Fast algorithms for hard graph problems: Bidimensionality, minors, and local treewidth

Abstract. This paper surveys the theory of bidimensional graph problems. We summarize the known combinatorial and algorithmic results of this theory, the foundational Graph Minor results on which this theory is based, and the remaining open problems.

Photosynthesis on individual leaves of sugar beet (Beta vulgaris) during the ontogeny at variable water regimes

It is well known that the extent of yield reduction depends not only on the severity of water stress but also on the stage of plant development. Assessing photosynthetic response of individual leaves to water deficit during the ontogeny may, therefore, offer a clue to better understand the whole plant behaviour. This research aimed at investigating the influence of early and late water stress on net photosynthesis (Pn), carbon-isotope discrimination and other related traits on individual leaves during ontogeny. Sugar beet plants were grown in rain-sheltered soil columns of relevant volume (300 L), subdivided into well-watered (WW); early (S1) and late (S2) stress. In general, water stress significantly reduced leaf lifespan and Pn. Relieving the stress at about one-third and two thirds of potential leaf life substantially restored Pn at the levels of WW. Stressing a previously WW leaf brought about a comparatively heavier loss than stressing a leaf since the beginning. As for leaves at different phenological times, the early leaves had higher initial photosynthetic peaks but steeper falls during their lives. An insight into the relationships between Pn and substomatal CO2 concentration (Ci) shows that in mature leaves the photosynthetic restoration following stress relief did not entail a full recovery of the electron transport rate, the parameter most severely affected by the stress. The partial reversibility of the effects of water deficiency, associated to the anticipated leaf senescence and to the natural slow-down of net assimilation during leaf life, may be seen as a key factor in predicting to what extent the plant can tolerate drought and the damages caused by water stress