Sentence examples for master equations that from inspiring English sources

We use Gillespies Monte Carlo sampling technique [11] to simulate the Master equations that describe the set of chemical reactions given in the equation Eq. (2).

Our approach makes use of a master equation that describes the dynamics of the weight space probability density.

A common approach to modeling such networks is by a master equation that governs the dynamic evolution of the joint probability mass function of the underlying population process and naturally leads to Markovian dynamics for such process.

One possibility is to consider a Langevin version of the Wilson-Cowan equations involving some form of extrinsic additive white noise [57, 58], whereas another is to view the Wilson-Cowan rate equations as the thermodynamic limit of an underlying master equation that describes the effects of intrinsic noise [20 23].

A Markov process gives rise to a master equation that describes how the microstate probabilities change over time.

Their probabilistic description is given by the corresponding master equation that is exactly sampled by means of the Gillespie algorithm in a N-cells system [ 43].

We now conclude this article commenting on the feasibility of our approach connecting microscopic Markov models to deterministic macroscopic equations when dealing with different master equation formulations that appear in the literature.

However, since gene expression is inherently a stochastic process [ 51- 53], we will also make use of a stochastic description based on a master equation approach, that has Equations 3 as a "mean-field" limit (complete model in Additional file 1).

Stan's heart and soul is software, a master formula of elaborate differential equations that represent the interrelationships of human physiology.

One limitation of both versions of the neural master equation is that they neglect the dynamics of synaptic currents.

The other version of the neural master equation assumes that population activity is approximately characterized by a Poisson process [17, 20].