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Maintaining extensivity in evolutionary multiplex networks.

Chris G Antonopoulos1, Murilo S Baptista2

  • 1Department of Mathematical Sciences, University of Essex, Wivenhoe Park, United Kingdom.

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|April 14, 2017
PubMed
Summary
This summary is machine-generated.

Network topology significantly impacts entropy

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Area of Science:

  • Complex Systems
  • Statistical Physics
  • Network Science
  • Computational Neuroscience

Background:

  • Extensive properties, like entropy, are crucial in understanding large systems.
  • Multiplex networks, composed of interconnected layers, present unique challenges for analyzing system properties.
  • The relationship between network topology and the extensivity of entropy in such complex structures remains an active research area.

Purpose of the Study:

  • To investigate how network topology influences the maintenance of entropy's extensive property in multiplex networks.
  • To analytically and numerically determine the conditions under which entropy remains extensive in layered network structures.

Main Methods:

  • Utilized the sum of positive Lyapunov exponents (HKS), a measure related to entropy, to study network dynamics.
  • Conducted analytical derivations for idealized network models of size N.
  • Performed numerical simulations on multiplex networks of coupled neurons (electrically and chemically).

Main Results:

  • Demonstrated that entropy extensivity depends on the interplay between intra- and inter-layer coupling strengths and node degrees.
  • Derived scaling laws: extensivity is maintained if intra-coupling strength scales as N⁻ᶿ when intra-degree sum scales as Nᶿ⁺¹, for θ > 0.
  • Validated analytical findings through simulations on neuronal multiplex networks.

Conclusions:

  • Network topology, specifically node degrees and coupling strengths, plays a critical role in maintaining entropy extensivity in multiplex systems.
  • The derived scaling relationships provide a quantitative framework for understanding entropy behavior in complex, layered networks.
  • Findings have implications for understanding information processing and stability in biological and artificial complex networks.