If the image satisfies periodic boundary conditions and if we use total-variation regularization, then the matrix (B^{T}B) is block circulant; hence, it can be diagonalized by the Fourier transform matrix as noted in [27].
The application of the biproportional adjustment algorithm here is similar to its application in the construction of an economic input-output matrix, as noted above: marginal input and output (row and column) totals are known precisely, but interindustry product flows the elements of the matrix are not.
The outgrowth (Figure 3D-F, arrows) is accompanied by matrix banding, as noted above, and is ongoing.
However, their approach makes the assumption that changes in diameter necessarily mean a change in matrix volume, but as noted above (Section 8.2), this is not necessarily the case.
We can formally define a set of clauses for each non-'−' entry in the read matrix as follows: Note that ⇔ is the logical equivalence operator and that (x ⇔ y ⇔ z) is a shorthand notation for the clauses (x ν y ν z), (¬ x ν ¬ y ν z), (¬ x ν y ν ¬ z), (x ν ¬ y ν ¬ z).
As noted in [24], the above two random matrix ensembles are representative of the random matrices frequently encountered in compressed sensing.
As noted by Millward-Sadler et al., matrix turnover has implications for the pathogenesis of human disc degeneration [ 19].
The 4 values for the matrix are derived from the output of the 'Hpi' routine (as noted above).
However, as noted above (Section 8.2), we believe that without direct measurements of matrix volume these data must be treated with caution.
However, as noted, while program outputs are being systematically reported based on a results based planning matrix, outcomes and impact are not recorded as systematically and comprehensively.
As noted in [ 36], cell spreading, proliferation, and survival are modulated by focal adhesions linking extracellular matrix proteins, integrins, and the cytoskeleton.
