Comparison tests for dendrograms: A comparative evaluation

Classifications are generally pictured in the form of hierarchical trees, also called dendrograms. A dendrogram is the graphical representation of an ultrametric (=cophenetic) matrix; so dendrograms can be compared to one another by comparing their cophenetic matrices. Three methods used in testing the correlation between matrices corresponding to dendrograms are evaluated. The three permutational procedures make use of different aspects of the information to compare dendrograms: the Mantel procedure permutes label positions only; the binary tree methods randomize the topology as well; the double-permutation procedure is based on all the information included in a dendrogram, that is: topology, label positions, and cluster heights. Theoretical and empirical investigations of these methods are carried out to evaluate their relative performance. Simulations show that the Mantel test is too conservative when applied to the comparison of dendrograms; the methods of binary tree comparisons do slightly better; only the doublepermutation test provides unbiased type I error. Les arbres utilisés pour illustrés les groupements sont généralement représentés sous la forme de classifications hiérarchiques ou dendrogrammes. Un dendrogramme représente graphiquement l’information contenue dans la matrice ultramétrique (=cophénétique) correspondant à la classification. Dès ultramétriques correspondantes. Nous comparons trois méthodes permettant d’évaluer la signification statistique du coefficient de correlation mesuré entre deux matrices ultramétriques. Ces trois tests par permutations tiennent compte d’aspects différents pour comparer des dendrogrammes: le test de Mantel permute les feuilles de l’arbre, les méthodes pour arbres binaires permutent les feuilles et la topologie, alors que la procédure à double permutation permute les feuilles, la topologie et les niveaux de fusion des dendrogrammes comparés. L’efficacité relative des trois méthodes est évaluée empiriquement et théoriquement. Nos résultats suggèrent l’utilisation préférentielle du test à double permutation pour la comparaison de dendrogrammes: le test de Mantel s’avère trop conservateur, tandis que les méthodes pour arbres binaires ne sont pas toujours adéquates.

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This work was supported by NSERC grant no. A7738 to Pierre Legendre and by a NSERC scholarship to F.-J. Lapointe.     

Newly identified loci that influence lipid concentrations and risk of coronary artery disease

To identify genetic variants influencing plasma lipid concentrations, we first used genotype imputation and meta-analysis to combine three genome-wide scans totaling 8,816 individuals and comprising 6,068 individuals specific to our study (1,874 individuals from the FUSION study of type 2 diabetes and 4,184 individuals from the SardiNIA study of aging-associated variables) and 2,758 individuals from the Diabetes Genetics Initiative, reported in a companion study in this issue. We subsequently examined promising signals in 11,569 additional individuals. Overall, we identify strongly associated variants in eleven loci previously implicated in lipid metabolism (ABCA1, the APOA5-APOA4-APOC3-APOA1 and APOE-APOC clusters, APOB, CETP, GCKR, LDLR, LPL, LIPC, LIPG and PCSK9) and also in several newly identified loci (near MVK-MMAB and GALNT2, with variants primarily associated with high-density lipoprotein (HDL) cholesterol; near SORT1, with variants primarily associated with low-density lipoprotein (LDL) cholesterol; near TRIB1, MLXIPL and ANGPTL3, with variants primarily associated with triglycerides; and a locus encompassing several genes near NCAN, with variants strongly associated with both triglycerides and LDL cholesterol). Notably, the 11 independent variants associated with increased LDL cholesterol concentrations in our study also showed increased frequency in a sample of coronary artery disease cases versus controls.     

