Measuring centrality by a generalization of degree

Network analysis has emerged as a key technique in communication studies, economics, geography, history and sociology, among others. A fundamental issue is how to identify key nodes in a network, for which purpose a number of centrality measures have been developed. This paper proposes a new parametric family of centrality measures called generalized degree. It is based on the idea that a relationship to a more interconnected node contributes to centrality in a greater extent than a connection to a less central one. Generalized degree improves on degree by redistributing its sum over the network with the consideration of the global structure. Application of the measure is supported by a set of basic properties. A sufficient condition is given for generalized degree to be rank monotonic, excluding counter-intuitive changes in the centrality ranking after certain modifications of the network. The measure has a graph interpretation and can be calculated iteratively. Generalized degree is recommended to apply besides degree since it preserves most favorable attributes of degree, but better reflects the role of the nodes in the network and has an increased ability to distinguish between their importance.

A generalization of correlated equilibrium: A new protocol

A new correlation scheme (leading to a special equilibrium called “soft” correlated equilibrium) is introduced for finite games. After randomization over the outcome space, players have the choice either to follow the recommendation of an umpire blindly or freely choose some other action except the one suggested. This scheme can lead to Pareto-better outcomes than the simple extension introduced by [Moulin, H., Vial, J.-P., 1978. Strategically zero-sum games: the class of games whose completely mixed equilibria cannot be improved upon. International Journal of Game Theory 7, 201–221]. The informational and interpretational aspects of soft correlated equilibria are also discussed in detail. The power of the generalization is illustrated in the prisoners’s dilemma and a congestion game.

Agrobacterium vitis strains lack tumorigenic ability on in vitro grown grapevine stem segments

Grapevine stem segments were cocultivated with three different Agrobacterium tumefaciens and three different A. vitis strains. A. tumefaciens strains induced tumors at variable frequencies, while A. vitis-infected stem segments never formed crown galls. The tumorous nature of tissues grown on hormone free medium was confirmed by opine assays. Bioinformatic and PCR analysis of the virulence regions of various A. tumefaciens and A. vitis Ti plasmids showed that virH2 and virK genes are common in A. tumefaciens but they are lacking from A. vitis. Thus virH2 and virK genes may be essential for grapevine stem segment transformation, but expression of certain T-DNA genes of A. vitis may also prevent the growth of transformed cells. Our data indicate that the tumorigenic ability of A. vitis is different on intact plant and on their explants, and that the specific host association of A. vitis on grapevine is probably determined by physiological and biochemical factors (e. g., better colonizing ability) rather than by its increased tumorigenic ability. Therefore it is not reasonable to develop „helper” plasmids for grapevine transformation from A. vitis pTis, unless their avirulence on in vitro explants is determined by T-DNA gene(s). Due to the inability of A. vitis to induce tumors on grapevine stem segments, the use of in vitro explant assays cannot be reliably used to select A. vitis resistant grapevine genotypes or transgenic lines.