Sequence and analysis of chromosome 1 of the plant Arabidopsis thaliana

The genome of the flowering plant Arabidopsis thaliana has five chromosomes. Here we report the sequence of the largest, chromosome 1, in two contigs of around 14.2 and 14.6 megabases. The contigs extend from the telomeres to the centromeric borders, regions rich in transposons, retrotransposons and repetitive elements such as the 180-base-pair repeat. The chromosome represents 25% of the genome and contains about 6,850 open reading frames, 236 transfer RNAs (tRNAs) and 12 small nuclear RNAs. There are two clusters of tRNA genes at different places on the chromosome. One consists of 27 tRNA(Pro) genes and the other contains 27 tandem repeats of tRNA(Tyr)-tRNA(Tyr)-tRNA(Ser) genes. Chromosome 1 contains about 300 gene families with clustered duplications. There are also many repeat elements, representing 8% of the sequence.     

Minimum sum of diameters clustering

The problem of determining a partition of a given set ofN entities intoM clusters such that the sum of the diameters of these clusters is minimum has been studied by Brucker (1978). He proved that it is NP-complete forM3 and mentioned that its complexity was unknown forM=2. We provide anO(N ³ logN) algorithm for this latter case. Moreover, we show that determining a partition into two clusters which minimizes any given function of the diameters can be done inO(N ⁵) time.Acknowledgments: This research was supported by the Air Force Office of Scientific Research Grant AFOSR 0271 to Rutgers University. We are grateful to Yves Crama for several insightful remarks and to an anonymous referee for detailed comments.     

Maximum sum-of-splits clustering

ConsiderN entities to be classified, and a matrix of dissimilarities between pairs of them. The split of a cluster is the smallest dissimilarity between an entity of this cluster and an entity outside it. The single-linkage algorithm provides partitions intoM clusters for which the smallest split is maximum. We study here the average split of the clusters or, equivalently, the sum of splits. A (N ²) algorithm is provided to determine maximum sum-of-splits partitions intoM clusters for allM betweenN – 1 and 2, using the dual graph of the single-linkage dendrogram.

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Résumé SoientN objets à classifier et une matrice de dissimilarit és entre paires de ces objets. L'écart d'une classe est la plus petite dissimilarité entre un objet de cette classe et un objet en dehors d'elle. L'algorithme du lien simple fournit des partitions enM classes dont le plus petit écart est maximum. On étudie l'écart moyen des classes, ou, ce qui est équivalent, la somme des écarts. On propose un algorithme en (N ²) pour déterminer des partitions enM classes dont la somme des écarts est maximum pourM allant deN – 1 à 2, basé sur le graphe dual du dendrogramme de la méthode du lien simple.

     

Espaliers: A generalization of dendrograms

Dendrograms are widely used to represent graphically the clusters and partitions obtained with hierarchical clustering schemes. Espaliers are generalized dendrograms in which the length of horizontal lines is used in addition to their level in order to display the values of two characteristics of each cluster (e.g., the split and the diameter) instead of only one. An algorithm is first presented to transform a dendrogram into an espalier without rotation of any part of the former. This is done by stretching some of the horizontal lines to obtain a diagram with vertical and horizontal lines only, the cutting off by diagonal lines the parts of the horizontal lines exceeding their prescribed length. The problem of finding if, allowing rotations, no diagonal lines are needed is solved by anO(N ²) algorithm whereN is the number of entities to be classified. This algorithm is the generalized to obtain espaliers with minimum width and, possibly, some diagonal lines.Work of the first and second authors has been supported by FCAR (Fonds pour la Formation de Chercheurs et l'Aide à la Recherche) grant 92EQ1048, and grant N00014-92-J-1194 from the Office of Naval Research. Work of the first author has also been supported by NSERC (Natural Sciences and Engineering Research Council of Canada) grant to École des Hautes Études Commerciales, Montréal and by NSERC grant GP0105574. Work of the second author has been supported by NSERC grant GP0036426, by FCAR grant 90NC0305, and by an NSF Professorship for Women in Science at Princeton University from September 1990 until December 1991. Work of the third author was done in part during a visit to GERAD, Montréal.     

