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The distributions of a wide variety of physical, biological, and human-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares, [2] cloud sizes, [3] the foraging pattern of various species, [4] the sizes of activity patterns of neuronal populations, [5] the frequencies of words in most languages ...
In mathematical statistics, the concept has been formalized as the Zipfian distribution: A family of related discrete probability distributions whose rank-frequency distribution is an inverse power law relation. They are related to Benford's law and the Pareto distribution.
The Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto, [2] is a power-law probability distribution that is used in description of social, quality control, scientific, geophysical, actuarial, and many other types of observable phenomena; the principle originally applied to describing the distribution of wealth in a society, fitting the trend ...
Since Newton, scientists have extensively attempted to model the world. In particular, when a mathematical model is available (for instance, Newton's gravitational law or Coulomb's equation for electrostatics), we can foresee, given some parameters that describe a physical system (such as a distribution of mass or a distribution of electric charges), the behavior of the system.
Degree distribution for a network with 150000 vertices and mean degree = 6 created using the Barabási–Albert model (blue dots). The distribution follows an analytical form given by the ratio of two gamma functions (black line) which approximates as a power-law.
In numerical analysis, inverse iteration (also known as the inverse power method) is an iterative eigenvalue algorithm. It allows one to find an approximate eigenvector when an approximation to a corresponding eigenvalue is already known. The method is conceptually similar to the power method. It appears to have originally been developed to ...
The Sutherland potential (orange) represents two hard spheres that attract according to an inverse power law, and the Lennard-Jones potential (black) represents the induced-dipole--induced-dipole interaction of two non polar molecules. Both are simple realistic molecular models. [16]
Bassingthwaighte's power law can be shown to directly relate to the variance-to-mean power law. Regional organ blood flow can thus be modelled by the Tweedie compound Poisson–gamma distribution., [ 23 ] In this model tissue sample could be considered to contain a random (Poisson) distributed number of entrapment sites, each with gamma ...