Sentence examples for an elementary path from inspiring English sources

A principally elementary path in N is an elementary path in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_0 N $$\end{document }T 0 (N ).

The basic idea is to check for each edge u → s v in P whether there is an elementary path u ⇒ s v not involving this edge, which can then be seen as an explanation for the observed influence u → s v allowing one to remove this edge.

An elementary path is constructed from v 1 to v |p|since Suff (vi, k − 1) = Pref (v i+1, k − 1), for 1 ≤ i < |p|.

Suppose also that N is not a tree with two leaves, which is equivalent to have that u is not the root of N. The DAG N TR (i, j ) is obtained by removing from N the leaf j and its incoming arc, and collapsing the created elementary path into a single arc (Fig. 6).

The resulting pricing subproblem is an elementary shortest path problem with resource constraints, and we employ acceleration strategies to solve this subproblem effectively.

The DAG N H (i, j ) is obtained by removing from N the arc (u, v) and collapsing the resulting elementary path with intermediate node v into a single arc (Fig. 7).

Furthermore, we show how similar modelling techniques enable an enhanced polynomial size formulation to be derived for the shortest elementary path.

Alternative paths can be computed for each elementary path in two phases (Fig. 4): (1) abstraction of the elementary paths and (2) computation of all the corresponding alternative paths.

For instance, in the elementary path EP4, GenopageCDS is mapped with the abstract entity CDS and GenopageProtein with Protein.

Albeit a negative effect in B might be observed transiently, we generally consider non-elementary paths containing a negative cycle as not sufficient for explaining an edge; only elementary paths with appropriate sign and weight are accepted.

Given an undirected network G≡[N,E], a source sink pair of nodes (s,t) in N, a non-negative number ui,j representing the capacity of edge (i,j) for each (i,j ∈E, and a positive integer q, an "elementary q-path flow" from s to t is defined as a flow of q units from s to t, with one unit of flow along each path in a set of q edge-disjoint s t paths.