Emergent hypernetworks in weakly coupled oscillators.

Networks of weakly coupled oscillators had a profound impact on our understanding of complex systems. Studies on model reconstruction from data have shown prevalent contributions from hypernetworks with triplet and higher interactions among oscillators, in spite that such models were originally defined as oscillator networks with pairwise interactions. Here, we show that hypernetworks can spontaneously emerge even in the presence of pairwise albeit nonlinear coupling given certain triplet frequency resonance conditions. The results are demonstrated in experiments with electrochemical oscillators and in simulations with integrate-and-fire neurons. By developing a comprehensive theory, we uncover the mechanism for emergent hypernetworks by identifying appearing and forbidden frequency resonant conditions. Furthermore, it is shown that microscopic linear (difference) coupling among units results in coupled mean fields, which have sufficient nonlinearity to facilitate hypernetworks. Our findings shed light on the apparent abundance of hypernetworks and provide a constructive way to predict and engineer their emergence.

Non-stochastic behavior in sodium chlorate crystallization.

NaClO3 is achiral in solution. If crystallization is performed under a static set-up, it is recognized that the stochastic nucleation probability results in a racemic mixture of the conglomerate. In this paper, we report a reexamination of the crystallization of NaClO3 from static solution in petri dishes that was conducted over a number of years and is based on the count and analysis of several thousand d- vs. l-NaClO3 crystals. Remarkably, instead of an expected nearly 50/50 coin-tossing situation for the d/l crystal frequency, in most of our experiments a statistically significant bias in favor of d- over l-NaClO3 crystals was found. The experiments also showed that the NaClO3 system was relatively insensitive regarding the intentional addition of a variety of optically active agents. Only in some cases, the persisting d-bias observed in the unseeded experiments slightly increased upon the presence of such additives. Nevertheless, experiments in plastic petri dishes or in presence of fungal spores were able to reverse this bias. A literature survey shows that mainly d-directed non-stochastic behavior in the NaClO3 system has been previously observed in other laboratory settings and by the application of different crystallization techniques. So far, the kind of chiral influence that could be at the origin of the observed bias remains unknown. After the examination of several possible chiral influences of physical, chemical and biological origin, we carefully consider the presence of bio-contaminants as most likely for the cause of this effect.