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Writing and optimizing distributed-memory kernels for each transposition and contraction is tedious since the number of contractions scales combinatorially with the number of tensor indices.
For each transposition, 24 plasmids were isolated from individual colonies using the Millipore Montage miniprep system (Millipore, Bedford, USA).
This is consistent with their origin via alternative transposition, because the duplication endpoints are determined by the position of the transposon insertion site, which is expected to differ for each transposition event.
However, further work, outside the scope of the global survey presented here but now in progress, will be required to study purified transposases and their functional interaction with β in vitro, as well as the development of in vivo assays of the interaction for each transposition system.
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Insertion time of LTRs in the foxtail millet genome was calculated to predict the time taken for the occurrence of each transposition events, which facilitates the movement of LTRs from one position to another in the genome.
In the following, we use variables in bold lower case for vec-tors, bold upper case for matrices, superscript for transposition, for the identity matrix, "*" for convolution, and for expectation.
The presence of an ORF coding for the DDE/DDD transposase, required for transposition, is characteristic for the autonomous PIF/Harbinger-like elements.
The notation T stands for transposition for vectors and matrices and expectation operation is denoted by E. Any other mathematical operators used in this paper will be defined as and when introduced in the paper.
We then amplified DNA flanking both ends of the integrated plasmid sequence by inverse PCR [31], for each of the 28 transposition products (Table S1).
The region between those repeats includes two overlapping reading frames, orfA and orfB, encoding for a transposase, an enzyme responsible for transposition of the insertion sequence.
The superscript 'T' stands for matrix transposition.
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