A new algorithm – Compression-Complexity-Causality (CCC) to identify causal relationships between time series was invented. CCC performs reliably on short, noisy, sampled and filtered time series that occur in practical scenarios can be applied to wide range of applications in econometrics, cognitive science, climatology, measuring consciousness and sustainability research.
Network Causal Activity (NCA) was tested on ECoG datasets from monkeys to characterise the level of consciousness in awake and anesthesia states based on causal activity in brain networks. NCA could be applied to help neurosurgeons determine the level of consciousness in patients who are unable to report their experience. A causal stability synchronisation theorem which is a necessary and sufficient condition for coupled dynamical systems to achieve complete synchronization has been proved. Its potential applications include determining when a group of coupled neurons will synchronise indicating the onset of a seizure.