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I said something garbled about the principle of least action and then tried to invoke a third spatial dimension, which is quite hard to do when you are already using all four limbs and your mouth on keeping the blanket taut.
Other researchers have taken advantage of automated image acquisition and analysis to measure shoot growth features over time (Zhang et al. 2012; Tisné et al. 2013) or to acquire rotational series of branching root systems growing in a transparent gel to capture a third spatial dimension instead of time (Iyer-Pascuzzi et al. 2010; Clark et al. 2011).
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In the JPEG 2000 standard, the 1D processing shown in Fig. 2 is applied to a 4D signal along the x, y, z, and t dimensions, where x and y denote two spatial dimensions within a slice, z denotes the third spatial dimension within a volume, and t denotes the fourth, temporal, dimension.
However, when different functions are layered the third spatial dimension, height, becomes an important parameter.
Determining when a substrate can be treated as infinitely thick is difficult in the absence of any direct information about the extent of deformation in the third spatial dimension (i.e., the thickness direction).
Since currently in ECT [ 28, 29] and NTIRE [ 49- 52] of deep-seated tumors the electrodes are normally inserted into tissue parallel to each other, the fact that we do not consider the third spatial dimension is not of particular concern.
The generation of the 3D dataset (called a spectral cube) is achieved by sample movement along a scanning platform, which is responsible for the second spatial dimension (Imspector from Specim, Linescan from imec).
But if extra dimensions were real, the possibility would suddenly exist to exit our 3D universe, traverse through the fourth spatial dimension, and re-enter at a completely disconnected point in spacetime.
They suggested that the fifth spatial dimension existed only on the Planck scale at distances of the order of 10^-35 10^-35
It should be remembered that only the surface of the barrel has physical significance; the dimension off the surface toward the axle of the barrel represents the fourth spatial dimension, which is not part of the real three-dimensional world.
To incorporate additional dimensions of spatial variability, we develop a diffusion model in a second spatial domain Ω.
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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