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In experimental psychology, the RMSD is used to assess how well mathematical or computational models of behavior explain the empirically observed behavior. In GIS, the RMSD is one measure used to assess the accuracy of spatial analysis and remote sensing. In hydrogeology, RMSD and NRMSD are used to evaluate the calibration of a groundwater ...
Typically RMSD is used as a quantitative measure of similarity between two or more protein structures. For example, the CASP protein structure prediction competition uses RMSD as one of its assessments of how well a submitted structure matches the known, target structure.
In statistical mechanics, the mean squared displacement (MSD, also mean square displacement, average squared displacement, or mean square fluctuation) is a measure of the deviation of the position of a particle with respect to a reference position over time.
In the physics of gas molecules, the root-mean-square speed is defined as the square root of the average squared-speed. The RMS speed of an ideal gas is calculated using the following equation: v RMS = 3 R T M {\displaystyle v_{\text{RMS}}={\sqrt {3RT \over M}}}
The MSE either assesses the quality of a predictor (i.e., a function mapping arbitrary inputs to a sample of values of some random variable), or of an estimator (i.e., a mathematical function mapping a sample of data to an estimate of a parameter of the population from which the data is sampled).
The Kabsch algorithm, also known as the Kabsch-Umeyama algorithm, [1] named after Wolfgang Kabsch and Shinji Umeyama, is a method for calculating the optimal rotation matrix that minimizes the RMSD (root mean squared deviation) between two paired sets of points.
A molecular dynamics simulation requires the definition of a potential function, or a description of the terms by which the particles in the simulation will interact. In chemistry and biology this is usually referred to as a force field and in materials physics as an interatomic potential.
The data set [90, 100, 110] has more variability. Its standard deviation is 10 and its average is 100, giving the coefficient of variation as 10 / 100 = 0.1; The data set [1, 5, 6, 8, 10, 40, 65, 88] has still more variability. Its standard deviation is 32.9 and its average is 27.9, giving a coefficient of variation of 32.9 / 27.9 = 1.18