Assessing Causality with Conditional Recurrence Plots

In many fields of the natural sciences, from biology to physics, information tools are acquiring more and more importance. For the analysis of information transfer between time series in particular, the use of the transfer entropy is spreading. A typical application is synchronization experiments, which involve coupled quantities, a “target” and a “source”, with quasi-periodic behaviours. On the other hand, in complex systems very rarely a couple of quantities can be really considered fully isolated and immune from other influences. It is therefore important to consider not only the relative influence of their past, but also the possible influence of additional factors. In order to tackle this problem, an advanced application of the recurrence plots, called Conditional Recurrence plots, has been developed. The innovative technique is corroborated by the application of the conditional transfer entropy. Preliminary results from experimental data of sawteeth pacing with radio frequency and ELMs pacing with Pellets in thermonuclear plasmas are very encouraging. Being quasi periodic, sawteeth occurs naturally and, especially in H-mode plasmas, the effectiveness of the pacing with RFF can be difficult to establish. ELMs also can occur naturally, without being triggered by an injected pellet. The proposed data analysis procedure is aimed at better isolating the effects of the external perturbations, like natural sawteeth or ELMs, providing both a more accurate quantification of the pacing efficiency and a deeper insight of the physical processes involved, thanks to a better understanding of the relevant causal relations.