These investigators treated the distribution of responses within a population of E. coli cells to model fluctuations in gene expression and determine the effect of fluctuations in one gene on expression of other linked or independent genes.
In contrast to our model fluctuations of the chain are taken into account and it was shown that the variance in locus positioning is well explained by the model provided that the packing density is sufficiently high.
The retrospective and bootstrap analyses use identical settings to the constant insolation scenario, with the one change being that they model fluctuations in the annual global insolation.
In fact, if we want to model fluctuations of hours worked in the aggregate economy, the elasticity of labor supply should be estimated using aggregate data and not individual data.
Indeed, in the stochastic model, fluctuations due to demographic stochasticity were larger than the differences seen here.
In other words, our model shows good robustness, and can produce stable cell fate patterns even we intentionally add the noise to capture the behaviors of the model fluctuations.
The deterministic model has a unique asymptotically stable equilibrium point, but in a stochastic model, fluctuations may push the molecular numbers beyond a certain threshold, inducing a dynamical response along a slow manifold, which corresponds to one oscillatory period [ 24].
The results for the footprint variability show that stochastic methods are suitable to model these fluctuations, and it is also shown that this approach yields accurate estimates of the average profile after multiple jet passes with error less than 5%.
The experiment depicted in Fig. 6a and b corresponds to modeling in a model with random fluctuations and migration in a smooth background model.
It was first discussed by Louis Bachelier (1900), who was interested in modeling fluctuations in prices in financial markets, and by Albert Einstein (1905), who gave a mathematical model for the irregular motion of colloidal particles first observed by the Scottish botanist Robert Brown in 1827.
