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We introduce a novel, computable measure for quantifying complex system dynamics. This method successfully identifies key molecular sites in HIV1 protease evolution and reveals patterns in foreign exchange rates.

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Area of Science:

  • Complexity Science
  • Computational Biology
  • Quantitative Finance

Background:

  • Natural systems exhibit complex dynamics, crucial for characterization and perturbation analysis.
  • Previous methods relied on theoretical entropy concepts (e.g., Shannon entropy, Kolmogorov complexity).

Purpose of the Study:

  • To develop a new, pragmatically computable measure for quantifying complex system dynamics.
  • To demonstrate the measure's applicability across diverse scientific domains.

Main Methods:

  • A novel computational measure for dynamic complexity was developed.
  • The method was applied to a toy model with a control parameter.
  • Analysis extended to molecular evolution of HIV1 protease under drug treatment.
  • Application to foreign exchange rate data.

Main Results:

  • The new measure effectively quantifies complex dynamics in natural systems.
  • Identified specific residues in HIV1 protease crucial for drug binding.
  • Demonstrated applicability and validity in foreign exchange rate analysis.

Conclusions:

  • The proposed measure offers a practical approach to quantifying complex dynamics.
  • It provides insights into molecular evolution and financial markets.
  • This method has broad applicability in characterizing and understanding complex systems.