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Blast, a disease caused by Magnaporthe oryzae, is a major constraint for rice production worldwide. Introgression of durable blast resistance genes into high-yielding rice cultivars has been considered a priority to control the disease. The blast resistance Pik locus, located on chromosome 11, contains at least six important resistance genes, but these genes have not been widely employed in resistance breeding since existing markers hardly satisfy current breeding needs due to their limited scope of application. In this study, two PCR-based markers, Pikp-Del and Pi1-In, were developed to target the specific InDel (insertion/deletion) of the Pik-p and Pi-1 genes, respectively. The two markers precisely distinguished Pik-p, Pi-1, and the K-type alleles at the Pik locus, which is a necessary element for functional genes from rice varieties. Results also revealed that only several old varieties contain the two genes, of which nearly half carry the K-type alleles. Therefore, these identified varieties can serve as new gene sources for developing blast resistant rice. The two newly developed markers will be highly useful for the use of Pik-p, Pi-1 and other resistance genes at the Pik locus in marker-assisted selection (MAS) breeding programs.

The computation of channel capacity is a classical issue in information theory. We prove that algorithms based on self-concordant functions can be used to deal with such issues, especially when constrains are included. A new algorithm to compute the channel capacity per unit cost is proposed. The same view is suited to the computation of maximum entropy. All the algorithms are of polynomial time.