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In this case, Phase 1 returns no conditional supertree; that is, the conditional problem has no solution.
A basic tree S V) globally minimizes the functional c(V) in the conditional problem for V if the problem is solvable.
Evidently, if the second conditional problem is solvable, then V0 is a basic set, and the tree S V0) is the solution according to Theorem 8. Theorem 8 A basic tree S (V ) globally minimizes the functional c (V ) in the conditional problem for V if the problem is solvable.
If there exists a tree S ′ over V 0 such that each basic tree S (V ) can be obtained by pruning S ′ to contain only species from V, then the augmentation leads to a species tree with the zero cost, and the conditional problem is solved.
Working memory capacity also predicts how well people will perform on problem-solving tasks, such as conditional reasoning problems.
The branch of mathematical programming which deals with the theory and methods for the solution of conditional extremum problems under incomplete information about the random parameters is called stochastic programming.
Then the optimization problem converts to a conditional extremum problem applying the mathematical model.
The problem we are interested in, namely the Conditional Robustness Problem, is that of shifting such a density to a desired region in order to achieve the suitable global behavior.
To overcome this limitation, we reformulate the problem of unconstrained optimization into a biologically justified constrained (conditional) optimization problem.
An exact solution is obtained during Phase 1, provided that the conditional optimization problem is solved under a certain condition.
Based on this model, the optimization can be converted into a conditional extremum problem.
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