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To obtain a length n sample-path, that is, a truncated realization, of any one of the random processes θ, x, or η described in this work, a draw from n IID standard Gaussian random variables is made (mean-zero, unit variance).
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Open image in new window Fig. 2 Truncated Gaussian simulation with a the realization of a Gaussian random function; b the resulting facies realization after applying truncation; c the threshold mask.
The method is an extension of truncated balanced realization method for the general descriptor system.
We assume that a seismic event is a realization of the uniform random point process and that the truncated Gutenberg-Richter law holds for the frequency-magnitude relation unless otherwise stated.
Much of the music is truncated — some of it is kitsch — but, over all, it's the greatest realization of classical music in images (at least, prior to Jean-Luc Godard's "First Name: Carmen").
It is nature's realization of chaos.
"This is the realization of a dream".
Then a realization: Of course!
"This is a realization of a dream.
"It's a realization of potential".
In Germany, a Realization of Fears.
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