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The Causal Efficacy of Consciousness
Article

Computing Integrated Information (Φ) in Discrete Dynamical Systems with Multi-Valued Elements

1
Department of Psychiatry, Wisconsin Institute for Sleep and Consciousness, University of Wisconsin-Madison, Madison, WI 53719, USA
2
Neuroscience Training Program, University of Wisconsin-Madison, Madison, WI 53719, USA
*
Author to whom correspondence should be addressed.
Current address: Kettering University, 1700 University Ave., Flint, MI 48504, USA.
Current address: New York University, Department of Biology, 100 Washington Square E #1009, New York, NY 10003, USA.
§
These authors contributed equally to this work.
Entropy 2021, 23(1), 6; https://doi.org/10.3390/e23010006
Received: 21 November 2020 / Revised: 15 December 2020 / Accepted: 17 December 2020 / Published: 22 December 2020
(This article belongs to the Special Issue Integrated Information Theory and Consciousness)
Integrated information theory (IIT) provides a mathematical framework to characterize the cause-effect structure of a physical system and its amount of integrated information (Φ). An accompanying Python software package (“PyPhi”) was recently introduced to implement this framework for the causal analysis of discrete dynamical systems of binary elements. Here, we present an update to PyPhi that extends its applicability to systems constituted of discrete, but multi-valued elements. This allows us to analyze and compare general causal properties of random networks made up of binary, ternary, quaternary, and mixed nodes. Moreover, we apply the developed tools for causal analysis to a simple non-binary regulatory network model (p53-Mdm2) and discuss commonly used binarization methods in light of their capacity to preserve the causal structure of the original system with multi-valued elements. View Full-Text
Keywords: causation; regulatory networks; binarization; coarse graining causation; regulatory networks; binarization; coarse graining
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MDPI and ACS Style

Gomez, J.D.; Mayner, W.G.P.; Beheler-Amass, M.; Tononi, G.; Albantakis, L. Computing Integrated Information (Φ) in Discrete Dynamical Systems with Multi-Valued Elements. Entropy 2021, 23, 6. https://doi.org/10.3390/e23010006

AMA Style

Gomez JD, Mayner WGP, Beheler-Amass M, Tononi G, Albantakis L. Computing Integrated Information (Φ) in Discrete Dynamical Systems with Multi-Valued Elements. Entropy. 2021; 23(1):6. https://doi.org/10.3390/e23010006

Chicago/Turabian Style

Gomez, Juan D.; Mayner, William G.P.; Beheler-Amass, Maggie; Tononi, Giulio; Albantakis, Larissa. 2021. "Computing Integrated Information (Φ) in Discrete Dynamical Systems with Multi-Valued Elements" Entropy 23, no. 1: 6. https://doi.org/10.3390/e23010006

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