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The Ackermann function, due to its definition in terms of extremely deep recursion, can be used as a benchmark of a compiler's ability to optimize recursion. The first published use of Ackermann's function in this way was in 1970 by Dragoș Vaida [ 27 ] and, almost simultaneously, in 1971, by Yngve Sundblad.
For a sequence of m addition, union, or find operations on a disjoint-set forest with n nodes, the total time required is O(mα(n)), where α(n) is the extremely slow-growing inverse Ackermann function. Although disjoint-set forests do not guarantee this time per operation, each operation rebalances the structure (via tree compression) so that ...
A combinatorial explosion can also occur in some puzzles played on a grid, such as Sudoku. [2] A Sudoku is a type of Latin square with the additional property that each element occurs exactly once in sub-sections of size √ n × √ n (called boxes).
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In particular, some modified functions simplify the expression by eliminating the −3 and similar terms. Here's an example of a modified Ackermann function which simplifies the explicit formulas for each level in the hierarchy. This function is defined for positive integers m,n both starting at 1 instead of 0:
The following hierarchy is an example of a cognitive model task performance for the knowledge and skills in the areas of ratio, factoring, function, and substitution (called the Ratios and Algebra hierarchy). [9] This hierarchy is divergent and composed of nine attributes which are described below.
Through an exploratory analysis of the Big Five literature, John Digman came up with two superordinate factors on a higher level than the Big Five. He referred to these factors as "alpha" and "beta". Alpha refers to a combination of agreeableness, conscientiousness and emotional stability (the inverse of neuroticism).
An onion model used in social penetration theory. The onion model is a graph-based diagram and conceptual model for describing relationships among levels of a hierarchy, evoking a metaphor of the layered "shells" exposed when an onion (or other concentric assembly of spheroidal objects) is bisected by a plane that intersects the center or the innermost shell.