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Universality Classes and Information-Theoretic Measures of Complexity via Group Entropies.

ABSTRACT: We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series of natural axioms. In addition, we require extensivity in order to ensure that our information measures are meaningful. The entropic measures proposed are suitably defined for describing universality classes of complex systems, each characterized by a specific state space growth rate function.

SUBMITTER: Tempesta P

PROVIDER: S-EPMC7136250 | biostudies-literature | 2020 Apr

REPOSITORIES: biostudies-literature

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Universality Classes and Information-Theoretic Measures of Complexity via Group Entropies.

Tempesta Piergiulio P Jensen Henrik Jeldtoft HJ

Scientific reports 20200406 1

We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series of natural axioms. In addition, we require extensivity in order to ensure that our information measures are meaningful. The entropic measures proposed are suitably defined for describing universality classes of complex systems, each characterized by a specific ...[more]

PMID: 32249779

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Project description:Converging evidence suggests that human cognition and behavior emerge from functional brain networks interacting on local and global scales. We investigated two information-theoretic measures of functional brain segregation and integration-interaction complexity C I (X), and integration I(X)-as applied to electroencephalographic (EEG) signals and how these measures are affected by choice of EEG reference. CI(X) is a statistical measure of the system entropy accounted for by interactions among its elements, whereas I(X) indexes the overall deviation from statistical independence of the individual elements of a system. We recorded 72 channels of scalp EEG from human participants who sat in a wakeful resting state (interleaved counterbalanced eyes-open and eyes-closed blocks). CI(X) and I(X) of the EEG signals were computed using four different EEG references: linked-mastoids (LM) reference, average (AVG) reference, a Laplacian (LAP) "reference-free" transformation, and an infinity (INF) reference estimated via the Reference Electrode Standardization Technique (REST). Fourier-based power spectral density (PSD), a standard measure of resting state activity, was computed for comparison and as a check of data integrity and quality. We also performed dipole source modeling in order to assess the accuracy of neural source CI(X) and I(X) estimates obtained from scalp-level EEG signals. CI(X) was largest for the LAP transformation, smallest for the LM reference, and at intermediate values for the AVG and INF references. I(X) was smallest for the LAP transformation, largest for the LM reference, and at intermediate values for the AVG and INF references. Furthermore, across all references, CI(X) and I(X) reliably distinguished between resting-state conditions (larger values for eyes-open vs. eyes-closed). These findings occurred in the context of the overall expected pattern of resting state PSD. Dipole modeling showed that simulated scalp EEG-level CI(X) and I(X) reflected changes in underlying neural source dependencies, but only for higher levels of integration and with highest accuracy for the LAP transformation. Our observations suggest that the Laplacian-transformation should be preferred for the computation of scalp-level CI(X) and I(X) due to its positive impact on EEG signal quality and statistics, reduction of volume-conduction, and the higher accuracy this provides when estimating scalp-level EEG complexity and integration.

Dataset Information

Universality Classes and Information-Theoretic Measures of Complexity via Group Entropies.

Publications

Universality Classes and Information-Theoretic Measures of Complexity via Group Entropies.

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