For clarity, note that is the component allocation variable associated with gene i in model k, and that is the mixture proportion associated with component in model k.
For the sake of clarity, note that we have used the notation N ( μ, σ 2 ) for some {μ,σ2} in order to represent a Gaussian (i.e., normal) distribution with mean μ and variance σ2.
In figure 2, we plot the same slopes derived from a model of SSD against log(male size) for increased visual clarity; note that the slopes in table 1 and figure 2 are statistically identical, differing only by a constant 1.
For clarity, we note that the shorthand labels were never used in the experiment.
Since the ring R = RFM N ( K ) ≅ End K ( V ) has module type ( 1, 2 ), by Lemma there necessarily exists a set of four elements in R which satisfy the appropriate relations; for clarity, we note that one such set is given by Y 1 = ( δ i, 2 i - 1 ), Y 2 = ( δ i, 2 i ), X 1 = ( δ 2 i - 1, i ), and X 2 = ( δ 2 i, i ).
For clarity we note that gene-set approaches are often referred to as pathway methods and sometimes, confusingly, as network methods.
In the interests of clarity, we note that coordinate systems alternative to that shown in Figure 23 are often employed; for example, the z-direction is often defined as the direction of the X-ray beam with x being the orthogonal horizontal axis and y being vertical.
In the interests of fairness and clarity, I should note that Fraser Nelson in the Spectator (unlike some of today's daily newspapers) was writing about foreign nationals as opposed to foreign-born citizens.
For the sake of clarity, let us note that the procedure proposed in [2] does not allow one to exploit the potential advantage of a rotationally variant constellation when the WL MMSE receiver is employed.
For the sake of clarity, let us note that, if symbols and noise are circularly symmetric, then the additive disturbance and the equalizer output will be circularly symmetric too; on the other hand, if is rotationally variant, then will be rotationally variant too, but nothing can be stated about the circularity properties of also when.
For clarity's sake, I should note that his remark was spoken, not written.
