However, since our approach is probabilistic and we limit the maximum number of iterations, corresponding entries in the upper and lower triangular sections of the matrix may differ.
But, if non-overlapping sections of the matrix exist, we consider connected components separately; let d i be the ith connected component of the set of all components D and n d i be the number of columns with at least one 1 in the SNPs of d i.
The fluorescence images from different sections of the matrices revealed uniform cells growth, most likely due to the large pores created by the particles which allows for rapid provision of oxygen and nutrient or removal of cellular wastes in and out of the matrix.
We depicted a compressed view of the matrix, where each data dot represent a 50 × 50 square of the original matrix and the gradient represents how many 1's are present in that section of the matrix, for space constraints.
The encoded result z 0 i, j, Δ z i, j of each multiplication z i, j = B i, j ⊗ x j can be obtained in a constant time as explained in Section "Preprocessing of matrix-vector ⊗ computations".
The overall preprocessing time of all these blocks is O r 1 2 + λ | D | (see Section "Preprocessing of matrix-vector ⊗ computations"), and so the computation time required for each step r2 ≤ r < r1 is O r 1 1 + λ | D | = O r 1 + λ | D |.
As shown in Section "Preprocessing of matrix-vector ⊗ computations", the time required for processing a single q × q block is O (q| D| q -1), and so the total time for processing all O r q blocks is O (q r | D| q -1).
In the upper right hand section of the matrix, correlations between crime rates and three of the four visitor variables range from 0.72 to 0.95.
When each of these rows is added to the corresponding row of index N - m + 2, N - m + 3,..., N, respectively, in the bottom section of the matrix the 1 entries in the leftmost m columns are effectively moved m positions to the right.
