96 research outputs found

    The strong thirteen spheres problem

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    The thirteen spheres problem is asking if 13 equal size nonoverlapping spheres in three dimensions can touch another sphere of the same size. This problem was the subject of the famous discussion between Isaac Newton and David Gregory in 1694. The problem was solved by Schutte and van der Waerden only in 1953. A natural extension of this problem is the strong thirteen spheres problem (or the Tammes problem for 13 points) which asks to find an arrangement and the maximum radius of 13 equal size nonoverlapping spheres touching the unit sphere. In the paper we give a solution of this long-standing open problem in geometry. Our computer-assisted proof is based on a enumeration of the so-called irreducible graphs.Comment: Modified lemma 2, 16 pages, 12 figures. Uploaded program packag

    Genetic dissection of fruit quality traits in the octoploid cultivated strawberry highlights the role of homoeo-QTL in their control

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    Fruit quality traits are major breeding targets in the Rosaceae. Several of the major Rosaceae species are current or ancient polyploids. To dissect the inheritance of fruit quality traits in polyploid fleshy fruit species, we used a cultivated strawberry segregating population comprising a 213 full-sibling F1 progeny from a cross between the variety ‘Capitola’ and the genotype ‘CF1116’. We previously developed the most comprehensive strawberry linkage map, which displays seven homoeology groups (HG), including each four homoeology linkage groups (Genetics 179:2045–2060, 2008). The map was used to identify quantitative trait loci (QTL) for 19 fruit traits related to fruit development, texture, colour, anthocyanin, sugar and organic acid contents. Analyses were carried out over two or three successive years on field-grown plants. QTL were detected for all the analysed traits. Because strawberry is an octopolyploid species, QTL controlling a given trait and located at orthologous positions on different homoeologous linkage groups within one HG are considered as homoeo-QTL. We found that, for various traits, about one-fourth of QTL were putative homoeo-QTL and were localised on two linkage groups. Several homoeo-QTL could be detected the same year, suggesting that several copies of the gene underlying the QTL are functional. The detection of some other homoeo-QTL was year-dependent. Therefore, changes in allelic expression could take place in response to environmental changes. We believe that, in strawberry as in other polyploid fruit species, the mechanisms unravelled in the present study may play a crucial role in the variations of fruit quality

    New applications of statistical tools in plant pathology

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    Citation: Garrett, K., Madden, L., Hughes, G., and Pfender, W. (2007). New Applications of Statistical Tools in Plant Pathology. Phytopathology, 94(9), 999-1003. https://doi.org/10.1094/PHYTO.2004.94.9.999The series of papers introduced by this one address a range of statistical applications in plant pathology, including survival analysis, nonparametric analysis of disease associations, multivariate analyses, neural networks, meta-analysis, and Bayesian statistics. Here we present an overview of additional applications of statistics in plant pathology. An analysis of variance based on the assumption of normally distributed responses with equal variances has been a standard approach in biology for decades. Advances in statistical theory and computation now make it convenient to appropriately deal with discrete responses using generalized linear models, with adjustments for overdispersion as needed. New nonparametric approaches are available for analysis of ordinal data such as disease ratings. Many experiments require the use of models with fixed and random effects for data analysis. New or expanded computing packages, such as SAS PROC MIXED, coupled with extensive advances in statistical theory, allow for appropriate analyses of normally distributed data using linear mixed models, and discrete data with generalized linear mixed models. Decision theory offers a framework in plant pathology for contexts such as the decision about whether to apply or withhold a treatment. Model selection can be performed using Akaike's information criterion. Plant pathologists studying pathogens at the population level have traditionally been the main consumers of statistical approaches in plant pathology, but new technologies such as microarrays supply estimates of gene expression for thousands of genes simultaneously and present challenges for statistical analysis. Applications to the study of the landscape of the field and of the genome share the risk of pseudoreplication, the problem of determining the appropriate scale of the experimental unit and of obtaining sufficient replication at that scale
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