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Another perturbation method is to assume that there is a solution to the perturbed equation of the form f + εg1 + ε2g2 +... etc., in which the g1, g2,... etc., are unknown, and then to substitute this series into the equation, resulting in a collection of equations to solve corresponding to each power of ε.
This means that in reality the shock never comes to a steady state, because during the recovery process it will most likely be hit by another perturbation, which will not allow the shock to evolve to the initial state.
For each step in the search, part of the model is randomly perturbed, the effect on the fits to the observations is assessed, and if the fits improve, we keep the new model, otherwise we try another perturbation.
For example if the system were multistable, phase amplitude coordinates would track trajectories near these other structures and back again, should another perturbation return the dynamics to the basin of attraction of the limit cycle.
Another perturbation to the system can be due to an abrupt change in the prestige of a language because of political actions such as invasion, occupation, etc.
DOI: http://dx.doi.org/10.7554/eLife.03779.007 Another perturbation that has been shown to transiently up-regulate TORC2-Ypk1-mediated signaling is heat shock (Sun et al., 2012).
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In the Gulf of Mexico and East China Sea, coastal eutrophication, another anthropogenic perturbation, has been shown to enhance subsurface acidification as additional respired carbon accumulates at depth (Cai et al. [2011]).
Taking advantage of the above prior biological knowledge on the yeast diauxic shift, we added another environmental perturbation node ("diauxic shift").
We also solve the primal and resilience optimization problems using two another smaller perturbation regions for each enzyme, i.e., the lower and upper factors [ γ e i L B, γ e i U B ] are set to [0.4, 2.5] and [0.8, 1.25], to illustrate the effect of resilience phenomena on optimal productivity under different perturbation regions.
These variations can be computed in a number of ways, but we establish, via a variety of computational experiments, the superior effectiveness of our new approach as compared with another popular Boundary Perturbation algorithm (the method of Operator Expansions).
In this section, we present another version of perturbation for Bochner pg-frames.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com