These configurations can be represented within a connectivity matrix which corresponds to a network representation.
In order reconstruct the simulated data, with STIR, we had to calculate system probability matrix which corresponds to this non standard geometry.
If there is no step of list decoding of subspace codes, the matrix which corresponds to the message will not be of low rank in the sense of subspace distance and therefore will not be sparse in Hamming metric.
The broad absorption band around 3,427 cm−1 is caused by the presence of OH− groups in the glass matrix, which corresponds to the fundamental vibration of OH− groups [33].
Taking the trace of the anti-diagonals of the matrix, which corresponds to taking the logical disjunction of the subset of (heteronuclear) mass fractions that correspond to isotopically labeled moieties with the same number of additional neutrons, yields a vector; specifically, the mass fraction vector that is obtained by low-resolution MS of the same sample.
Maximum likelihood (ML) values are calculated for each 1-PAM substitution frequency matrix, which corresponds to the time duration of 1 amino acid substitution per 100 amino acids, of the JTT [5], the WAG [10], the LG [11], the cpREV [8], and the mtREV [6] amino acid substitution matrices, and of the KHG codon substitution matrix [14].
B2N calculates the Jaccard distance for both dimensions of the phylogenetic profiles matrix, which corresponds to the distance between plasmids in term of shared genes, and the distance between occurrence patterns of protein clusters in plasmids.
In the following two lemmas, we determine the eigenvalues and eigenvectors of the matrices which correspond to the glide reflections.
Proof We consider the set A = { i A ( 1 ), i A ( 2 ), …, i A } of skew-Hermitian matrices which correspond to the generators in, i.e. i h k = i ∑ p, q = 1 d A p q ( k ) ( f p † f q − δ p q 1 / 2 ).
Both methods proceed by multiplying the matrix by suitable elementary matrices, which correspond to permuting rows or columns and adding multiples of one row to another row.
