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That is: The default d with the lowest priority min is converted into the following default rule which forms the root node of T: begin{aligned} mathrm{If},mathrm{{True},mathrm{then}},varvec{betaa }_{mathrm{default}} end{aligned}.
If a 'true-branch' leads to a terminal node t, and the condition of t is not fulfilled then the conclusion of the rule in the parent node of t is taken.
The default d with the lowest priority min is converted into the following default rule which forms the root node of T: begin{aligned} mathrm{If},mathrm{{True},mathrm{then}},varvec{betaa }_{mathrm{default}} end{aligned} 2.
The parent node of t is denoted P t).
At a leaf node of T, append the column corresponding to the leaf to the required ordering.
Constraints 4a, 4b and 4c state the conditions under which an internal node of T may represent a speciation, duplication and transfer, respectively.
Similar(43)
A conflict occurs if two or more nodes of T are mapped to the same memory module.
An embedding from P to T is an injective function m mapping nodes of P to nodes of T, such that: (1) for any node (xin P), lb(x) = lb(m(x)); and (2) (x, y) is an edge in P iff m(x) is an ancestor of m y) in T. Clearly, an embedding is also a homomorphism.
Furthermore, we denote by K ℓ the set of nodes of T ℓ.
The set of internal nodes of T, denoted I(T), is defined to be V(T ∖Le(T).
The set of internal nodes of T, denoted I(T), is defined to be V (T ) ∖ L e (T ).
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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