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CREx produces transformational pathways in which the common strong intervals, shared by the pairs of GOs, are preserved in all intermediate steps.
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The analysis is performed using a unique type of graph called a strong interval tree (SIT).
Gene rearrangements with respect to other amphipod mitogenomes or to the hypothesized pancrustacean ancestral gene order were deduced using strong interval trees on the CREx webserver (http://pacosy.informatik.uni-leipzig.de/crex) [ 22].
A common interval is defined a strong common interval if it commutes with every common interval.
Internal nodes (strong common intervals) are connected by branches according to a minimal inclusion relation among the intervals (i.e., there is a branch between node c and c′ if c′ ⊂ c and there is no node c″ with c′ ⊂ c″ ⊂ c).
The internal nodes are the strong common intervals shared by the two GOs.
The CREx program considers only strong common intervals in its analyses.
When two strong common intervals are compared, their intersection is either empty or one is totally contained within the other.
Once the whole set of strong common intervals has been determined for a pair of GOs (e.g., GO1 and GO2) CREx heuristically identifies the most parsimonious transformational pathways that connect GO1 GO2 and vice versa.
It was shown in Bresolin et al. (2009) that the expressively strongest such interval logic is the neighborhood interval logic, which was proved there to be expressively complete for FO\(^{2}.\) On the other hand, even the full \(\mathsf{HS}\) is less expressive than the three-variable fragment FO\(^{3},\) for which Venema (1991) proved that the logic CDT is expressively complete.
Yamamoto (2012) documents a strong relationship for intervals of up to five minutes in a sample covering 2006 and 2007.
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