Pearson correlation coefficient

In statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations. As a simple example, one would expect the age and height of a sample of teenagers from a high school to have a Pearson correlation coefficient significantly greater than 0, but less than 1 (as 1 would represent an unrealistically perfect correlation). Naming and history It was developed by Karl Pearson from a related idea introduced by Francis Galton in the 1880s, and for which the mathematical formula was derived and published by Auguste Bravais in 1844.

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We present first-principles calculations of the dynamic susceptibility in strained and doped ferromagnetic MnBi using time-dependent density functional theory. In spite of being a metal, MnBi exhibits signatures of strong correlation and a proper description in the framework of density functional theory requires Hubbard corrections to the Mn d orbitals. To permit calculations of the dynamic susceptibility with Hubbard corrections applied to the ground-state electronic structure, we use a consistent rescaling of the exchange-correlation kernel maintaining the delicate balance between the magnon dispersion and the Stoner continuum. We find excellent agreement with the experimentally observed magnon dispersion for pristine MnBi and show that the material undergoes a phase transition to helical order under application of either doping or strain. The presented methodology paves the way for future linear response time-dependent density functional theory studies of magnetic phase transitions, also for the wide range of materials with pronounced static correlation effects that are not accounted for at the local density approximation level.

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Correlation between quench pressure and normal zone voltage observed in the QUELL experiment

An interesting correlation between the quench pressure and the generated power was observed in the quench runs of the QUELL experiment. The experimental results indicate that the instantaneous values of the quench pressure and power generated by the normal zone are linearly correlated during the quench propagation. For quenches with constant operating current, the linear correlation holds for quench pressure and the normal zone resistance or voltage. This correlation can be used to improve the accuracy of the quench detection systems based on voltage taps. It could be also a useful tool for the validation of numerical codes for quench propagation. (C) 2001 Elsevier Science Ltd. All rights reserved.

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Ground state properties of large atoms and quantum dots

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