Abstract
Integrated information has been recently suggested as a possible measure to identify a necessary condition for a system to display conscious features. Recently, we have shown that astrocytes contribute to the generation of integrated information through the complex behavior of neuron–astrocyte networks. Still, it remained unclear which underlying mechanisms governing the complex behavior of a neuron–astrocyte network are essential to generating positive integrated information. This study presents an analytic consideration of this question based on exact and asymptotic expressions for integrated information in terms of exactly known probability distributions for a reduced mathematical model (discrete-time, discrete-state stochastic model) reflecting the main features of the “spiking–bursting” dynamics of a neuron–astrocyte network. The analysis was performed in terms of the empirical “whole minus sum” version of integrated information in comparison to the “decoder based” version. The “whole minus sum” information may change sign, and an interpretation of this transition in terms of “net synergy” is available in the literature. This motivated our particular interest in the sign of the “whole minus sum” information in our analytical considerations. The behaviors of the “whole minus sum” and “decoder based” information measures are found to bear a lot of similarity—they have mutual asymptotic convergence as time-uncorrelated activity increases, and the sign transition of the “whole minus sum” information is associated with a rapid growth in the “decoder based” information. The study aims at creating a theoretical framework for using the spiking–bursting model as an analytically tractable reference point for applying integrated information concepts to systems exhibiting similar bursting behavior. The model can also be of interest as a new discrete-state test bench for different formulations of integrated information.
Highlights
Integrated information (II) [1,2,3,4] is a measure of internal information exchange in complex systems and it has recently attracted a lot of interest, because initially it was proposed to quantifyEntropy 2020, 22, 1334; doi:10.3390/e22121334 www.mdpi.com/journal/entropyEntropy 2020, 22, 1334 consciousness [5]
We have suggested a possible explanation that a generation of positive II was the reason why mammal brain evolved to develop an astrocyte network to overlap with a network of neurons, but, still, it remained unclear what are the underlying mechanisms driving a complex neural behavior to generate positive II
The present study aims at creating a theoretical formalism for using the spiking–bursting model of [19] as an analytically tractable reference point for applying integrated information concepts to systems exhibiting similar bursting behavior
Summary
Integrated information (II) [1,2,3,4] is a measure of internal information exchange in complex systems and it has recently attracted a lot of interest, because initially it was proposed to quantify. This choice among other empirical II measures is inherited from the preceding study [19] and is in part due to its easy analytical tractability, and due to its ability to change sign, which naturally identifies a transition point in the parameter space This property may be considered a violation of the natural non-negativeness requirement for II [16]; on the other hand, the sign of the “whole minus sum” information has been given interpretation in terms of “net synergy” [25] as a degree of redundancy in the evolution of a system [18]. Despite their inherent difference consisting in changing or not changing sign, the two compared measures are shown to bear similarities in their dependence upon model parameters, including the same scaling with the time correlation parameter
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