Identification of the gene responsible for methylmalonic aciduria and homocystinuria, cblC type

Methylmalonic aciduria and homocystinuria, cblC type (OMIM 277400), is the most common inborn error of vitamin B(12) (cobalamin) metabolism, with about 250 known cases. Affected individuals have developmental, hematological, neurological, metabolic, ophthalmologic and dermatologic clinical findings. Although considered a disease of infancy or childhood, some individuals develop symptoms in adulthood. The cblC locus was mapped to chromosome region 1p by linkage analysis. We refined the chromosomal interval using homozygosity mapping and haplotype analyses and identified the MMACHC gene. In 204 individuals, 42 different mutations were identified, many consistent with a loss of function of the protein product. One mutation, 271dupA, accounted for 40% of all disease alleles. Transduction of wild-type MMACHC into immortalized cblC fibroblast cell lines corrected the cellular phenotype. Molecular modeling predicts that the C-terminal region of the gene product folds similarly to TonB, a bacterial protein involved in energy transduction for cobalamin uptake.     

Algorithms for ℓ<Subscript>1</Subscript>-Embeddability and Related Problems

Assouad has shown that a real-valued distance d = (d_ij)_{1 ≤ i < j ≤ n} is isometrically embeddable in ℓ₁space if and only if it belongs to the cut cone on n points. Determining if this condition holds is NP-complete. We use Assouad's result in a constructive column generation algorithm for ℓ₁-embeddability. The subproblem is an unconstrained 0-1 quadratic program, solved by Tabu Search and Variable Neighborhood Search heuristics as well as by an exact enumerative algorithm. Computational results are reported. Several ways to approximate a distance which is not ℓ₁-embeddable by another one which is are also studied.     

一种求解带有阻塞限制的混合流水车间的禁忌搜索算法

针对带有阻塞限制的混合流水车间调度问题,提出一种禁忌搜索算法和优先级规则相结合的方法.开发了启发式调度算法求出问题初始解,应用禁忌搜索算法对工件在第一级的排序进行优化,采用优先级规则进行其他级工件的排序.实验结果表明,该方法大大缩减了搜索空间,能够较好地解决此类调度问题.     

A high C/O ratio and weak thermal inversion in the atmosphere of exoplanet WASP-12b

The carbon-to-oxygen ratio (C/O) in a planet provides critical information about its primordial origins and subsequent evolution. A primordial C/O greater than 0.8 causes a carbide-dominated interior, as opposed to the silicate-dominated composition found on Earth; the atmosphere can also differ from those in the Solar System. The solar C/O is 0.54 (ref. 3). Here we report an analysis of dayside multi-wavelength photometry of the transiting hot-Jupiter WASP-12b (ref. 6) that reveals C/O?≥?1 in its atmosphere. The atmosphere is abundant in CO. It is depleted in water vapour and enhanced in methane, each by more than two orders of magnitude compared to a solar-abundance chemical-equilibrium model at the expected temperatures. We also find that the extremely irradiated atmosphere (T?>?2,500?K) of WASP-12b lacks a prominent thermal inversion (or stratosphere) and has very efficient day-night energy circulation. The absence of a strong thermal inversion is in stark contrast to theoretical predictions for the most highly irradiated hot-Jupiter atmospheres.     

A massive protocluster of galaxies at a redshift of z ≈ 5.3

Massive clusters of galaxies have been found that date from as early as 3.9 billion years (3.9 Gyr; z = 1.62) after the Big Bang, containing stars that formed at even earlier epochs. Cosmological simulations using the current cold dark matter model predict that these systems should descend from 'protoclusters'-early overdensities of massive galaxies that merge hierarchically to form a cluster. These protocluster regions themselves are built up hierarchically and so are expected to contain extremely massive galaxies that can be observed as luminous quasars and starbursts. Observational evidence for this picture, however, is sparse because high-redshift protoclusters are rare and difficult to observe. Here we report a protocluster region that dates from 1 Gyr (z = 5.3) after the Big Bang. This cluster of massive galaxies extends over more than 13 megaparsecs and contains a luminous quasar as well as a system rich in molecular gas. These massive galaxies place a lower limit of more than 4 × 10(11) solar masses of dark and luminous matter in this region, consistent with that expected from cosmological simulations for the earliest galaxy clusters.