Recent research into analog computing has introduced new notions of real numbers. Huang, Klinge, Lathrop, Li, and Lutz defined a notion numbers in real-time with chemical reaction networks (CRNs), introducing the classes $\mathbb{R}_\text{LCRN}$ (the class all Lyapunov CRN-computable numbers) $\mathbb{R}_\text{RTCRN}$ numbers). In their paper, they show inclusion algebraic $ALG \subseteq \mathb...

Abstract Quantum mechanical methods like density functional theory (DFT) are used with great success alongside efficient search algorithms for studying kinetics of reactive systems. However, DFT is prohibitively expensive large scale exploration. Machine learning (ML) models have turned out to be excellent emulators small molecule calculations and could possibly replace in such tasks. For kinet...

All current formulations of nonequilibrium thermodynamics open chemical reaction networks rely on the assumption non-interacting species. We develop a general theory that accounts for interactions between species within mean-field approach using activity coefficients. Thermodynamic consistency requires rate equations do not obey standard mass-action kinetics but account with concentration depen...

Background The aim of this work is to make available to the community a large collection of mass-action reaction networks of a given size for further research. The set is limited to what can be computed on a modern multicore desktop in reasonable time (< 20 days). Results We have currently generated over 47 million unique reaction networks. All currently generated sets of networks are available...

Mathematical models of biochemical reaction networks are usually high dimensional, nonlinear, and have many unknown parameters, such as reaction rate constants, or unspecified types of chemical kinetics (such as mass-action, Michaelis-Menten, or Hill kinetics). On the other hand, important properties of these dynamical systems are often determined by the network structure, and do not depend on ...