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Time delays are a signature of many physical systems, including the brain, and considerably shape their dynamics; moreover, they play a key role in consciousness, as postulated by the temporo-spatial theory of consciousness (TTC). However, they are often not known a priori and need to be estimated from time series. In this study, we propose the use of permutation entropy (PE) to estimate time delays from neural time series as a more robust alternative to the widely used autocorrelation window (ACW). In the first part, we demonstrate the validity of this approach on synthetic neural data, and we show its resistance to regimes of nonstationarity in time series. Mirroring yet another example of comparable behavior between different nonlinear systems, permutation entropy–time delay estimation (PE-TD) is also able to measure intrinsic neural timescales (INTs) (temporal windows of neural activity at rest) from hd-EEG human data; additionally, this replication extends to the abnormal prolongation of INT values in disorders of consciousness (DoCs). Surprisingly, the correlation between ACW-0 and PE-TD decreases in a state-dependent manner when consciousness is lost, hinting at potential different regimes of nonstationarity and nonlinearity in conscious/unconscious states, consistent with many current theoretical frameworks on consciousness. In summary, we demonstrate the validity of PE-TD as a tool to extract relevant time scales from neural data; furthermore, given the divergence between ACW and PE-TD specific to DoC subjects, we hint at its potential use for the characterization of conscious states. [ABSTRACT FROM AUTHOR]

Time is a key element of consciousness as it includes multiple timescales from shorter to longer ones. This is reflected in our experience of various short-term phenomenal contents at discrete points in time as part of an ongoing, more continuous, and long-term 'stream of consciousness'. Can Integrated Information Theory (IIT) account for this multitude of timescales of consciousness? According to the theory, the relevant spatiotemporal scale for consciousness is the one in which the system reaches the maximum cause-effect power; IIT currently predicts that experience occurs on the order of short timescales, namely, between 100 and 300 ms (theta and alpha frequency range). This can well account for the integration of single inputs into a particular phenomenal content. However, such short timescales leave open the temporal relation of specific phenomenal contents to others during the course of the ongoing time, that is, the stream of consciousness. For that purpose, we converge the IIT with the Temporo-spatial Theory of Consciousness (TTC), which, assuming a multitude of different timescales, can take into view the temporal integration of specific phenomenal contents with other phenomenal contents over time. On the neuronal side, this is detailed by considering those neuronal mechanisms driving the non-additive interaction of pre-stimulus activity with the input resulting in stimulus-related activity. Due to their non-additive interaction, the single input is not only integrated with others in the short-term timescales of 100–300 ms (alpha and theta frequencies) (as predicted by IIT) but, at the same time, also virtually expanded in its temporal (and spatial) features; this is related to the longer timescales (delta and slower frequencies) that are carried over from pre-stimulus to stimulus-related activity. Such a non-additive pre-stimulus-input interaction amounts to temporo-spatial expansion as a key mechanism of TTC for the constitution of phenomenal contents including their embedding or nesting within the ongoing temporal dynamic, i.e., the stream of consciousness. In conclusion, we propose converging the short-term integration of inputs postulated in IIT (100–300 ms as in the alpha and theta frequency range) with the longer timescales (in delta and slower frequencies) of temporo-spatial expansion in TTC. [ABSTRACT FROM AUTHOR]