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It is worth pointing out that due to the property of the martingale generated by a finite-state Markov chain, the form of the monotone assumptions we employed here is different from that in Peng and Wu [14].
The number of groups that the database should be divided into is determined by trial and error; we employed here 20 groups in this analysis, which is large enough to illustrate most types of waves.
We employed here the data set "A" from the study in [31] on nonsmall cell lung carcinomas (NSCLC) that analyzed gene expression microarrays containing a total of 12600 transcripts each.
If we consider that we are free to choose any type of time functions given in Equation (1), the Hamiltonian we employed here is in a very general form.
Similar to that in Zhou and Wang (2000), we employed here the empirical bandwidth h=(h 1,h 2)′ with (h_{1}=2hat {sigma }_{Z} n^{-1/3}) and (h_{2}=2hat {sigma }_{W}n^{-1/3}), where (hat {sigma }_{Z}) and (hat {sigma }_{W}) are respectively the sample standard deviations of Z and W, which satisfy the bandwidth conditions required in this paper.
In contrast, the approach we employed here emphasised categorical relationships between stimuli, while controlling for word associations.
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We employ here ideas of [11] again.
Therefore, we employ here the interatomic Tersoff potential for SiNW.
The techniques that we employ here are based on local polynomial fitting (see Fan and Gijbels [5]).
For that purpose we employ here an effective multiresolution grid adaptation technique based on advanced multiscale methods.
We employ here the spherical Gaussian model, where the covariance matrix is identity and the two mean vectors are symmetric over the origin.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com