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By subtracting the bridging scale from the total solution, we arrive at a coarse-fine decomposition that, by a proper choice of projection operator, decouples the kinetic energy of the two simulations.
Proof is thoroughly provided that the stationary MC process is linear to first order approximation and that it transforms into one-dimensional autoregressive processes of order one (AR(1)) via the automated choice of projection vectors.
In this paper, we consider the statically condensed Perturbed Lagrangian formulation of Bercovier [50] and others [48,49], which may be conveniently thought of as a weakly penalized form with an optional choice of projection operator.
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Note that both projections force the values in y ̂ k to be feasible and that the choice of the projection subset depending on μ is in accordance with the complementary slackness constraint μ ( ∑ j = 1 J y j − C ) = 0 of the problem.
Particular attention is paid to the link between the choice of the projection and the efficiency of the reduced model.
The primary point of departure between the penalty and PL formulations comes in the choice of orthogonal projection.
As mentioned previously, the weakly penalized system can be thought of as a generalized formulation which can result in the PL, penalty or statically condensed PL formulations depending on the choice of the projection operator.
In this generalized form, with an appropriate choice of the projection operator, we may choose to strengthen or weaken the constraint resulting in the PL, LM or penalty formulations.
Axons of retinal ganglion cells (RGCs) exit the eyeball, form the optic tract and arrive at the optic chiasm, a point where RGC axons from the two eyes encounter and face the choice of crossing (contralateral projection) or uncrossing (ipsilateral projection).
Furthermore, in this study we have analysed only filtered back projection algorithms, but ES values have been shown to vary, depending upon the choice of filtered back projection or iterative reconstruction algorithms [ 18].
The BET theory, despite its popularity, has many unjustified assumptions, requires a choice of the molecular projection area and arbitrary adjustment of the relative pressure range of the BET plot to suit the requirement of a linear best fit.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com