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(g) The life cycle of documents can be described by a directed path through the dirhypergraph, the documents may contain one or more scenarios.
There is one descent graph in which the source of the chain is connected by a directed path to the sink of the chain.
Two genetic markers are associated if they are not marginally independent, which imply that the corresponding nodes are connected in a PDAG by a directed path or by a common ancestor node.
In that case it follows that there is some maximal ST-set X that contains X r and also contains at least one taxon labeling a leaf ℓ that is not reachable by a directed path from the reticulation of N∖{ x}.
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In a directed graph, an edge between two nodes, A and B, has a direction, either from A to B or from B to A. We denote an edge from a node A to a node B by A → B. A directed path, in G, from a node A to a node B is a set of edges leading from A to B, possibly through other nodes as depicted in Figure 12a.
Topology was kept in the DB by ordering cell neighbors counter-clockwisely around each cell, namely by following a directed path of cell cell junctions around each cell.
By definition, there is a directed path in G i from a to each of the terminals in T i.
Notice that a solution is already a directed path by construction; hence this is not required again in (vii).
Then, an initial sink node X will be followed directly by all users that had a directed path towards X in the initial network.
More precisely, since N p is a tree, there exists a most recent common ancestor m = mrca u, v; N p), a directed path P1 given by m = u0, u1,..., u k = u from m to u, and a directed path P2 given by m = v0, v1,..., v j = v from m to v. Define d (u, v ; N p ) = ∑ ω (u i, u i + 1 ) : i = 0, ⋯, k - 1 + ∑ ω (v i, v i + 1 ) : i = 0, ⋯, j - 1.
Given a directed path F in the graph, its reverse complement path is defined as the path R in which each edge in F is replaced by the edge.
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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