Ovidiu Radulescu

Symbolic Methods for Biological Networks D2.1 Report on Scalable Methods for Tropical Solutions (T1.2)

Tropical geometry can be used to find the order of time scales of variables in chemical reaction networks and search for model reductions [SGF+15]. In this report, we consider the problem of solving tropical equilibration problems in ODE systems of the BioModels model repository. We are interested in the existence of solutions both in R and Z […]

Fri, Apr 1, 2022

A constraint solving approach to model reduction by tropical equilibration

Model reduction is a central topic in systems biology and dynamical systems theory, for reducing the complexity of detailed models, finding important parameters, and developing multi-scale models for instance. While singular perturbation theory is a standard mathematical tool to analyze the different time scales of a dynamical system and decompose the system accordingly, tropical methods provide a simple algebraic framework to perform these analyses systematically in polynomial systems. The crux of these methods is in the computation of tropical equilibrations […]

Mon, Dec 1, 2014

A Constraint Solving Approach to Tropical Equilibration and Model Reduction

Model reduction is a central topic in systems biology and dynamical systems theory, for reducing the complexity of detailed models, finding important parameters, and developing multi-scale models for instance. While perturbation theory is a standard mathematical tool to analyze the different time scales of a dynamical system, and decompose the system accordingly, tropical methods provide a simple algebraic framework to perform these analyses systematically in polynomial systems. The crux of these tropicalization methods is in the computation of tropical equilibrations […]

Sun, Sep 1, 2013