Various systems in physics, biology, social sciences and engineering have been successfully modeled as networks of coupled dynamical systems, where the links describe pairwise interactions. This is, however, too strong a limitation, as recent studies have revealed that higher-order many-body interactions are present in social groups, ecosystems and in the human brain, and they actually affect the emergent dynamics of all these systems. Here, we introduce a general framework to study coupled dynamical systems accounting for the precise microscopic structure of their interactions at any possible order. We show that complete synchronization exists as an invariant solution, and give the necessary condition for it to be observed as a stable state. Moreover, in some relevant instances, such a necessary condition takes the form of a Master Stability Function. This generalizes the existing results valid for pairwise interactions to the case of complex systems with the most general possible architecture.

A stochastic version of the Brusselator model is proposed and studied via the system size expansion. The mean-field equations are derived and shown to yield to organized Turing patterns within a specific parameters region. When determining the Turing condition for instability, we pay particular attention to the role of cross-diffusive terms, often neglected in the heuristic derivation of reaction-diffusion schemes. Stochastic fluctuations are shown to give rise to spatially ordered solutions, sharing the same quantitative characteristic of the mean-field based Turing scenario, in term of excited wavelengths. Interestingly, the region of parameter yielding to the stochastic self-organization is wider than that determined via the conventional Turing approach, suggesting that the condition for spatial order to appear can be less stringent than customarily believed.

Objectives Behçet’s syndrome (BS) is a rare systemic vasculitis often complicated by thrombotic events. Given the lack of validated biomarkers, BS diagnosis relies on clinical criteria. In search of novel biomarkers for BS diagnosis, we determined the profile of plasmatic circulating microRNAs (ci-miRNAs) in patients with BS compared with healthy controls (HCs). Methods ci-miRNA profile was evaluated by microarray in a screening cohort (16 patients with BS and 18 HCs) and then validated by poly(T) adaptor PCR (PTA-PCR) in a validation cohort (30 patients with BS and 30 HCs). Two disease control groups (30 patients with systemic lupus erythematosus (SLE) and 30 patients with giant cell arteritis (GCA) were also analysed. Results From the microarray screening, 29 deregulated (differentially expressed (DE)) human ci-miRNAs emerged. A hierarchical cluster analysis indicated that DE ci-miRNAs clearly segregated patients from controls, independently of clinical features. PTA-PCR analysis on the validation cohort confirmed the deregulation of miR-224-5p, miR-206 and miR-653-5p. The combined receiver operating characteristic (ROC) curve analyses showed that such ci-miRNAs discriminate BS from HCs (and BS with active vs inactive disease), as well as BS from patients with SLE and GCA. The functional annotation analyses (FAAs) showed that the most enriched pathways affected by DE ci-miRNAs (ie, cell–matrix interaction, oxidative stress and blood coagulation) are related to thrombo-inflammatory mechanisms. Accordingly, the expression of the three ci-miRNAs from the validation cohort significantly correlated with leucocyte reactive oxygen species production and plasma lipid peroxidation. Conclusions The ci-miRNA profile identified in this study may represent a novel, poorly invasive BS biomarker, while suggesting an epigenetic control of BS-related thrombo-inflammation.

The process of stochastic Turing instability on a scale-free network is discussed for a specific case study: the stochastic Brusselator model. The system is shown to spontaneously differentiate into activator-rich and activator-poor nodes outside the region of parameters classically deputed to the deterministic Turing instability. This phenomenon, as revealed by direct stochastic simulations, is explained analytically and eventually traced back to the finite-size corrections stemming from the inherent graininess of the scrutinized medium.

We study a simplified scheme of $k$ coupled autocatalytic reactions, previously introduced by Togashi and Kaneko. The role of stochastic fluctuations is elucidated through the use of the van Kampen system-size expansion and the results compared with direct stochastic simulations. Regular temporal oscillations are predicted to occur for the concentration of the various chemical constituents, with an enhanced amplitude resulting from a resonance which is induced by the intrinsic graininess of the system. The associated power spectra are determined and have a different form depending on the number of chemical constituents $k$. We make detailed comparisons in the two cases $k=4$ and $k=8$. Agreement between the theoretical and numerical results for the power spectrum is good in both cases. The resulting spectrum is especially interesting in the $k=8$ system, since it has two peaks, which the system-size expansion is still able to reproduce accurately.