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A machine is deterministic if for each pair (s,i) ∈ S × I there exists at most one pair (o, s′)∈O × S such that (s, i, o, s′) ∈ h S ; otherwise, the machine is non-deterministic.
If T is a test of the form T i ∩ D j, then it again distinguishes at most one pair in P, and a similar reasoning holds.
We therefore adopted a conservative estimate of significance by taking only a subset of pairs containing at most one pair for any given window.
Since each element in X participates in at most one pair in M∗, M∗ contains at most n pairs, and so there are at most n distinct elements y ∈ Y such that y ∈ M.
A bipartite matching M between X and Y is a set of pairs M ⊆ X × Y, such that each element in X ∪ Y participates in at most one pair in M. If some element z ∈ X ∪ Y does not participate in any pair in M, we say that z is unmatched by M and denote z ∉ M.
For a maximum flow f in N, define the set of pairs M f = {(x, y) : x ∈ X, y ∈ Y X, f x, y) = 1}.From flow conservation constraints, it is simple to assert that every z ∈ X ∪ Y participates in at most one pair in M f, and thus M f is a valid matching, and in addition, M f ⊆ X × Y X.
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After each read fragment has been processed using the filter pipeline, the final result is a single merged file containing at most one mapping for each single-end read and at most one paired mapping or two unpaired mappings for each paired-end read.
Thus, since m e = 2, the pair [ s, t] is in conflict with at most one other pair, and therefore the corresponding vertex has degree at most one in the conflict graph: a contradiction to the fact that neither Rule (1) nor (2) apply.
A secondary structure B is a set of base pairs B={ i, i′) | 1≤ i< i′≤| S|} over S, where each base takes part in at most one base pair.
The Vienna RNA Package currently implements three different models for handling the dangling-end contributions: They can be (a) ignored, (b) taken into account for every combination of adjacent bases and base pairs, or (c) a more complex model can be used in which the unpaired base can stack with at most one base pair.
UDRC are codes that guarantee a Hamming distance of at most one between any pair of encoded symbols.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com