Let H →p,σ) denote the fiber Hamiltonian corresponding to the conserved total momentum →p∈R3 of the electron and the photon field, regularized by a fixed ultraviolet cutoff in the interaction term, and an infrared regularization parametrized by 0<σ≪1.
Misorientation of a few side chains has been manually corrected and the full model regularized by molecular dynamics simulated annealing, using the standard protocols implemented with the Phenix software [ 57].
We observed earlier in Section 2.2.2—"Physical significance and roles of α(x)"—that fixing α to 1 (α=1), for example, makes the super-resolution problem regularized by both TV and isotropic diffusion, and this promotes edge recovery and noise removal, respectively.
The resulting system of linear algebraic equations is ill-conditioned and therefore its solution is regularized by employing the zeroth-order Tikhonov functional, while the choice of the regularization parameter is based on the L-curve method.
The autocorrelation parameter was first regularized by spatial smoothing and used to "whiten" the data and design matrix.
The initial full atom models were regularized by constraining both Ramachandran geometry and secondary structures in Coot (Emsley and Cowtan, 2004) but without including hydrogen atoms.
This constraint is regularized by including a compact and linear operator S to guarantee existence of solutions.
For the filtering the geodesic mean curvature flow in level set formulation is used, for the cell center detection the motion of level sets by a constant speed regularized by mean curvature flow is used and the solution of the eikonal equation is essential for the cell trajectories extraction.
The proposed encoder is regularized by an extension of previous work on contractive regularization.
