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Amino acid sequences were aligned for each of the 31 conserved protein genes, and then all 31 alignments were concatenated and ambiguous portions were deleted before performing phylogenetic reconstruction.

Timing relative to the stressor was thus aligned for each subject.

The resulting ratio was normalized by the ratio of the total reads uniquely aligned for each sample.

Raw sequences for multiple factors (as listed above) were aligned for each group, since their binding motifs are extremely similar and probably not distinguishable via our bioinformatic tools.

Most importantly, the contours in the direction of movement (e.g. fingertips) were perfectly aligned for each frame and each clip of the biological and the symbolic conditions.

The sequences were aligned for each family using the Windows version of Clustal X 1.81 [22], [22] and manually inspected to improve incorrectly annotated sequences and remove incomplete sequences.

end{aligned} For each (win Y), let (x_{w}= 0).

end{aligned} for each (ninmathbb{N}) and (hinmathcal{H}) (see the argument in Zhang and Zheng [28]).

end{aligned} For each (sigmainmathbb{R}) we shall denote by (H^{sigma}(Omega)) the usual Sobolev space of order σ.

end{aligned} For each (tin Y) and (xin W), choose any (h t,x in F t,x)).

This is easily taken care of by defining begin{aligned} mu (A) = frac{dim (Icap A)}{dim (I)} end{aligned} for each linear subspace (A subset {mathcal A}).