The latter is obtained as part of the solution satisfying the terminal constraints in Eq. 2c, which strictly impose the values for a subset of the model states (see Table 1), and by the quadratic term Φ(x k (L)) of the objective function in Eq. 1, which loosely imposes some desired conditions on final state.
Note here how our model integrates gene expression data (as represented by the reaction sets H, M and L) via the objective functions in our three-stage minimization.
Since the length of the motif is l, the final objective function (i.e. the information content score) would contain 3 l independent variables.
The extra variable Z is introduced in order to decouple the minimization variables by separating the L variable in the objective function with the Z variable in the first constraint.
The term µ zl (x) indicates the desirability of solution X in terms of the objective l.
Then, the classical DOA problem can be formulated as a sparse representation problem, in which the sparsity constraint on the coefficient vector is manifested as a minimization of l 1-norm in the objective function.
For additional blood samples, fitting was achieved by adding further terms to Equation 5, so that for three samples taken at times t k, t l and t m, the objective function O = ∑ i N w i m tot t i − PET tot t i 2 + α. w ̄ ( b t k − C a t k ) 2 + … α. w ̄ b t l − C a t l 2 + α. w ̄ b t m − C a t m 2. was used.
At the start of the algorithm, each of the two classifiers is trained on L and U following the objective function in (2) as an ordinary SSL.
The optimum value of the objective function L defined by Eq. (11) is L =51.1, which is comparable with the value of expected for a variable drawn from a χz -squared distribution with (n + 3m − p) degrees of freedom (Menke, 1989), where p stands for the number of source parameters (n = 15, m = 13 and p = 11 in our case).
Thus, guided by a review in the literature, two metabolites were included in the objective function: L-valine and L-histidine both with a biologically meaningful role in nitrogen fixation.
These genes had the strongest knockout effect on the objective genes R a l l T, i.e. averaged over all 893 spatial areas of the brain.
