QTL mapping of grain appearance quality traits and grain weight using a recombinant inbred population in rice(Oryza sativa L.)

supported by a grant from the National High-Tech R＆D Program of China （2014AA10A603, 2014AA10A604）;a grant from the Youth Foundation in Sichuan, China （2011JTD0022）;the special fund for China Agricultural Research System （CARS-01-08）;the Provincial Specialized Funds for Innovation Ability Promotion in Sichuan, China （2013GXJS005）

Tilting objects on tubular weighted projective lines: A cluster tilting approach

Using the cluster tilting theory,we investigate the tilting objects in the stable category of vector bundles on a weighted projective line of weight type(2,2,2,2).More precisely,a tilting object consisting of rank-two bundles is constructed via the cluster tilting mutation.Moreover,the cluster tilting approach also provides a new method to classify the endomorphism algebras of the tilting objects in the category of coherent sheaves and the associated bounded derived category.

Prüfer Sheaves and Generic Sheaves Over the Weighted Projective Lines and Elliptic Curves

In the present paper, we introduce the concepts of Prüfer sheaves and adic sheaves over a weighted projective line of genus one or an elliptic curve, show that Prüfer sheaves and adic sheaves can characterize the category of coherent sheaves. Moreover, we describe the relationship between Prüfer sheaves and generic sheaves, and provide two methods to construct generic sheaves by using coherent sheaves and Prüfer sheaves.

Tilting sheaves for weighted projective lines of weight type （p）

We give a complete classification of tilting sheaves over weighted projective lines of weight type （p）.

Classification of tilting bundles over a weighted projective line of type （2, 3, 3）

We give a complete classification of tilting bundles over a weighted projective line of type （2, 3, 3）. This yields another realization of the tame concealed algebras of type E6.

Interpreting the vulnerability of power systems in cascading failures using multi-graph convolutional networks

Analyzing the vulnerability of power systems in cascading failures is generally regarded as a challenging problem. Although existing studies can extract some critical rules, they fail to capture the complex subtleties under different operational conditions. In recent years, several deep learning methods have been applied to address this issue. However, most of the existing deep learning methods consider only the grid topology of a power system in terms of topological connections, but do not encompass a power system’s spatial information such as the electrical distance to increase the accuracy in the process of graph convolution. In this paper, we construct a novel power-weighted line graph that uses power system topology and spatial information to optimize the edge weight assignment of the line graph. Then we propose a multi-graph convolutional network(MGCN) based on a graph classification task, which preserves a power system’s spatial correlations and captures the relationships among physical components. Our model can better handle the problem with power systems that have parallel lines, where our method can maintain desirable accuracy in modeling systems with these extra topology features. To increase the interpretability of the model, we present the MGCN using layer-wise relevance propagation and quantify the contributing factors of model classification.