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Convergent cross mapping is a principled causal discovery technique for signals, but its efficacy depends on a number of assumptions about the systems that generated the signals. We present a self-contained introduction to the theory of causality in state-space models, Takens’ theorem, and cross maps, and we propose conditions to check if a signal is appropriate for cross mapping. Further, we propose simple analyses based on Gaussian processes to test for these conditions in data. We show that our proposed techniques detect when convergent cross mapping may conclude erroneous results using several examples from the literature, and we comment on other considerations that are important when applying methods such as convergent cross mapping. 

Abstract The return of consciousness after traumatic brain injury (TBI) is associated with restoring complex cortical dynamics; however, it is unclear what interactions govern these complex dynamics. Here, we set out to uncover the mechanism underlying the return of consciousness by measuring local field potentials (LFP) using invasive electrophysiological recordings in patients recovering from TBI. We found that injury to the thalamus, and its efferent projections, on MRI were associated with repetitive and low complexity LFP signals from a highly structured phase space, resembling a low-dimensional ring attractor. But why do thalamic injuries in TBI patients result in a cortical attractor? We built a simplified thalamocortical model, which connotes that thalamic input facilitates the formation of cortical ensembles required for the return of cognitive function and the content of consciousness. These observations collectively support the view that thalamic input to the cortex enables rich cortical dynamics associated with consciousness.