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| In nature, dynamical systems with many interacting elements, such as neural networks, often change their modality of couplings over time. Here, we propose an information theoretic measure that effectively monitors these dynamic changes for information transfer. Dealing with time series in real-time inevitably introduces two issues: the impossibility of predefining the range of the state space and of obtaining the probability distribution of occurrence of states, because, in principle, the entire time series are not provided beforehand. We here propose a measure called ``temporal symbolic transfer entropy'' to overcome these issues in assessing information transfers in real-time. The measure is based on transfer entropy, with two modifications in its setting; one is the use of the permutation partitioning, and second is an introduction of the time evolution scheme of the probability distributions. We will illustrate the power of this measure in a number of experiments using time series data from model systems, neuroscience, and soft robotics by comparison with conventional approaches. |
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