where the dot operator represents element-wise multiplication.
From the first order optimality, we have (x^ = max{ |y|-lambda^, 0 } otimes operatorname{Sign} y)), where ⊗ represents element-wise multiplication and (operatorname{Sign}(cdot)) denotes the symbol function, i.e., (operatorname{Sign} y_{i}) = 1) if (y_{i} geq0); otherwise (operatorname{Sign} y_{i}) = -1).
Combining the static PPIN and the activity PPIN provides the dynamic coregulation protein network at each time point: (4) A t = Co E t ∘ Ac t t ∘ P p i, where Ppi denotes the static PPI network adjacency matrix and ∘ represents element-wise multiplication.
It is then possible to rewrite Equation 1 in its matrix form given by where θ = [β11 β12 …β pp], and the dot represents element-by-element multiplication of B and T. In the example given by Figure 1, the matrices B and T are 4 × 4 matrices and have only 4 nonzero elements each [(1,3), (1,4), (2,3), and (3,4 ], so the vector of parameters is θ = [β13 β14 β23 β34].
After taking the Fourier transform, one arrives the following expression for the interferometric component of the complex A-scan: (2) I (z ) = E s ⊙ E r * R r R s (z ) exp (i ψ (z ) ) (3) E r = J det J ref T J ref E src (4) E s = J det J samp T J s J samp E src The symbol ⊙ represents element-wise multiplication.
A stock represents elements that can be measured and accumulated, and are regulated by the flows.
THBS represents elements of Suppression 1 where transcript expression levels are down- regulated in response to ConA stimulation.
All families also occur in other vegetation types in those same regions and represent elements of regionally prominent groups that have adapted to arid environments.
These interaction weights representing elements of S and D are denoted by s and d respectively.
Three agent types exist in the game representing elements of RAT; offender, target, and guardian agents.
The model results in a directed graph with the vertices representing elements of identity and the edges representing inferences.
