Then for step I we proceed as follows: We first perform a linear kernel-PCA for X, that is, we take the kernel function to be the inner product between accessions of X. Subsequent to this, we subject the resulting eigenvalues to the Tracy Widom test to identify significant principal components (see, e.g., Peres-Neto et al. 2005) for a survey of attractive alternative approaches).
Subsequent to this, the first in vivo results obtained with the system are presented, in which an arbitrary tissue surface was imaged.
Subsequent studies failed to reproduce this result, concluding instead that the regime's clinical effects were largely independent of ER status [ 28], but may depend on other factors including age.
Although an effect of high numbers of repeats on cancer risk in carriers was first reported by Rebbeck and colleagues [ 12], three large subsequent studies failed to replicate this result [ 13- 15].
However, this line of reasoning would also suggest that low scanning similarity would be observed for true negatives because there are also no global irregularities to guide the subsequent search, but this result was not observed.
A subsequent theoretical analysis sought to explain this result (Norton and Day, 1992), and its validity was confirmed with the publication of the 10-year outcome data (Bonadonna et al, 1995).
Subsequent studies have extended this result to other genomes, sometimes proposing a slightly different threshold length, for example, nine nucleotides for mononucleotidic repeats (Sibly et al. 2001; Lai and Sun 2003).
The full proof of this result can be found in Bowden and Glimm [2008] but to motivate subsequent results we provide a summary of the main steps.
Once sensitized to peanut proteins, subsequent exposures can result in allergic reactions that become increasingly serious.
Theorem 2.1 ii) leads to the subsequent result.
Corollary 2.2, through Lemma 3.1(i), leads directly to the subsequent result.
