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These phase relationships can be expressed in form of matrices of bendability [12], [2], [5], where, according to the recent data of Gabdank et al. [5], the highest positional selectivity is displayed by the dinucleotides AT and CG.
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Moreover, the stability and stabilization results are formulated in form of matrix inequalities that are numerically feasible.
After logarithm, the equation (1) is linearized into (in forms of matrix): (2) log [ E r ] = [ C S ] log [ T F A r ] While the matrix [ Er] consists of elements [ Er] ij = E ij t)/ E ij 0) and similarly [ TFAr] ij = TFA ij t)/ TFA ij 0), represents the relative gene expression levels and TFs' activities.
For both modes the knowledge can be provided in form of connection matrices A = fix flexible and B = fix flexible resembling the system matrix and input matrix, respectively, as well as additional matrices containing reliability scores of the connections.
Finally, the collected prior knowledge was stored in form of interaction matrices (see Methods), which can be processed by NetGenerator.
The extended dissipativity criterion is derived in form of linear matrix inequalities.
Coupling mode theory (CMT) in form of transfer matrix was involved to determine the transfer power propagation between fibers.
By means of Lyapunov functional approaches, a sufficient condition for the admissibility of the residual system is expressed in form of linear matrix inequalities.
Based on the Lyapunov Krasovskii functional method and free weighting matrix technique, a delay-dependent criteria for the global exponential stability and stabilization of memristive neural networks are derived in form of linear matrix inequalities (LMIs).
Initially, all the pair-wise distances are given in form of a matrix D of size m × m, where m is the number of nodes (or input sequences).
As a result, linear algebraic algorithms, and in particular matrix decompositions, have proven extremely successful in the analysis of datasets in the form of matrices.
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