Abstract
We present a generically applicable four-step process for quantifying information movement in complex networks. (1) Construction of local entropy rate and specific entropy rate. Local entropy rate is a continuous, time-dependent measure that quantifies the information gained at time t on observing x(t) given the recent past. There is a statistically responsible procedure for specifying “recent”. Specific entropy rate is a related time-dependent locally determined measure that gives an estimate of uncertainty at time t. (2) Construct specific transfer entropy (i.e., a time-dependent generalization of epoch-determined transfer entropy) that gives a state- and time-resolved quantification of the predictive input of a candidate input system on a candidate output system. (3) Construct a time-dependent network adjacency matrix. Specific transfer entropy can be used to populate the adjacency matrix characterizing a network. In the case of multichannel EEG/MEG recordings, the nodes are electrodes, and specific transfer entropy quantifies information movement between electrodes. In this analysis, the adjacency matrix is real, time-dependent and asymmetric. Any of a large number of measures commonly used to characterize an adjacency matrix can be used. The result \(\Lambda (t)\) is a scalar function of time. (4) Identify hierarchical transition chronometries in \(\Lambda (t)\). The simple directive “find transitions in \(\Lambda (t)\)” is unacceptably naive. Dynamically meaningful transitions are timescale-dependent. In this analysis, \(\Lambda (t)\) is embedded and the structure of this embedded object is examined by quadrant scans of the corresponding recurrence diagram. A hierarchy of transitions can be identified by manipulating the embedding dimension. We note that \(\Lambda (t)\) can serve as the order parameter in phase transition experiments in which time is the tuning parameter.
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Rapp, P.E., Cellucci, C.J., Darmon, D. (2021). Quantifying Information Dynamics in CNS Networks. In: Lintas, A., Enrico, P., Pan, X., Wang, R., Villa, A. (eds) Advances in Cognitive Neurodynamics (VII). ICCN2019 2019. Advances in Cognitive Neurodynamics. Springer, Singapore. https://doi.org/10.1007/978-981-16-0317-4_39
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DOI: https://doi.org/10.1007/978-981-16-0317-4_39
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