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Atmospheric self-organization and activator-inhibitor dynamics in biology provide examples of checkerboard-like spatio-temporal organization. We study a simple model for local activation-inhibition processes. Our model, first introduced in the context of atmospheric moisture dynamics, is a continuous-energy and non-Abelian version of the fixed-energy sandpile model. Each lattice site is populated by a non-negative real number, its energy. Upon each timestep all sites with energy exceeding a unit threshold re-distribute their energy at equal parts to their nearest neighbors. The limit cycle dynamics gives rise to a complex phase diagram in dependence on the mean energy $\mu$: For low $\mu$, all dynamics ceases after few re-distribution events. For large $\mu$, the dynamics is well-described as a diffusion process, where the order parameter, spatial variance $\sigma$, is removed. States at intermediate $\mu$ are dominated by checkerboard-like period-two phases which are however interspersed by much more complex phases of far longer periods. Phases are separated by discontinuous jumps in $\sigma$ or $\partial_{\mu}\sigma$ - akin to first and higher-order phase transitions. Overall, the energy landscape is dominated by few energy levels which occur as sharp spikes in the single-site density of states and are robust to noise., Comment: 13 pages, 7 figures, plus supplement, to be submitted to Physical Review E

Common respiratory viruses cause seasonal epidemics in sequential patterns. The underlying mechanisms for this pattern have been debated for some time. For influenza, contenders include temperature, humidity, and vitamin D levels. While such seasonal drivers may be sufficient to explain midwinter peaking it is unclear if other respiratory viruses peaking in spring, summer, or fall have individual environmental drivers. Here we present a dynamic model of interacting diseases, in an effort to explain observed seasonal patterns without requiring multiple seasonal drivers. Our model extends the classical SIRS-model to include multiple diseases that interact via a short-lasting, non-specific immunity component. This temporal protection is triggered by exposure to any epidemic disease and lasts only a couple of weeks. We show that the inhibiting disease-interaction allows recurrent epidemic behaviour without any seasonal driving. In the presence of a single seasonal driver our model parsimoniously predicts epidemic patterns such as sequentially occurring epidemic diseases. We also present a two-disease simulation reproducing multiple features observed in time series of parainfluenza strains PIV-3 and biennial PIV-1 epidemic patterns. Complex epidemic patterns of seasonal diseases may be explained by non-specific innate or cloub cell (T-cell) mediated immune responses that result in interaction between unrelated respiratory epidemic diseases., Comment: 8 pages, 6 figures

Social discrimination seems to be a persistent phenomenon in many cultures. It is important to understand the mechanisms that lead people to judge others by the group to which they belong, rather than individual qualities. It was recently shown that evolutionary (imitation) dynamics can lead to a hierarchical discrimination between agents marked with observable, but otherwise meaningless, labels. These findings suggest that it can give useful insight, to describe the phenomenon of social discrimination in terms of spontaneous symmetry breaking. The investigations so far have, however, only considered binary labels. In this contribution we extend the investigations to models with up to seven different labels. We find the features known from the binary label model remain remarkably robust when the number of labels is increased. We also discover a new feature, namely that it is more likely for neighbours to have strategies which are similar, in the sense that they agree on how to act towards a subset of the labels., Comment: 8 pages, 5 figures + supplement (6 pages, 8 figures)

The occurrence of discrimination is an important problem in the social and economical sciences. Much of the discrimination observed in empirical studies can be explained by the theory of in-group favoritism, which states that people tend to act more positively towards peers whose appearances are more similar to their own. Some studies, however, find hierarchical structures in inter-group relations, where members of low-status groups also favor the high-status group members. These observations cannot be understood in the light of in-group favoritism. Here we present an agent based model in which evolutionary dynamics can result in a hierarchical discrimination between two groups characterized by a meaningless, but observable binary label. We find that discriminating strategies end up dominating the system when the selection pressure is high, i.e. when agents have a much higher probability of imitating their neighbor with the highest payoff. These findings suggest that the puzzling persistence of hierarchical discrimination may result from the evolutionary dynamics of the social system itself, namely the social imitation dynamics. It also predicts that discrimination will occur more often in highly competitive societies., Comment: 13 pages 7 figures (5 of which are supplementary material). This is a pre-print of an article published in Scientific Reports. The final authenticated version is available online at: https://doi.org/10.1038/s41598-019-40583-w