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Entropy 2017, 19(1), 5; doi:10.3390/e19010005

Information Decomposition in Multivariate Systems: Definitions, Implementation and Application to Cardiovascular Networks

1
Bruno Kessler Foundation, Trento 38123, Italy
2
BIOtech, Department of Industrial Engineering, University of Trento, Trento 38123, Italy
3
Department of Biomedical Sciences for Health, University of Milan, Milan 20122, Italy
4
Department of Cardiothoracic, Vascular Anesthesia and Intensive Care, IRCCS Policlinico San Donato, Milan 20097, Italy
5
Department of Physiology, Jessenius Faculty of Medicine, Comenius University in Bratislava, Mala Hora 4C, Martin 03601, Slovakia
6
Biomedical Center Martin, Jessenius Faculty of Medicine, Comenius University in Bratislava, Mala Hora 4C, Martin 03601, Slovakia
*
Author to whom correspondence should be addressed.
Academic Editor: Anne Humeau-Heurtier
Received: 21 November 2016 / Revised: 14 December 2016 / Accepted: 19 December 2016 / Published: 24 December 2016
(This article belongs to the Special Issue Multivariate Entropy Measures and Their Applications)
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Abstract

The continuously growing framework of information dynamics encompasses a set of tools, rooted in information theory and statistical physics, which allow to quantify different aspects of the statistical structure of multivariate processes reflecting the temporal dynamics of complex networks. Building on the most recent developments in this field, this work designs a complete approach to dissect the information carried by the target of a network of multiple interacting systems into the new information produced by the system, the information stored in the system, and the information transferred to it from the other systems; information storage and transfer are then further decomposed into amounts eliciting the specific contribution of assigned source systems to the target dynamics, and amounts reflecting information modification through the balance between redundant and synergetic interaction between systems. These decompositions are formulated quantifying information either as the variance or as the entropy of the investigated processes, and their exact computation for the case of linear Gaussian processes is presented. The theoretical properties of the resulting measures are first investigated in simulations of vector autoregressive processes. Then, the measures are applied to assess information dynamics in cardiovascular networks from the variability series of heart period, systolic arterial pressure and respiratory activity measured in healthy subjects during supine rest, orthostatic stress, and mental stress. Our results document the importance of combining the assessment of information storage, transfer and modification to investigate common and complementary aspects of network dynamics; suggest the higher specificity to alterations in the network properties of the measures derived from the decompositions; and indicate that measures of information transfer and information modification are better assessed, respectively, through entropy-based and variance-based implementations of the framework. View Full-Text
Keywords: autonomic nervous system; autoregressive processes; cardiorespiratory interactions; cardiovascular interactions; Granger causality; dynamical systems; information dynamics; information transfer; redundancy and synergy; multivariate time series analysis autonomic nervous system; autoregressive processes; cardiorespiratory interactions; cardiovascular interactions; Granger causality; dynamical systems; information dynamics; information transfer; redundancy and synergy; multivariate time series analysis
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MDPI and ACS Style

Faes, L.; Porta, A.; Nollo, G.; Javorka, M. Information Decomposition in Multivariate Systems: Definitions, Implementation and Application to Cardiovascular Networks. Entropy 2017, 19, 5.

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