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Coutsias, et al. presented a simple derivation, based on quaternions, for the optimal solid body transformation (rotation-translation) that minimizes the RMSD between two sets of vectors. [2] They proved that the quaternion method is equivalent to the well-known Kabsch algorithm . [ 3 ]
Let P and Q be two sets, each containing N points in .We want to find the transformation from Q to P.For simplicity, we will consider the three-dimensional case (=).The sets P and Q can each be represented by N × 3 matrices with the first row containing the coordinates of the first point, the second row containing the coordinates of the second point, and so on, as shown in this matrix:
RMSD is a measure of accuracy, to compare forecasting errors of different models for a particular dataset and not between datasets, as it is scale-dependent. [1] RMSD is always non-negative, and a value of 0 (almost never achieved in practice) would indicate a perfect fit to the data. In general, a lower RMSD is better than a higher one.
The RMSD of two aligned structures indicates their divergence from one another. Structural alignment can be complicated by the existence of multiple protein domains within one or more of the input structures, because changes in relative orientation of the domains between two structures to be aligned can artificially inflate the RMSD.
Simplified Deep Space Perturbations (SDP) models apply to objects with an orbital period greater than 225 minutes, which corresponds to an altitude of 5,877.5 km, assuming a circular orbit. [ 3 ] The SGP4 and SDP4 models were published along with sample code in FORTRAN IV in 1988 with refinements over the original model to handle the larger ...
[2] The application of secondary chemical shifts to characterize protein flexibility is based on an assumption that the proximity of chemical shifts to random coil values is a manifestation of increased protein mobility, while significant differences from random coil values are an indication of a relatively rigid structure.
The artificial landscapes presented herein for single-objective optimization problems are taken from Bäck, [1] Haupt et al. [2] and from Rody Oldenhuis software. [3] Given the number of problems (55 in total), just a few are presented here. The test functions used to evaluate the algorithms for MOP were taken from Deb, [4] Binh et al. [5] and ...
In traffic flow modeling, the intelligent driver model (IDM) is a time-continuous car-following model for the simulation of freeway and urban traffic. It was developed by Treiber, Hennecke and Helbing in 2000 to improve upon results provided with other "intelligent" driver models such as Gipps' model , which loses realistic properties in the ...