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Therefore, the representation presented in this paper is optimal (up to an additive lower order term).
model UCB attains a regret of and by Lai and Robbins' lower bound this is optimal (up to a multiplicative variance-like term).
In addition, the computational time is optimal, up to a constant.
However, given what is known from theoretical analyses in CS, we expect our method to be close to optimal, up to logarithmic corrections and a possible improvement of the constant factor C appearing in the relation n∼ C s log p. For more detailed comparisons of earlier methods, see [ 24].
As the noise level is increased, the filter blocks optimized for a SNR of 25 dB become more optimal up to around 36 dB, when the filter blocks optimized for 60 dB become more appropriate.
This bound is optimal up to a constant factor.
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Optimal size obtained with the traditional deterministic approach are found to be sub-optimal (up to 30% larger) and the predicted annual cost saving is always lower when accounting for uncertainties.
We prove optimal bounds, up to constants only depending on p and q, for the entropy numbers of natural embeddings between SNp and SNq.
Test bacteria were grown to logarithmic phase under optimal conditions (up to 0.3 OD) and the test was performed in triplicates.
Among various lay-up ratios studied, the optimal lay-up ratio for quasi-static and dynamic stiffness was 0 ±45:90 = 3 1 1.
For this analysis, we created three scenarios to describe a situation of stable programme coverage, likely scale-up of programmes, and optimal scale-up of coverage (Table 1).
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