These developments have enabled detailed simulations of neutron scattering experiments, with non-trivial samples, for time-of-flight inelastic instruments at the Spallation Neutron Source.
Consider (3) y i = sign ∑ j = 1 s v α j y j d j, d i + b sign (y i ) = relevant if y i ≥ 0, unrelevant if y i < 0. For nonlinear cases (ϕ is not trivial), input samples are mapped to a feature space, dimensionally higher than original one, where a linear separation may be feasible (see Figure 2).
Although the missing for each covariate is trivial, the final sample size would have been reduced to less than half of the total if the complete case analysis approach was adopted.
Actually, very accurate XRD patterns are necessary to differentiate a trioctahedral smectite from a dioctahedral smectite (Thien et al. 2010); this task is non-trivial if the sample contains some amorphous material (e.g., glass, amorphous silica).
Therefore, implementation of the proposed method becomes trivial, whence the samples' population memberships are known (either self-reported or identified using the Eigenstrat method or any other methods, such as STRUCTURE).
But choosing the appropriate birefringence Δn value is not trivial, since the samples are turbid and the overall pathlength is not known before simulations.
This was extremely difficult in our last clinical trial on ovarian cancer, but it's not trivial to take samples when you've got patients who are very sick.
We implemented two approaches in MATLAB (using polymake as a preprocessing step) for approximating the volume of a spherical polytope P. One approach is trivial: it simply samples uniformly from the sphere, and counts how many points are inside P.
Such a comparison is not trivial, as for each sample thousands of data points are generated with each of these omics technologies.
Although such assessment is not trivial given the small sample size (entire dataset = 47; segmental dataset = 21 [ 21]), we were able to find significant differences in at least two independent analyses.
