Exact Solution Methods for the kk-item Quadratic Knapsack Problem

The purpose of this paper is to solve the 0-1 $k$-item quadratic knapsack problem $(kQKP)$, a problem of maximizing a quadratic function subject to two linear constraints. We propose an exact method based on semidefinite optimization. The semidefinite relaxation used in our approach includes simple rank one constraints, which can be handled efficiently by interior point methods. Furthermore, we strengthen the relaxation by polyhedral constraints and obtain approximate solutions to this semidefinite problem by applying a bundle method. We review other exact solution methods and compare all these approaches by experimenting with instances of various sizes and densities.Comment: 12 page

Local and systemic responses induced by aphids in Solanum tuberosum plants

The aphids Macrosiphum euphorbiae (Thomas) and Myzus persicae (Sulzer) (Homoptera: Aphididae) are serious pests of potato (Solanum tuberosum L.) (Solanaceae), notably in transmitting several plant viruses. Heterospecific interactions may occur between these two species as they are often seen at the same time on the same potato plant in the field. As aphid infestation is known to induce both local and systemic changes, we conducted experiments to determine the effect of previous infestation on probing behaviour and feeding-related parameters. We used the DC electrical penetration graph technique to characterize the influence of previous infestation by conspecific M. persicae or by heterospecific Ma. euphorbiae on M. persicae feeding behaviour at both local and systemic levels, i.e., on previously infested leaves and on non-previously infested leaves of infested plants, respectively. Conspecific and heterospecific infestation led to similar modification of M. persicae feeding activities. However, the effects of previous infestation occurring at the local level were opposite to those observed at the systemic level. Myzus persicae food acceptance was slightly enhanced on previously infested leaves, whereas it was inhibited on non-infested leaves of infested plants, which indicated an induced resistance mechanism. Our results advance the understanding of the mechanisms involved in aphid-host plant acceptance and colonization processes on potato plants in conspecific and heterospecific situations