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The exponential decay error structure allows for any residual serial correlation, above and beyond the exchangeable correlation structure that is induced by the subject specific random intercept in the mixed-effects model (Diggle et al. 1994).
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In addition, it is extremely accurate, providing much reduced period elongation and amplitude decay errors, compared to standard methods.
Thus, if the set of solutions can be approximated by linear subspaces with an exponentially decaying error term, then the POD-Greedy algorithm will in fact find an approximation with an exponentially decaying error term, though possibly with suboptimal parameters in the error bound.
Research in the last twenty years has substantially advanced our understanding of quality control mechanisms within a cell such as targeting of misfolded proteins to the proteasome, removal of faulty mRNAs by nonsense-mediated mRNA decay and error corrections by DNA repair mechanisms.
To increase the speed of convergence of the system states to the equilibrium points or to decay state errors to zero, the fast terminal sliding mode controller is used.
For example, in a motor adaptation paradigm the movement has an exponentially decaying mean error curve.
We observe that the indicator η has almost the same exponential decay as the error e, whereas it overestimates the error, which is consistent with our theoretical results.
To overcome this problem, we exploit the fact that the residual error decay exponentially and therefore can be fitted by a decaying exponential.
The error decay curve is shown in Figure 8, displaying an exponential error decay as also observed for the switch example.
These estimators guarantee that the mean of the estimation error decays to the origin with a prescribed decay rate and that the error covariance decays to an ultimate bound, also with a prescribed decay rate.
It is seen that the error decay is O ( h ).
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CEO of Professional Science Editing for Scientists @ prosciediting.com