A classification of plane and planar 2-trees

We present new functional equations for the species of plane and of planar (in the sense of Harary and Palmer, 1973) 2-trees and some associated pointed species. We then deduce the explicit molecular expansion of these species, i.e a classification of their structures according to their stabilizers. There result explicit formulas in terms of Catalan numbers for their associated generating series, including the asymmetry index series. This work is closely related to the enumeration of polyene hydrocarbons of molecular formula C_nH_n+2.Comment: 26 pages, 14 figure

Resistance to fungicides and streptomycin in Phytophthora parasitica : genetic determinism and use in hybrid determination

Progeny of #Phytophthora parasitica$ derived from the pairings between metalaxyl-resistant MET.1 (A2) carrying homozygous dominant resistance and S1 (A1) wild-type consisted of selfs from each parent and hybrids carrying heterozygous dominant resistance. Similar results were obtained when dimetomorph-resistant DT.1 (A1) carrying homozygous dominant resistance was paired with wild-type S2 (A2). Progeny from the pairing between homozygous Str resistant (A1) to streptomycin and A2 resistant to metalaxyl consisted of selfs and hybrids resistant to either streptomycin or metalaxyl but not both. These results suggest that streptomycin-resistance is cytoplasmic. Progeny from the pairing between homozygous metalaxyl-resistant MET.1 (A1) and homozygous Str (A2) resistant to streptomycin consisted of 28 selfs from A1, 32 selfs form A2, 2 hybrids resulting from the union of A1 oogonium with an A2 antheridium. Progeny from the pairing between homozygous dimetomorph and streptomycin-resistant DT.1 (A1) with wild-type S2 (A2) consisted of 22 selfs A1, 14 selfs A2 and 12 hybrids, two of them resulted from the union A2 oogonium with an A1 antheridium. (Résumé d'auteur

Renormalization : A number theoretical model

We analyse the Dirichlet convolution ring of arithmetic number theoretic functions. It turns out to fail to be a Hopf algebra on the diagonal, due to the lack of complete multiplicativity of the product and coproduct. A related Hopf algebra can be established, which however overcounts the diagonal. We argue that the mechanism of renormalization in quantum field theory is modelled after the same principle. Singularities hence arise as a (now continuously indexed) overcounting on the diagonals. Renormalization is given by the map from the auxiliary Hopf algebra to the weaker multiplicative structure, called Hopf gebra, rescaling the diagonals.Comment: 15 pages, extended version of talks delivered at SLC55 Bertinoro,Sep 2005, and the Bob Delbourgo QFT Fest in Hobart, Dec 200

Optoelectronic developments for remote-handled maintenance tasks in ITER

Remotely handled maintenance tools operated in the future International Thermonuclear Experimental Reactor (ITER) will face a harsh radiation environment, with total dose level requirements of several MGy. Optical fiber data communication has been considered as an alternative to conventional electronic transmission between the control room and remote handled maintenance equipment, mainly owing to its insentivity to electro-magnetic interference and to its wavelength encoded multiplexing capabilities. In this paper we summarise main results obtained at SCK•CEN over the past years towards the development of radiation tolerant fibre-optic communication links and report on the radiation tolerance of various individual optical components such as optical fibres, laser diodes and photodetectors, as well as their associated electronic driver circuits

Mountain trail formation and the active walker model

We extend the active walker model to address the formation of paths on gradients, which have been observed to have a zigzag form. Our extension includes a new rule which prohibits direct descent or ascent on steep inclines, simulating aversion to falling. Further augmentation of the model stops walkers from changing direction very rapidly as that would likely lead to a fall. The extended model predicts paths with qualitatively similar forms to the observed trails, but only if the terms suppressing sudden direction changes are included. The need to include terms into the model that stop rapid direction change when simulating mountain trails indicates that a similar rule should also be included in the standard active walker model.Comment: Introduction improved. Analysis of discretization errors added. Calculations from alternative scheme include

Dimethomorph and metalaxyl sensitivity in somatic hybrids of Phytophthora parasitica obtained by protoplast fusion

Protoplasts were successfully isolated from wild-type and mutant strains of #Phytophthora nicotianae var. #parasitica using Novozym 234. Putative somatic hybrids were recovered following protoplast fusions from the first time to dimethomorph resistant strain P 310 (Dim r) or metalaxyl P 26 (Met r) by selection on agar amended with dimethomorph and metalaxyl. Fusion products from this cross were resistant to dimethomorph and metalaxyl. Zoospore progeny from the fusion products retained this phenotype, suggesting that nuclear fusion had taken place. (Résumé d'auteur