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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, which was recently introduced to describe a specific type of dynamics in a neuron-astrocyte network. 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 motivates our particular interest to the sign of the whole minus sum information in our analytical consideration. The behavior of the whole minus sum and decoder based information measures are found to bear a lot of similarity, showing their mutual asymptotic convergence as time-uncorrelated activity is increased, with the sign transition of the whole minus sum information associated to a rapid growth in the decoder based information. The study aims at creating a theoretical base for using the spiking-bursting model as a well understood reference point for applying Integrated Information concepts to systems exhibiting similar bursting behavior (in particular, to neuron-astrocyte networks). The model can also be of interest as a new discrete-state test bench for different formulations of Integrated Information.
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
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 betwe
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
Finite-sized populations of spiking elements are fundamental to brain function, but also used in many areas of physics. Here we present a theory of the dynamics of finite-sized populations of spiking units, based on a quasi-renewal description of neu
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