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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 ...
Level of analysis is used in the social sciences to point to the location, size, or scale of a research target. It is distinct from unit of observation in that the former refers to a more or less integrated set of relationships while the latter refers to the distinct unit from which data have been or will be gathered.
The sampling theory of Shannon can be generalized for the case of nonuniform samples, that is, samples not taken equally spaced in time. The Shannon sampling theory for non-uniform sampling states that a band-limited signal can be perfectly reconstructed from its samples if the average sampling rate satisfies the Nyquist condition. [1]
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]
The Obukhov length (), a characteristic length scale of surface layer turbulence derived by Obukhov in 1946, [4] is used for non-dimensional scaling of the actual height. M–O similarity theory marked a significant landmark of modern micrometeorology , providing a theoretical basis for micrometeorological experiments and measurement techniques.
The scale of analysis encompasses both the analytical choice of how to observe a given system or object of study, and the role of the observer in determining the identity of the system. [ 2 ] [ 3 ] This analytical tool is central to multi-scale analysis (see for example, MuSIASEM , land-use analysis).
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The ratio of uniforms is a method initially proposed by Kinderman and Monahan in 1977 [1] for pseudo-random number sampling, that is, for drawing random samples from a statistical distribution. Like rejection sampling and inverse transform sampling , it is an exact simulation method.