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First of all, we propose an abstraction of the underlying sensor data using Normal Distribution Transform (NDT) maps that are suitable for making our approach independent from the used sensor and the dimension of the generated maps.
Section 2.2 treats modal reduction to reduce the dimension of the generated models.
The fractal dimension of the generated topology, as shown in Fig. 4a, is equal to 3.42 ((begin{aligned} = {{log left[ 4 right]} mathord{left/ {vphantom {{log left[ 4 right]} {log left[ {1.5} right]}}} right. kern-0pt} {log left[ {1.5} right]}} hfill hfill end{aligned})).
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The dimensions of the generated corrugated webs are assumed based on the average dimensions of the available bridges with corrugation webs.
Then, we have properly designed the DLCA experiments, using different radii of the primary particles, and determined the fractal dimensions of the generated clusters.
The dimensions of the generated empirical feature spaces are approximate to N. When dealing with large-scale problems, MEKL cannot handle them properly due to the severe computation and memory burden.
The face form of the producible velocity space does not clarify the directions and number of dimensions of the generated velocities.
We then embed our models in spatial areas of different aspect ratios and study how this geometric factor affects the network structure, as well as the box-counting fractal dimension of the grids generated by our models.
The mass conservation laws as determined by P-invariants can be exploited to automatically reduce the dimension of the ODEs generated for the continuous simulation experiments of a given continuous Petri net.
For a dimension higher than three, the size of the generated tree depends on the bisected LE.
The large fractal dimensions of the clusters generated by very small nanoparticles could be explained by thermal restructuring due to their low bonding energies, but no clear explanation can be given for the small fractal dimensions of the clusters made of large particles.
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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