LNetReduce

LNetReduce reduces linear dynamic networks with separated time scales by applying graph and label rewriting to directed graphs labeled with integer timescale orders to produce reduced networks that approximate deterministic and stochastic monomolecular chemical reaction network dynamics across all time scales.

Key Features:

• Timescale-labeled representation: Networks are represented as directed graphs (digraphs) with integer timescale order labels on nodes or edges.
• Graph and label rewriting: Uses graph and label rewriting rules to generate a reduced network that approximates the dynamics of the original network across all time scales.
• Monomolecular reaction support: Handles both deterministic and stochastic monomolecular chemical reaction networks.
• Random-walk modeling: Models random walks on weighted protein-protein interaction (PPI) networks.
• Time-scale versus topology analysis: Facilitates exploration of the relationship between time scales and network topology.
• Network design and analysis: Produces reduced models that support analysis and design of dynamic networks.

Scientific Applications:

• Biochemistry: Models random walks on weighted protein-protein interaction networks to analyze molecular interactions and pathways.
• Epidemiology: Simulates network dynamics to study spreading of infectious diseases and transmission patterns.
• Social sciences: Simulates opinion dynamics within social networks to study propagation of information or influence.
• Computer science: Applies to communication networks to analyze and optimize data flow and connectivity.

Methodology:

LNetReduce applies graph and label rewriting rules to directed graphs labeled with integer timescale orders to generate reduced networks that approximate the original dynamics across all time scales.