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As a result, when the LCE sample is constrained at the two boundaries, the small deflection bending theory is no longer applicable, and we need to use the large deflection theory.
Given the discrete nature of the 3D voxel space, it will be assumed that every sample is constrained to occupy a single voxel or discrete 3D coordinate and there cannot be two samples placed in the same location.
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In this procedure, the freely estimated parameters of the validation sample are constrained to equal the estimates from the calibration sample and a chi-square difference test is performed.
Following the procedure used in studies like PISA or PIAAC (OECD 2012; 2013), those item parameters that showed no significant difference for the German and Austrian sample were constrained to be equal for both groups.
To preserve axisymmetry, the center of the tissue sample was constrained to have zero displacement perpendicular to the channel axis.
First, the size of the sample was constrained by the small number of people in the service with sufficiently detailed knowledge to participate.
This contradiction might be due to the fact that our sample was constrained to include primarily low-income women; obesity may be more strongly related to income than race, ethnicity or educational level.
However, the problem of spatially limited sampling is constrained largely by the cost of establishing networks of commercially available turbidimeters.
Our understanding of metagenomic samples is constrained by the large number of hypothetical proteins for which reliable functions are not available (Galperin & Koonin, 2004; Ellrott et al., 2010) and the high degree of misannotation of some functional families of proteins (Schnoes et al., 2009; Radivojac et al., 2013).
In previous experiments (Neuhausen et al. 2017), we found that the classification results improve if samples are constrained to be rectified.
As shown in Figs. 3 and 4, most samples are constrained in PSD range and characterized by a prevailing oblate shape of anisotropy, indicating limited post-depositional alteration.
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