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The term hyperuniformity (also independently called super-homogeneity in the context of cosmology [22]) was coined and studied by Salvatore Torquato and Frank Stillinger in a 2003 paper, [1] in which they showed that, among other things, hyperuniformity provides a unified framework to classify and structurally characterize crystals, quasicrystals, and exotic disordered varieties.
Homogeneity and heterogeneity; only ' b ' is homogeneous Homogeneity and heterogeneity are concepts relating to the uniformity of a substance, process or image.A homogeneous feature is uniform in composition or character (i.e., color, shape, size, weight, height, distribution, texture, language, income, disease, temperature, radioactivity, architectural design, etc.); one that is heterogeneous ...
In uniform scaling with a non-zero scale factor, all non-zero vectors retain their direction (as seen from the origin), or all have the direction reversed, depending on the sign of the scaling factor. In non-uniform scaling only the vectors that belong to an eigenspace will retain their direction. A vector that is the sum of two or more non ...
Allometry (Ancient Greek ἄλλος állos "other", μέτρον métron "measurement") is the study of the relationship of body size to shape, [1] anatomy, physiology and behaviour, [2] first outlined by Otto Snell in 1892, [3] by D'Arcy Thompson in 1917 in On Growth and Form [4] and by Julian Huxley in 1932. [5]
Many of these systems evolve in a self-similar fashion in the sense that data obtained from the snapshot at any fixed time is similar to the respective data taken from the snapshot of any earlier or later time. That is, the system is similar to itself at different times. The litmus test of such self-similarity is provided by the dynamic scaling.
A scale-free network is a network whose degree distribution follows a power law, at least asymptotically.That is, the fraction P(k) of nodes in the network having k connections to other nodes goes for large values of k as
Use of the term "scale" is unrelated to the concept of weighing; rather it is related to cognate terms in mathematics (e.g., geometric scaling, the linear transformation that enlarges or shrinks objects, and scale parameters in probability theory), and in applied areas (e.g., in the scaling of images in architecture, engineering, cartography ...
An extension of metric multidimensional scaling, in which the target space is an arbitrary smooth non-Euclidean space. In cases where the dissimilarities are distances on a surface and the target space is another surface, GMDS allows finding the minimum-distortion embedding of one surface into another. [5]