In matrix formulation, (2) can be written as (5).
Finally, the matrix formulation of the system can be expressed as follows: mathbf{r}_{k,n}=mathbf{H}_{k,n}left(mathbf{a}_{k,n}+jmathbf{u}_{k,n}right)+boldsymbol{gamma}_{k,n}, (11).
The Jacobian matrix of the LM formulation can be derived from the Jacobian of the PL formulation by assuming k → ∞, as (A.11) J λ = A B B ^ 0, where the 0 block matrix results in a non-positive definite Jacobian matrix which may cause numerical difficulties.
This principle is used to build a self-consistent matrix formulation of functional similarity that can be evaluated iteratively using only knowledge of the adjacency matrix of the network (based on functional annotations of genes).
A matrix formulation for the submerged laminate, which can have a stack of an arbitrary number of anisotropic layers, subject to a plane sound wave is derived to obtain the reflection and transmission coefficients in the frequency domain.
Since invariants associated with matrix formulation are well-known, individual sequences can be indexed by one or more such invariants of various orders; it is expected that these would be sufficiently characteristic of the underlying sequences to enable unique characterization.
In this way, the matrix formulation obtained is sparse so that it can easily and efficiently be solved.
This equation can be rewritten in a matrix formulation: (5) Err Z − C D X = Z − C D C D T C D − 1 C D T Z.
Thus, the model can be rewritten in a matrix formulation: (3) Z C D X, X = C D T C D − 1 C D T Z, where Z = (g k ); X = (x i ) and C is the marking matrix recording whether the DHS sites are within the transcriptional regulatory regions of differentially expressed genes or not.
In order to keep the representation standard, the quadratic cost function can also be shown in the matrix formulation as, C τ ( s τ, u τ ) = s τ T Q s τ + u τ T R u τ (19).
