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Alternatives to the standard Poincaré section are proposed to cater for some conditions arising in the study of chaotic ray propagation where the usual method of dimension reduction by the Poincaré section is inadequate because the driving is not periodic.
PCA is a well-known method of dimension reduction [ 17].
One must notice that, this method of dimension reduction is approximate due to the small amount of time points.
Our simulations also suggest that the RMT method of dimension estimation, proposed by Teschendorff et al. (2011), performs well for estimating the dimension of the latent structure.
> -wrap-foot> The results of the simulation experiment described in Section IV suggest that the RMT method of dimension estimation has good accuracy in estimating the correct latent variable dimension when the magnitude of the latent effects is sufficiently large relative to other error components, superior to simpler methods based on AIC and BIC.
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Three different versions of the device, corresponding to domestic, agricultural and light equipment needs, respectively, are worked out using a rationnal method of dimensioning.
Together with prior test results, the test specimens advanced design recommendations for SCBFs, which result in thinner, more compact corner gusset plate connections, a rational method of dimensioning mid-span gusset plates, and a balanced-design procedure for enhanced ductility.
Aimed at the difficulty of the extracting of the cylindricity error evaluating on line, two compensation methods of dimension deviation are presented, Archimedes Helix Compensation Method and Slope Compensation Method.
In each simulation (except those conducted to compare methods of dimension estimation), the RMT method of Teschendorff et al. (2011) was used to estimate the latent dimension.
Section IV describes a simulation experiment designed to investigate the effect of different scales of error variability on the accuracy of different methods of dimension estimation (both in estimating the dimension itself and in the impact on Root-Mean-Squared-Error (RMSE)).
There are essentially two methods of dimensioning features: there is the addition of numerical values to dimension lines and there is the use of symbols.
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