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In mathematics, a zero-dimensional topological space (or nildimensional space) is a topological space that has dimension zero with respect to one of several inequivalent notions of assigning a dimension to a given topological space. [1] A graphical illustration of a zero-dimensional space is a point. [2]
The practice/theory is based on universal patterns of nature and of man as part of a universal design/order and was named by Laban: Space Harmony or Choreutics. Laban, who laid the foundation for Laban Movement Analysis , was interested in the series of natural sequences of movements that we follow in our various everyday activity. [ 1 ]
Pattern theory, formulated by Ulf Grenander, is a mathematical formalism to describe knowledge of the world as patterns.It differs from other approaches to artificial intelligence in that it does not begin by prescribing algorithms and machinery to recognize and classify patterns; rather, it prescribes a vocabulary to articulate and recast the pattern concepts in precise language.
Gordon music-learning theory is a model for music education based on Edwin Gordon's research on musical aptitude and achievement in the greater field of music learning theory. [1] [2] The theory is an explanation of music learning, based on audiation (see below) and students' individual musical differences. The theory takes into account the ...
However, BESS is not the only organisation of Laban's theory in use. In the U.K. for example, more influenced by Lisa Ullmann, another student of Laban, the categories are Body, Effort, Space and Relationship with Shape being interwoven into Body, Space and Relationship. [4] The categories of BESS are as follows: [5]
The generative theory of tonal music (GTTM) is a system of music analysis developed by music theorist Fred Lerdahl and linguist Ray Jackendoff. [1] First presented in their 1983 book of the same title, it constitutes a "formal description of the musical intuitions of a listener who is experienced in a musical idiom" [1] with the aim of illuminating the unique human capacity for musical ...
An open cover of a topological space X is a family of open sets U α such that their union is the whole space, U α = X. The order or ply of an open cover A {\displaystyle {\mathfrak {A}}} = { U α } is the smallest number m (if it exists) for which each point of the space belongs to at most m open sets in the cover: in other words U α 1 ∩ ...
Early patterns with unknown futures, such as the R-pentomino, led computer programmers to write programs to track the evolution of patterns in the Game of Life. Most of the early algorithms were similar: they represented the patterns as two-dimensional arrays in computer memory. Typically, two arrays are used: one to hold the current generation ...