Invariant subsets of scattered trees. An application to the tree alternative property of Bonato and Tardif

A tree is scattered if no subdivision of the complete binary tree is a subtree. Building on results of Halin, Polat and Sabidussi, we identify four types of subtrees of a scattered tree and a function of the tree into the integers at least one of which is preserved by every embedding. With this result and a result of Tyomkyn, we prove that the tree alternative property conjecture of Bonato and Tardif holds for scattered trees and a conjecture of Tyomkin holds for locally finite scattered trees

Indivisible ultrametric spaces

A metric space is indivisible if for any partition of it into finitely many pieces one piece contains an isometric copy of the whole space. Continuing our investigation of indivisible metric spaces, we show that a countable ultrametric space embeds isometrically into an indivisible ultrametric metric space if and only if it does not contain a strictly increasing sequence of balls.Comment: 21 page

Monosaccharide transporters in plants: structure, function and physiology

AbstractMonosaccharide transport across the plant plasma membrane plays an important role both in lower and higher plants. Algae can switch between phototrophic and heterotrophic growth and utilize organic compounds, such as monosaccharides as additional or sole carbon sources. Higher plants represent complex mosaics of phototrophic and heterotrophic cells and tissues and depend on the activity of numerous transporters for the correct partitioning of assimilated carbon between their different organs. The cloning of monosaccharide transporter genes and cDNAs identified closely related integral membrane proteins with 12 transmembrane helices exhibiting significant homology to monosaccharide transporters from yeast, bacteria and mammals. Structural analyses performed with several members of this transporter superfamily identified protein domains or even specific amino acid residues putatively involved in substrate binding and specificity. Expression of plant monosaccharide transporter cDNAs in yeast cells and frog oocytes allowed the characterization of substrate specificities and kinetic parameters. Immunohistochemical studies, in situ hybridization analyses and studies performed with transgenic plants expressing reporter genes under the control of promoters from specific monosaccharide transporter genes allowed the localization of the transport proteins or revealed the sites of gene expression. Higher plants possess large families of monosaccharide transporter genes and each of the encoded proteins seems to have a specific function often confined to a limited number of cells and regulated both developmentally and by environmental stimuli