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Creating Virtual-hand and Virtual-face Illusions to Investigate Self-representation
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The Observable Representation.

L S Schulman1

  • 1Physics Department, Clarkson University, Potsdam, NY 13699-5820, USA.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

We introduce the observable representation (OR), a method to embed complex dynamics into a low-dimensional space. This technique preserves the underlying dynamics, aiding in the analysis of phase transitions and complex systems.

Keywords:
foraginglinguisticsobservable representationphase transitionrandom walkspectral analysisspin-glassstochastic matrix

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Area of Science:

  • Complex Systems Analysis
  • Dynamical Systems Theory
  • Mathematical Modeling

Background:

  • Stochastic dynamics occur in various scientific fields, often in high-dimensional spaces.
  • Visualizing and understanding these dynamics can be challenging due to complexity and dimensionality.

Purpose of the Study:

  • To introduce a novel embedding technique called the observable representation (OR).
  • To demonstrate that the OR preserves the essential dynamics of the system.
  • To showcase the applicability of OR across diverse scientific domains.

Main Methods:

  • Developing an embedding of the dynamical space into a low-dimensional Euclidean space.
  • Ensuring the embedding, the OR, respects the inherent stochastic dynamics.
  • Applying the OR to model phase transitions, random walks, and complex systems.

Main Results:

  • The observable representation (OR) effectively embeds dynamical spaces into lower dimensions.
  • OR preserves the dynamics, offering insights into system behavior.
  • Demonstrated utility in defining phase transitions, including metastable states.

Conclusions:

  • The observable representation (OR) provides a powerful tool for analyzing complex stochastic dynamics.
  • OR facilitates understanding of systems where traditional methods are insufficient.
  • This method offers a new perspective on complex systems, random walks, and phase transitions.