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This study extends moment-based semidefinite programming (SDPs) to address the closure problem in stochastic chemical kinetics. It enables calculation of time-varying bounds for dynamic systems, improving analysis of molecular counts and variances.

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Area of Science:

  • Chemical kinetics
  • Computational chemistry
  • Applied mathematics

Background:

  • The method of moments applied to the chemical master equation in stochastic chemical kinetics faces a closure problem.
  • Moment-based semidefinite programs (SDPs) have been developed to provide rigorous bounds on stationary distributions.

Purpose of the Study:

  • To extend moment-based SDPs to the dynamic problem in stochastic chemical kinetics.
  • To enable calculation of time-varying bounds for dynamic systems.

Main Methods:

  • Application of moment-based semidefinite programming (SDPs).
  • Extension of techniques used for stationary distributions to dynamic systems.

Main Results:

  • Demonstrated that moment-based SDPs can be extended to the dynamic problem.
  • Developed a method for calculating time-varying bounds on descriptions of dynamic stochastic chemical kinetic systems.

Conclusions:

  • The developed method provides a powerful tool for analyzing dynamic stochastic chemical kinetic systems.
  • This approach offers rigorous time-varying bounds for molecular counts and variances, advancing the field.