Efficient algorithms for divisive hierarchical clustering with the diameter criterion

Divisive hierarchical clustering algorithms with the diameter criterion proceed by recursively selecting the cluster with largest diameter and partitioning it into two clusters whose largest diameter is smallest possible. We provide two such algorithms with complexitiesO( N ²) andO(N ²logN) respectively, where denotes the maximum number of clusters in a partition andN the number of entities to be clustered. The former algorithm, an efficient implementation of an algorithm of Hubert, allows to find all partitions into at most clusters and is inO(N ²) for fixed . Moreover, if in each partitioning the size of the largest cluster is bounded byp times the number of entities in the set to be partitioned, with 1/2<=p<1, it provides a complete hierarchy of partitionsO(N ² logN) time. The latter algorithm, a refinement of an algorithm of Rao allows to build a complete hierarchy of partitions inO(N ² logN) time without any restriction. Comparative computational experiments with both algorithms and with an agglomerative hierarchical algorithm of Benzécri are reported.

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Résumé Les algorithmes de classification hiérarchique descendante utilisant le critère du diamètre, sélectionnent récursivement la classe de plus grand diamètre et la partitionnent en deux classes, dont le plus grand diamètre est le plus, petit possible. Nous proposons deux tels algorithmes, avec des complexités enO ( N²) etO(N ² logN) respectivement, où désigne le nombre maximum de classes d'une partition etN le nombre d'objets à classifier. Le premier algorithme, une implantation d'un algorithme de Hubert, permet de construire des partitions avec au plus classes et est enO(N ²) pour fixé. De plus, si dans chaque bipartition le nombre d'objets de la plus grande classe, est borné parp fois le nombre d'objets de l'ensemble à partitionner, où 1/2≤p<1, cet algorithme permet de construire une hiérarchie complète de partitions en tempsO(N ² logN). Le second algorithme, un raffinement d'un algorithme de Rao, permet de construire une hiérarchie complète de partitions en tempsO(N ² logN) sans aucune restriction On présente également des résultats de calcul comparatifs pour les deux algorithmes et pour l'algorithme de classification hiérarchique ascendante de Benzécri.

     

Does ammonium uptake influence xylem sap composition inPhaseolus vulgaris L. andGlycine max (L.) Merill?

The question of whether ammonium uptake influences the occurrence of ureides in legumes has been addressed in this study by investigating threeP. vulgaris genotypes as well as one cultivar ofGlycine max. All plants were raised in sand culture during the dry season in northern Thailand and irrigated daily with nitrogen-free nutrient solution, or the same solution containing 12 mol m^–3 nitrogen in the form of (NH₄)₂SO₄ or KNO₃, each treatment consisting of different proportions of either compound. Regression analyses of xylem sap composition relative to ammonium vs. nitrate supply of plants harvested at V4, R1 and R6 indicated close positive correlations of xylem amino nitrogen content and negative correlations with xylem nitrate content and ammonium supply. Statistically significant correlations between relative xylem ureide content and ammonium availability could be established for theP. vulgaris cultivar Brilliant up to stage R1, but not for the other plants investigated. It was concluded that at least for some genotypes of common bean a relationship exists between ureide production and ammonium uptake by the root system. Since the extent to which ureide production is stimulated remains quite small, its relevance to the xylem solute technique for measurement of N₂ fixation may be limited. Nevertheless, due to the possibility of large genotypic differences in the impact of ammonium on ureide production, this factor must be considered in calculations if N₂ fixation is to be determined in soils containing significant amounts of ammonium, e.g. in paddy fields.     

Resequencing of 200 human exomes identifies an excess of low-frequency non-synonymous coding variants

Targeted capture combined with massively parallel exome sequencing is a promising approach to identify genetic variants implicated in human traits. We report exome sequencing of 200 individuals from Denmark with targeted capture of 18,654 coding genes and sequence coverage of each individual exome at an average depth of 12-fold. On average, about 95% of the target regions were covered by at least one read. We identified 121,870 SNPs in the sample population, including 53,081 coding SNPs (cSNPs). Using a statistical method for SNP calling and an estimation of allelic frequencies based on our population data, we derived the allele frequency spectrum of cSNPs with a minor allele frequency greater than 0.02. We identified a 1.8-fold excess of deleterious, non-syonomyous cSNPs over synonymous cSNPs in the low-frequency range (minor allele frequencies between 2% and 5%). This excess was more pronounced for X-linked SNPs, suggesting that deleterious substitutions are primarily recessive.