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The nucleolus
(1994)
In distance geometry problems and many other applications, we are faced with the optimization of high-dimensional quadratic functions subject to linear equality constraints. A new approach is presented that projects the constraints, preserving sparsity properties of the original quadratic form such that well-known preconditioning techniques for the conjugate gradient method remain applicable. Very-largescale cell placement problems in chip design have been solved successfully with diagonal and incomplete Cholesky preconditioning. Numerical results produced by a FORTRAN 77 program illustrate the good behaviour of the algorithm.
Plants attacked by herbivorous insects emit a blend of volatile compounds that serve as important host location cues for parasitoid wasps. Variability in the released blend may exist on the whole-plant and within-plant level and can affect the foraging efficiency of parasitoids. We comprehensively assessed the kinetics of herbivore-induced volatiles in soybean in the context of growth stage, plant organ, leaf age, and direction of signal transport. The observed patterns were used to test the predictions of the optimal defence hypothesis (OD). We found that plants in the vegetative stage emitted 10-fold more volatiles per biomass than reproductive plants and young leaves emitted >2.6 times more volatiles than old leaves. Systemic induction in single leaves was stronger and faster by one day in acropetal than in basipetal direction while no systemic induction was found in pods. Herbivore-damaged leaves had a 200-fold higher release rate than pods. To some extent these findings support the OD: i) indirect defence levels were increased in response to herbivory and ii) young leaves, which are more valuable, emitted more volatiles. However, the fact that reproductive structures emitted no constitutive or very few inducible volatiles is in seeming contrast to the OD predictions. We argue that in case of volatile emission the OD can only partially explain the patterns of defence allocation due to the peculiarity that volatiles act as signals not as toxins or repellents.