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Recently, several multiscale methods [20 23] are proposed to simulate models with dimensions of the order of microns and thus minimize the possibility of the contamination of the results by the boundary conditions arising from the small model size.
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The highest prediction power was obtained for models with dimension 35*35.
In order to evaluate the functions f 1, f 2, and A for models with dimension larger than two, we need to calculate d ζ / d θ.
Statistical performance of models with dimension 35*35 depending on number of learning epochs is represented on Figure 1 and Figure 2 for models with MDL (model A) and Dragon (model B) descriptors correspondingly.
For example, the block Toeplitz matrices corresponding to covariances of a stable singular AR model with dimensions high enough will be singular and thus only positive semidefinite.
Subsequent scrutiny of models with three dimensions suggested that the third dimension was contributed almost entirely by one or two specialities such as forensic medicine, which have a high public and media profile, but which form only a small proportion of medical personnel.
We selected an optimal model with dimension of neural network 35*35 and number of learning epochs equal to 200.
The geological model (Fig. 9) for our study zone extracted from Baillieux (2012) is derived from seismic and borehole data and consists in a 6 layer model with dimension ~30 × 20 × 5 km.
"Perhaps one can get even more bizarre models with different dimensions in different places," he said.
All one can ask is whether mathematical models with extra dimensions provide a good description of the universe".
Mathematical models and solution procedures using simplified models with reduced dimensions have been proposed to address this issue.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com