On the Pierce-Birkhoff Conjecture

International audienceThis paper represents a step in our program towards the proof of the Pierce--Birkhoff conjecture. In the nineteen eighties J. Madden proved that the Pierce-Birkhoff conjecture for a ring A$is equivalent to a statement about an arbitrary pair of points$\alpha,\beta\in\sper\ A$and their separating ideal$$; we refer to this statement as the Local Pierce-Birkhoff conjecture at$\alpha,\beta$. In this paper, for each pair$(\alpha,\beta)$with$ht()=\dim A$, we define a natural number, called complexity of$(\alpha,\beta)$. Complexity 0 corresponds to the case when one of the points$\alpha,\beta$is monomial; this case was already settled in all dimensions in a preceding paper. Here we introduce a new conjecture, called the Strong Connectedness conjecture, and prove that the strong connectedness conjecture in dimension n-1 implies the connectedness conjecture in dimension n in the case when$ht()$is less than n-1. We prove the Strong Connectedness conjecture in dimension 2, which gives the Connectedness and the Pierce--Birkhoff conjectures in any dimension in the case when$ht()$less than 2. Finally, we prove the Connectedness (and hence also the Pierce--Birkhoff) conjecture in the case when dimension of A is equal to$ht()=3$, the pair$(\alpha,\beta)$is of complexity 1 and$A$ is excellent with residue field the field of real numbers

Transcription Profile Analysis Reveals That Zygotic Division Results in Uneven Distribution of Specific Transcripts in Apical/Basal Cells of Tobacco

BACKGROUND: Asymmetric zygotic division in higher plants results in the formation of an apical cell and a basal cell. These two embryonic cells possess distinct morphologies and cell developmental fates. It has been proposed that unevenly distributed cell fate determinants and/or distinct cell transcript profiles may be the underlying reason for their distinct fates. However, neither of these hypotheses has convincing support due to technical limitations. METHODOLOGY/PRINCIPAL FINDINGS: Using laser-controlled microdissection, we isolated apical and basal cells and constructed cell type-specific cDNA libraries. Transcript profile analysis revealed difference in transcript composition. PCR and qPCR analysis confirmed that transcripts of selected embryogenesis-related genes were cell-type preferentially distributed. Some of the transcripts that existed in zygotes were found distinctly existed in apical or basal cells. The cell type specific de novo transcription was also found after zygotic cell division. CONCLUSIONS/SIGNIFICANCE: Thus, we found that the transcript diversity occurs between apical and basal cells. Asymmetric zygotic division results in the uneven distribution of some embryogenesis related transcripts in the two-celled proembryos, suggesting that a differential distribution of some specific transcripts in the apical or basal cells may involve in guiding the two cell types to different developmental destinies

Spatial and Temporal Trends of Global Pollination Benefit

Pollination is a well-studied and at the same time a threatened ecosystem service. A significant part of global crop production depends on or profits from pollination by animals. Using detailed information on global crop yields of 60 pollination dependent or profiting crops, we provide a map of global pollination benefits on a 5′ by 5′ latitude-longitude grid. The current spatial pattern of pollination benefits is only partly correlated with climate variables and the distribution of cropland. The resulting map of pollination benefits identifies hot spots of pollination benefits at sufficient detail to guide political decisions on where to protect pollination services by investing in structural diversity of land use. Additionally, we investigated the vulnerability of the national economies with respect to potential decline of pollination services as the portion of the (agricultural) economy depending on pollination benefits. While the general dependency of the agricultural economy on pollination seems to be stable from 1993 until 2009, we see increases in producer prices for pollination dependent crops, which we interpret as an early warning signal for a conflict between pollination service and other land uses at the global scale. Our spatially explicit analysis of global pollination benefit points to hot spots for the generation of pollination benefits and can serve as a base for further planning of land use, protection sites and agricultural policies for maintaining pollination services

Fine root dynamics across pantropical rainforest ecosystems

Fine roots constitute a significant component of the net primary productivity (NPP) of forest ecosystems but are much less studied than above-ground NPP. Comparisons across sites and regions are also hampered by inconsistent methodologies, especially in tropical areas. Here, we present a novel dataset of fine root biomass, productivity, residence time, and allocation in tropical old-growth rainforest sites worldwide, measured using consistent methods, and examine how these variables are related to consistently determined soil and climatic characteristics. Our pantropical dataset spans intensive monitoring plots in lowland (wet, semi-deciduous, deciduous) and montane tropical forests in South America, Africa, and Southeast Asia (n=47). Large spatial variation in fine root dynamics was observed across montane and lowland forest types. In lowland forests, we found a strong positive linear relationship between fine root productivity and sand content, this relationship was even stronger when we considered the fractional allocation of total NPP to fine roots, demonstrating that understanding allocation adds explanatory power to understanding fine root productivity and total NPP. Fine root residence time was a function of multiple factors: soil sand content, soil pH, and maximum water deficit, with longest residence times in acidic, sandy, and water-stressed soils. In tropical montane forests, on the other hand, a different set of relationships prevailed, highlighting the very different nature of montane and lowland forest biomes. Root productivity was a strong positive linear function of mean annual temperature, root residence time was a strong positive function of soil nitrogen content in montane forests, and lastly decreasing soil P content increased allocation of productivity to fine roots. In contrast to the lowlands, environmental conditions were a better predictor for fine root productivity than for fractional allocation of total NPP to fine roots, suggesting that root productivity is a particularly strong driver of NPP allocation in tropical mountain regions.Output Status: Forthcoming/Available Online Additional co-authors: Christopher E. Doughty, Imma Oliveras, Darcy F. Galiano Cabrera, Liliana Durand Baca, Filio Farfán Amézquita, Javier E. Silva Espejo, Antonio C.L. da Costa, Erick Oblitas Mendoza, Carlos Alberto Quesada, Fidele Evouna Ondo, Josué Edzang Ndong, Vianet Mihindou, Natacha N’ssi Bengone, Forzia Ibrahim, Shalom D. Addo-Danso, Akwasi Duah-Gyamfi, Gloria Djaney Djagbletey, Kennedy Owusu-Afriyie, Lucy Amissah, Armel T. Mbou, Toby R. Marthews, Daniel B. Metcalfe, Luiz E.O. Aragão, Ben H. Marimon-Junior, Beatriz S. Marimon, Noreen Majalap, Stephen Adu-Bredu, Miles Silman, Robert M. Ewers, Patrick Meir, Yadvinder Malh