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Critical Pólya urn.

Avinash Chand Yadav1

  • 1Department of Physics and Astronomical Sciences, Central University of Jammu, Samba 181 143, India.

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|September 27, 2018
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Summary
This summary is machine-generated.

We introduce a new Pólya urn model with competing growth suppression and dormancy enhancement. This self-organizing system exhibits scale invariance and criticality, explaining avalanche events and potential neural network mechanisms.

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Area of Science:

  • Statistical Physics
  • Complex Systems Modeling

Background:

  • The Pólya urn process is a fundamental model in probability theory.
  • Understanding self-organizing systems and criticality is crucial in various scientific fields.

Purpose of the Study:

  • To propose a novel variant of the Pólya urn model incorporating competing dynamics.
  • To investigate the emergence of self-organization, scale invariance, and criticality within this model.
  • To explore universality classes of avalanche-type events and potential applications.

Main Methods:

  • Development of a modified Pólya urn process with internal parameter control.
  • Analysis of system dynamics involving growth suppression and dormancy enhancement.
  • Investigation of characteristic observables for scale invariance and criticality.

Main Results:

  • The proposed model demonstrates self-organization driven by random internal parameter fluctuations.
  • Scale invariance of observables suggests the system operates near a critical point.
  • The model explains different universality classes for avalanche-type events.

Conclusions:

  • The variant Pólya urn model provides a framework for understanding self-organization and criticality.
  • The underlying mechanism may be relevant to phenomena observed in neural networks.
  • Further exploration of model variations can yield deeper insights into complex systems.