Sentence examples for master equation and from inspiring English sources
We investigated a general model of a two-gene network, using the chemical master equation and a moment generating function approach.
The methods developed so far integrate on the one side the theory of probabilistic systems (master equation) and of nonlinear dynamics, and on the other side overarching concepts (such as dynamic utilities) from the social sciences.
Instead, we suggest that one should use a mean first passage time expression derived from a master equation, and show how this approach can be used to glean information about the underlying dynamics of barrier crossing.
The program employs an Adams predictor formula second order in time to integrate the quantum optical master equation and a Lax Wendroff scheme second order in space and time to evolve the wave equations for the fields.
This can be shown either by comparing the path integral representations of the generating functional for both stochastic processes or by comparing the WKB approximation of the master equation and corresponding Fokker-Planck equation.
This implies that when approximatingthe neural master equation of Buice et al. [46, 54] by a Langevin equation in the form of Equation 5.1 with σ ~ 1 N, where N is the system size, the resulting Hamiltonian differs from that obtained directly from the master equation and can thus generate a poor estimate of the extinction time.
These moments are derived from both the hierarchical master equations and the equivalent Fokker-Planck approximation.
In this paper, we consider models of GRN based on chemical master equations and study the problem of estimating stochastic rate constants therein.
The resulting expressions, both master equations and rate equations, were integrated numerically using a numerical integrator.
In fact, each variable can be derived from a set of master equations and complete parity can be brought to all three acid base approaches.
As is thoroughly discussed in [5] establishing the connection between master equation models and mean field equations involves two limit procedures.
