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

Juan D Gomez1, William G P Mayner1,2, Maggie Beheler-Amass1

  • 1Department of Psychiatry, Wisconsin Institute for Sleep and Consciousness, University of Wisconsin-Madison, Madison, WI 53719, USA.

Entropy (Basel, Switzerland)
|December 30, 2020
PubMed
Summary
This summary is machine-generated.

Integrated Information Theory (IIT) now analyzes multi-valued systems with updated PyPhi software. This advances causal analysis for complex networks and biological models.

Keywords:
binarizationcausationcoarse grainingregulatory networks

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Area of Science:

  • * Cognitive Science
  • * Theoretical Neuroscience
  • * Computational Neuroscience

Background:

  • * Integrated Information Theory (IIT) quantifies consciousness and cause-effect structures in physical systems using integrated information (Φ).
  • * The PyPhi software package previously enabled IIT analysis for discrete dynamical systems with binary elements.
  • * Analyzing multi-valued systems is crucial for a more comprehensive understanding of complex causal structures.

Purpose of the Study:

  • * To extend the PyPhi software package to accommodate discrete, multi-valued elements in dynamical systems.
  • * To enable the analysis and comparison of causal properties in networks with binary, ternary, quaternary, and mixed-valued nodes.
  • * To evaluate the impact of binarization methods on preserving causal structure in multi-valued systems.

Main Methods:

  • * Modification and extension of the PyPhi Python package to handle multi-valued elements.
  • * Generation and analysis of random networks composed of various node types (binary, ternary, quaternary, mixed).
  • * Application of the enhanced PyPhi tools to a non-binary p53-Mdm2 regulatory network model.

Main Results:

  • * Successful extension of PyPhi to analyze multi-valued discrete dynamical systems.
  • * Demonstrated ability to compare causal properties across networks with diverse node valuations.
  • * Identified limitations of binarization methods in maintaining the original causal structure of multi-valued systems.

Conclusions:

  • * The updated PyPhi software significantly broadens the scope of IIT applications to more complex systems.
  • * Analysis of multi-valued systems provides a more nuanced understanding of causal relationships than binary approximations.
  • * Careful consideration of binarization techniques is necessary when applying IIT to biological or other complex networks.