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As we smooth only one realization instead of averaging several realizations, we cannot recover the statistical characteristics of the additional noise.
During this time, he settled on the idea of studying art — something that came as a gradual realization instead of one big aha moment.
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According to Weyl (1948, 295), both the theory of general relativity and quantum mechanics force upon us the realization that "instead of a real spatio-temporal material being what remains for us is only a construction in pure symbols".
True, we might have preferred to have our internet singularity lead us to a collective realization of peace and love, instead of a despairing recognition of our inevitable alienation and the fact that we all die alone.
The proposed technique depends on current mode realization of doubly terminated LC ladder filters instead of voltage mode realizations presented by Constantinides and Dimopoulos in [1].
Furthermore, we investigate global synchronizability properties of stochastic network structure ensembles (instead of single realizations of a network architecture).
Instead of constraining realizations to match a parametric target covariance model over a wide range of spatial lags, we constrain the realizations only at smaller lags where the available geophysical data cannot provide enough information.
Chen's 陳雅玲 (2010, 2012) realization rates were indicated by ranges instead of averages because multiple locations were sampled.
In Algorithm 1, M independent copies (left (zeta ^{m}_{k-1}right)_{1le m le M}) of ζk−1 are sampled and the empirical mean of the associated estimates of the transition density are used to compute (widehat {omega }^{ell }_{k}) instead of a single realization.
Koziarz actually made use of the Ohsawa–Takegoshi extension theorem for the case (q=0) by passing to the sheaf-theoretic realization of cohomology; in other words, instead of using forms to represent cohomology, one uses Čech cocycles, and these are locally given by holomorphic functions.
The tragedy of Partition, he wrote, was not that there were now two countries instead of one but the realization that "human beings in both countries were slaves, slaves of bigotry . . .
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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