end{aligned}The same computation for the case of (K = mathrm {USp}_N) shows that begin{aligned} delta = sum _{k=1}^n k, (mathrm {i} psi _k - phi _{n-k+1}).
In principle, these values may change between the different groups; therefore, we made the same computation for different pairs of values (0.15 to 0.85, 0.25 to 0.75, 0.5 to 0.5, respectively).
The same computation for 120 MBq of 131I gives mathrm{S}mathrm{f}left(120kern0.5em mathrm{MBq}right)in left[10%,16%right] (8). Figure 1 shows the predicted survival fraction Sf and the TCP for 107 and 109 cells as functions of the dimensionless variable ( widehat{alpha}A ).
By repeating the same computation for each voxel, a parametric map can be formed to represent the heterogeneity distribution.
In order to be able to also account for temporal relationships, the same computations as above were repeated on sliding windows of variable length (1-hour, 4-hour and 1 day), producing second-order features that capture spatio-temporal relationships, thus preserving useful source data properties.
This suggests that the biophysical oscillatory behavior of neurons and synapses leads to selecting the corresponding frequency of the inputs and performing the same computation as for the Hebbian linear case of the previous section: computing the correlation of the (filtered) inputs.
Let (p ρ,q ρ and (P ρ,Q ρ be, respectively, the solution of Eq. (15) and (16) with ((bar {x}(cdot),bar {y}(cdot),bar {z}(cdot),bar {u}(cdot))) replaced by (x ρ,y ρ,z ρ,u ρ, and all the coefficients endowed with the superscript ρ. Then, the same computation as for Theorem 1 leads to: y_{rho}^{varepsilon}(0 -y_{rho}(0 -y_{rho}{rho}(0)+o(varepsilon), (62).
The same computation carried out for 3 × 1019 atoms would show that one would have to wait interminably (i.e., enormously longer than the age of the universe) for the number on one side to fluctuate even by as little as one part per million.
The same computation was used for gene ontology analyses of the initial gene list.
To ensure a fair comparison we set the same computation time as for the eSS and local multistart procedures: we carry out 10 DE optimizations, each with a time limit of one day.
The same computation was carried out for KEGG pathways.
