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Two metabolites were only connected in case of carbon atom transfer between them; exchange of phosphate groups, electrons, etc. were ignored, as recommended by several authors [ 27, 32].
Given any two nodes i and j of a network, they are said to be connected in case there is a sequence of edges extending from one of those nodes to the other, possibly passing through several relay nodes.
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For example, the Gas-Trapping/BMI pair had significant negative connections in both groups, but was more strongly connected in the case group than the control group.
"If I would have been given the right to not only judge the facts in this case, but also the law and the actions taken by the government, the prosecutor, local and federal law enforcement officers connected in this case would be in jail and not the defendants," juror Patrick L. McNeil wrote afterward.
Thus NUE and NIS could be connected in the case of wheat and rice blast diseases.
This observation suggests that the high clustering coefficient of the value-based networks is partially because their non-singleton nodes are almost completely connected, in which case the structure cannot be destroyed by any random rewiring.
Then some examples illustrate that the SOCBLP is generally a nonconvex and nondifferentiable optimization problem, whose feasible set may be not connected in some cases and constraint region is generally not polyhedral for m ≥ 3. Finally, the SOCBLP in the optimistic case is reformulated as a single level optimization problem by using the KKT conditions for the lower level problem.
It is well known that the BLP problem is usually nonconvex, nondifferentiable and its feasible set may be not connected in some cases.
When n → ∞, if p is larger than a critical value p c, ((p_{c} propto ln ;n/n)), then the generated random graphs are connected in most cases.
It is illustrated that the SOCBLP is generally a nonconvex and nondifferentiable optimization problem, whose feasible set may be not connected in some cases and the constraint region is generally not polyhedral.
The two levels of selection may nonetheless be connected in some cases: in addition to conditional phenotypic plasticity, the capacity for microbial mutiny can also emerge by the evolution of "enabling constraints" that create a high-probability trajectory of evolution towards increasing virulence within the host when the appropriate conditions occur.
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