Sentence examples for but in a stochastic from inspiring English sources
During the growth of sand patches, sand particles transported from upstream are incorporated into sand patches and decelerated (like cars on a congested road); this local state is not in equilibrium, but in a stochastic (statistical) sense, it does not violate the equilibrium of the entire system, because sand patches repeatedly appear and disappear in many places.
Our results indicate that this happens on an average after every 2 3 bp unwinding steps, but in a stochastic manner.
We have shown that the persistent activation of ERK1/2 increases the activity of the parallel PI-3K AKT PI-3K AKT module, but in a signalingc module in cells within an acinus.
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].
In a deterministic simulation, the level of the mRNA or protein remains fixed under basal conditions, but in a stochastic simulation, the levels may fluctuate around the mean value (compare Supplementary Figure 5 [available on the Arthritis & Rheumatology web site at http://online library.wiley.com/doi/10.1002/art.38297/abstract] with Figure 1).
We will mathematically define the Markov property but in words, a stochastic process with the Markov property, or memorylessness, is one for which conditional on the present state of the system, its future and past are independent.
This means that the provided single-DOA estimations are being estimated from different sources but are 'given' in a stochastic manner.
In many applications, the data model p(D | θ) is computationally intractable but instead is implemented in a stochastic model (SM), so many realizations from p(D | θ) are available by running the model many times at each of many trial values of θ.
This investigation takes one step further by not only comparing ensemble and deterministic forecasts to observed values, but by employing the forecasts in a stochastic decision-making assistance tool for hydroelectricity production, during a flood event on the Gatineau River in Canada.
However, due to the assumed stochastic component of Nanog transcription, the actually realized oscillations do not show a strictly fixed period, but are shortened or prolonged in a stochastic manner (example trajectories in the Nanog vs. X phase space are shown in green in Figure 3E).
We believe that the dynamical aspects of the current results would still hold broadly in a stochastic context but a quantification of the probabilities associated with extinction events calculated by examining the outcomes of a large ensemble of model runs would, however, perhaps be more realistic in guiding control programme design and management.
