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Stochastic simulation algorithms for Interacting Particle Systems.

Timothy C Stutz1, Alfonso Landeros1, Jason Xu2

  • 1Department of Computational Medicine, University of California, Los Angeles, CA, United States of America.

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|March 2, 2021
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Summary
This summary is machine-generated.

This study introduces a new algorithmic framework to simulate Interacting Particle Systems (IPSs) by converting them into well-mixed Chemical Reaction Networks (CRNs). This method enhances computational efficiency and broadens the applicability of simulation techniques for complex spatial phenomena.

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Area of Science:

  • Computational modeling
  • Stochastic systems
  • Interdisciplinary science

Background:

  • Interacting Particle Systems (IPSs) are crucial for modeling spatio-temporal stochastic processes across various scientific fields.
  • Simulating large-scale IPSs presents significant computational challenges due to their dependence on lattice size.

Purpose of the Study:

  • To develop an algorithmic framework that simplifies IPS simulation by reducing it to the simulation of well-mixed Chemical Reaction Networks (CRNs).
  • To minimize reaction channels and decouple computational cost from lattice size for efficient IPS modeling.

Main Methods:

  • Designed an algorithmic framework to transform IPS simulations into CRN simulations.
  • Implemented the direct stochastic simulation algorithm using the Julia programming language.
  • Applied the framework to model phenomena such as rock-paper-scissors dynamics, cancer growth, and lipid oxidation.

Main Results:

  • The framework successfully reduces IPS simulation complexity.
  • Computational cost is decoupled from lattice size, enabling scalable simulations.
  • Demonstrated applicability across diverse complex spatial stochastic phenomena.

Conclusions:

  • The developed framework standardizes mathematical models for spatial stochastic systems.
  • It facilitates hypothesis generation by revealing concrete mechanistic behaviors.
  • This approach offers a unified method for analyzing a wide range of spatial phenomena.