分子标记与QTL间连锁的检测与估计Ⅱ.利用双单倍体(DH)群体

将数量性状基因定位的“相关方法”应用到双单倍体（ＤＨ）群体，给出了适用于ＤＨ群体之标记座位（ＭＬ）与数量性状座（ＱＴＬ）间连锁测验的统计方法，并进而给出了重组值及其抽样误差估计的理论公式．     

Homothetic transformations and geometric loci: properties of triangles and quadrilaterals

In this paper, we use geometric transformations to find some interesting properties related with geometric loci. In particular, given a triangle or a cyclic quadrilateral, the locus generated by the centroid or by the orthocentre (for triangles) or by the anticentre (for cyclic quadrilaterals) when one vertex moves on the circumcircle of the figure are considered. These loci are studied in paragraphs 3 and 4. By means of the homothetic transformations some properties of triangles and quadrilaterals are found. The study of these properties can be used, with profit, in a classroom activity supported by Dynamic Geometry System.     

Geometric loci and homothetic transformations

In this paper, we use a property of the centroids to study two general types of geometric loci: one in the plane and one in the space. Then from this result, we examine in detail the case of quadrilaterals and tetrahedra and, in particular, we determine some properties of the nine-point circle of a triangle. The study of those geometric loci is carried out by means of the homothetic transformations that facilitate and make more immediate the proofs of the properties.     

Statistical Approach of Gene Set Analysis with Quantitative Trait Loci for Crop Gene Expression Studies

Genome-wide expression study is a powerful genomic technology to quantify expression dynamics of genes in a genome. In gene expression study, gene set analysis has become the first choice to gain insights into the underlying biology of diseases or stresses in plants. It also reduces the complexity of statistical analysis and enhances the explanatory power of the obtained results from the primary downstream differential expression analysis. The gene set analysis approaches are well developed in microarrays and RNA-seq gene expression data analysis. These approaches mainly focus on analyzing the gene sets with gene ontology or pathway annotation data. However, in plant biology, such methods may not establish any formal relationship between the genotypes and the phenotypes, as most of the traits are quantitative and controlled by polygenes. The existing Quantitative Trait Loci (QTL)-based gene set analysis approaches only focus on the over-representation analysis of the selected genes while ignoring their associated gene scores. Therefore, we developed an innovative statistical approach, GSQSeq, to analyze the gene sets with trait enriched QTL data. This approach considers the associated differential expression scores of genes while analyzing the gene sets. The performance of the developed method was tested on five different crop gene expression datasets obtained from real crop gene expression studies. Our analytical results indicated that the trait-specific analysis of gene sets was more robust and successful through the proposed approach than existing techniques. Further, the developed method provides a valuable platform for integrating the gene expression data with QTL data.     

On Combinatorics of Quiver Component Formulas

Buch and Fulton [9] conjectured the nonnegativity of the quiver coefficients appearing in their formula for a quiver cycle. Knutson, Miller and Shimozono [24] proved this conjecture as an immediate consequence of their component formula. We present an alternative proof of the component formula by substituting combinatorics for Gröbner degeneration [23, 24]. We relate the component formula to the work of Buch, Kresch, Tamvakis and the author [10] where a splitting formula for Schubert polynomials in terms of quiver coefficients was obtained. We prove analogues of this latter result for the type BCD-Schubert polynomials of Billey and Haiman [4]. The form of these analogues indicate that it should be interesting to pursue a geometric context that explains them.     

Genome-wide linkage analysis for ocular and nasal anthropometric traits in a Mongolian population

Anthropometric traits for eyes and nose are complex quantitative traits influenced by genetic and environmental factors. To date, there have been few reports on the contribution of genetic influence to these traits in Asian populations. The aim of this study was to determine the genetic effect and quantitative trait locus (QTL) of seven traits eyes- and nose-related anthropometric measurements in an isolated Mongolian population. Frontal and lateral photographs were obtained from 1,014 individuals (434 males and 580 females) of Mongolian origin. A total of 349 short tandem repeat markers on 22 autosomes were genotyped for each individual. Heritability estimates of the seven ocular and nasal traits, adjusted for significant covariates, ranged from 0.48 to 0.90, providing evidence for a genetic influence. Variance-component linkage analyses revealed 10 suggestive linkage signals on 5q34 (LOD=3.2), 18q12.2 (LOD=2.7), 5q15 (LOD=2.0), 9q34.2 (LOD=1.9), 5q34 (LOD=1.9), 17q22 (LOD=1.9), 13q33.3 (LOD=2.7), 1q36.22 (LOD=1.9), 4q32.1 (LOD=2.1) and 15q22.31 (LOD=2.9). Our study provides the first evidence that genetics influences nasal and ocular traits in a Mongolian population. Additional collaborative efforts will further extend our understanding of the link between genetic factors and human anthropometric traits.     

Dihedral side extensions and class groups

We present a non-abelian mirror-type principle relating the p-ranks of class groups of subfields of a dihedral field of degree 2p for an odd prime p with a limited ramification condition.     

水稻剑叶叶绿素含量相关性状的QTL分析

利用包含117个株系的籼粳杂交来源(窄叶青8号×京系17)的水稻加倍单倍体(DH)群体,对剑叶叶绿素含量相关的4个生理性状(叶绿素a、叶绿素b、叶绿素a+b和叶绿素a/b)进行数量性状基因座位(quantitativetrait loci,QTL)分析.在DH群体中,剑叶叶绿素a、叶绿素b与总叶绿素含量彼此之间均呈极显著正相关,叶绿素a/b比值与叶绿素b含量呈极显著负相关.叶绿素a、叶绿素b、总叶绿素含量及叶绿素a/b值均呈现出连续性分布,且有明显的超亲分离,表明受微效多基因控制.4个性状共检测到11个QTL位点,分布在6条染色体上,这些QTL对相应性状的贡献率介于9.2%~19.6%之间.其中控制叶绿素a含量的2个QTL位点位于第2、5染色体上;影响叶绿素b含量的4个QTL分别定位在第2、3、5、9染色体上;控制总叶绿素含量的3个QTL位于第3、5、9染色体上;影响叶绿素a/b值的2个QTL位点位于第6、11染色体上.文章系统讨论了这4个叶绿素相关性状的相互关系及其定位结果在水稻育种上的实践意义.