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・ DISJ
・ DisJam
・ Disjecta
・ Disjecta (Beckett)
・ Disjecta membra
・ Disjoining pressure
・ Disjoint
・ Disjoint sets
・ Disjoint union
・ Disjoint union (topology)
・ Disjoint-set data structure
・ Disjointed Parallels
・ Disjunct
・ Disjunct (linguistics)
・ Disjunct distribution
Disjunct matrix
・ Disjunction and existence properties
・ Disjunction elimination
・ Disjunction introduction
・ Disjunction property of Wallman
・ Disjunctive
・ Disjunctive cognition
・ Disjunctive graph
・ Disjunctive normal form
・ Disjunctive population
・ Disjunctive pronoun
・ Disjunctive sequence
・ Disjunctive sum
・ Disjunctive syllogism
・ Disjunctivism


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Disjunct matrix : ウィキペディア英語版
Disjunct matrix

Disjunct and separable matrices play a pivotal role in the mathematical area of non-adaptive group testing. This area investigates efficient designs and procedures to identify 'needles in haystacks' by conducting the tests on groups of items instead of each item alone. The main concept is that if there are very few special items (needles) and the groups are constructed according to certain combinatorial guidelines, then one can test the groups and find all the needles. This can reduce the cost and the labor associated with of large scale experiments.
The grouping pattern can be represented by a t\times n binary matrix, where each column represents an item and each row represents a pool. The symbol '1' denotes participation in the pool and '0' absence from a pool. The ''d''-disjunctness and the ''d''-separability of the matrix describe sufficient condition to identify ''d'' special items.
In a matrix that is ''d''-separable, the Boolean sum of every ''d'' columns is unique. In a matrix that is ''d''-disjunct the Boolean sum of every ''d'' columns does not contain any other column in the matrix. Theoretically, for the same number of columns (items), one can construct ''d''-separable matrices with fewer rows (tests) than ''d''-disjunct. However, designs that are based on ''d''-separable are less applicable since the decoding time to identify the special items is exponential. In contrast, the decoding time for ''d''-disjunct matrices is polynomial.
==''d''-separable==
Definition: A t\times n matrix M is d-separable if and only if \forall S_1 \neq S_2 \subseteq () where |S_1|,|S_2| \leq d such that \bigcup_ M_j \neq \bigcup_ M_i

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