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Furthermore, a 10% restoration of the resolution uniformity is obtained using the half depth assumption and an 18% restoration using measured DOI.
The values obtained in the lateral scan comparing the maximum collected signal on each side are not symmetric with respect to the half depth of the detector (i.e. the values shown in Fig. 8-right are confined in the asymmetric range [−0.8, 0.6]), conversely to the distribution of the calibration values used for the method of the cluster size asymmetry that is ranging in approximately [−0.4, 0.4].
The half depth (HD) of a point x in R d with respect to a probability measure P on R d is defined as the minimum probability mass carried by any closed half space containing x; that is, (1) HD (x, P ) = inf { P (H ) : H is a closed half space, x ∈ H }, x ∈ R d.
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For different point source radial positions along vertical and horizontal axes of a FOV transaxial plane we compare the results obtained by three methods: without DOI information, with the DOI provided by our system and with the assumption that all the γ-rays interact at half depth of the crystal thickness.
This study presents a new laboratory reflectance spectroscopy method that characterizes soil spectra in terms of the positions, depths, asymmetries at half depth, and widths at half depth of the clay diagnostic absorption bands (1400 nm, 1900 nm, and 2200 nm).
e Morphological study of the hole depth and the hole aspect ratio measured at the half hole depth as a function of the AlGaAs thickness.
In this study, we use half-space depth function to measure the depth of the residues because the concept and the definition of the half-space depth are simple and easy to implement.
The deviation increases as the channel half-depth decreases, i.e., the shallowest nanochannel (h = 27 nm) has the highest conductivities for NaCl concentrations of 0.1, 1, and 10 mM.
Electroosmotic mobilities in the nanochannels exhibit maxima at κ h ∼ 4, where κ is the Debye Hückel parameter and h is the channel half-depth, indicating that the degree of double layer overlap depends on both channel dimensions and Debye length.
Tukey [ 21] introduced the half-space depth to order the high dimensional data.
For a probability measure P, the half-space depth of any point in R d with respect to P can be defined.
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