small World-Repeated Game (CSWRG)—which integrates mobility models, constructing small world networks and a game-theoretic approach to the allocation of resources. Simulation results show that our mobility models can enhance the communication performance of the constructed small-world networks. Our strategy, based on repeated game, can suppress selfish behavior and compensate agents that encounter selfish or faulty neighbors. This model could be useful for the design of ad hoc communication networks.