Evaluation and reduction of stochastic reaction networks, differential equations, and Boolean networks
An all-in-one tool for the numerical solution, stochastic simulation, and minimization of dynamical systems with import/export options for a variety of third-party formats including SBML and Matlab.
Supported through the Apache Commons Math library and through a Java porting of the SUNDIALS library.
Gillespie's Direct Method, Gibson and Bruck's Next Reaction Method, tau-leaping.
Forward equivalence produces a reduced model where every macro-variable represents the sum of variables in each block.
Backward equivalence ensures that all variables in a block have the same solution at all times points.
Species equivalence identifies a partition of the species of in a network and produces a reduced one where the marginal probability distribution of each macro-species corresponds to the probability distribution of the sum of the species in each block.
Forward differential equivalence and backward differential equivalence are generalizations of the forward and backward equivalences when the derivatives have rational expressions, minimum/maximum functions, etc.
ε-forward and ε-backward equivalence: relaxations of forward and backward equivalence where the macro-variables approximately represent the sum of original variables within some computable bound.
Backward Invariance is a generalization of backward equivalence when the derivatives are linear and the differential equations are complemented by algebraic constraints (e.g., a constraint x1=x2+x3 implies that whatever value these 3 variables take, x1+x2 must always be equal to x1, constraining the space of admissible solutions).
Boolean backward equivalence: is a recasting of backward equivalence to Boolean networks. These are a popular qualitative model of biological models where variables and update functions are Boolean.