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Most information dynamics and statistical causal analysis frameworks rely on the common intuition that causal interactions are intrinsically pairwise -- every cause variable has an associated effect variable, so that a causal arrow can be drawn between them. However, analyses that depict interdependencies as directed graphs fail to discriminate the rich variety of modes of information flow that can coexist within a system. This, in turn, creates problems with attempts to operationalise the concepts of dynamical complexity or `integrated information. To address this shortcoming, we combine concepts of partial information decomposition and integrated information, and obtain what we call Integrated Information Decomposition, or $Phi$ID. We show how $Phi$ID paves the way for more detailed analyses of interdependencies in multivariate time series, and sheds light on collective modes of information dynamics that have not been reported before. Additionally, $Phi$ID reveals that what is typically referred to as integration is actually an aggregate of several heterogeneous phenomena. Furthermore, $Phi$ID can be used to formulate new, tailored measures of integrated information, as well as to understand and alleviate the limitations of existing measures.
The ability to integrate information in the brain is considered to be an essential property for cognition and consciousness. Integrated Information Theory (IIT) hypothesizes that the amount of integrated information ($Phi$) in the brain is related to
This study presents a comprehensive analytic description in terms of the empirical whole minus sum version of Integrated Information in comparison to the decoder based version for the spiking-bursting discrete-time, discrete-state stochastic model, w
The Integrated Information is a quantitative measure from information theory how tightly all parts of a system are interconnected in terms of information exchange. In this study we show that astrocyte, playing an important role in regulation of infor
The Integrated Information Theory provides a quantitative approach to consciousness and can be applied to neural networks. An embodied agent controlled by such a network influences and is being influenced by its environment. This involves, on the one
This paper has been withdrawn by the authors.