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The Hashin- Shtrikman (HS) lower bound gives good estimation results under this condition.
For SVMs with L2 soft-margin formulation, the radius margin bound gives a very good prediction of optimal hyperparameter values.
The a posteriori bound gives insight into the quality of the reduced system and it can be used to solve many problems accompanying the order reduction operation.
The Cramer Rao lower bound gives a lower bound on the variance of any unbiased parameter estimation method and therefore provides an important tool in the assessment of a parameter estimation method and for experimental design.
This new upper bound gives information on the mechanisms involved in the amplification/reduction of the mistuned response: (i) the number of modes participating in the response, and (ii) the ratio between the aerodamping of the directly forced mode and that of the of the rest of the modes.
The first bound gives the minimal velocity 1 / c below which the stationary state might be unstable, in this case, even for smaller speed, the state is stable as one can see from the CV boundary.
Similar(48)
Since the gap between the achievable rates and the bound given by (55) is bounded by bit/channel use when, the gap between the achievable rates and the bound given by (41) is also bounded by bit/channel use when and.
Next, we prove that as long as, this upper bound is always looser than the bound given by (38 - 39 38 - 39
Hence, it follows from Theorem 3.3 that the closed-loop system given by (4.17), (A.2), and (A.3) is globally ultimately bounded with respect to uniformly in with ultimate bound given by, where.
For comparison purposes, the distortion lower bound given by (44) and the distortion upper bound given by (45) are also included in the plot.
This improves the O(n(log log n 2) time bound given in M. Thorup (1998) in "Proc.
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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