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Statistical complexity is maximized in a small-world brain.

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  • 1Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Republic of Singapore.

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Area of Science:

  • Computational neuroscience
  • Complex systems theory

Background:

  • The brain operates near a critical state, termed the 'edge of chaos,' balancing stability and complexity.
  • Understanding this state is crucial for comprehending neural information processing.

Purpose of the Study:

  • To investigate the relationship between neural network architecture and computational properties at the edge of chaos.
  • To determine if small-world network properties are linked to optimal information processing in neural systems.

Main Methods:

  • Constructed the phase diagram for single Izhikevich excitatory neurons to identify the 'edge of chaos' region.
  • Coupled neuron outputs to parameters, creating an artificial energy landscape for phase transitions.
  • Applied the Watts-Strogatz rewiring algorithm to tune network topology from regular to random.
  • Measured statistical complexity of parameter time series across network rewiring stages.

Main Results:

  • Identified a parameter space region with numerous phase boundaries representing the edge of chaos.
  • Found that statistical complexity of parameter dynamics peaked in small-world-like networks.
  • Demonstrated that neural network dynamics can transition between phases on an energy landscape.

Conclusions:

  • The small-world architecture observed in biological neural networks may be essential for efficient information processing.
  • Neural network structure is not arbitrary but likely optimized for computational function at criticality.