Here, an adjoint variable method is employed, where the adjoint sensitivity formulation is derived from the discrete master equation, yield condition, and consistency condition.
Putting these terms together yields the master equation for the state of branch i: Migrations from state k to l at rate g kl cause the state to change l → k with probability p il/ Y l.
The graph yields a stochastic master equation for how microstate probabilities change over time.
The framework yields a stochastic master equation for the probabilities of DNA microstates.
Taking the possible transitions and the corresponding reaction propensities together yields the chemical master equation (CME), a linear differential equation where the variables are the probabilities that the system is in each of the possible molecular states x: (7) d dt p (t, x ) = ∑ j = 1 m (ν j (x − v j, θ ) p (t, x − v j ) − ν j (x, θ ) p (t, x ) ), for x ∈ N 0 n.
First, this update rule yields a much simpler master equation since the interactions in this update rule are for the nearby-neighbours only, and other update rules will usually lead to more non-local interactions.
Next, we return to the master equation (1.6) as discussed in this article in Sect.
It is not derived from a detailed microscopic model of synaptically coupled spiking neurons, and it is not yet clear under what circumstances such a microscopic model would yield population activity consistent with the master equation approach.
Their average result reproduces the master equation solution1,29,30.
A general master equation set is provided, describing multicomponent adsorption.
