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We study variants of Gale-Robinson sequences, as motivated by cluster algebras with principal coefficients. For such cases, we give combinatorial interpretations of cluster variables using brane tilings, as from the physics literature.

The ascomycetous fungus Taphrina wiesneri, the pathogen of cherry witches` broom, is highly pathogenic to Prunus yedoensis, the most widely planted cherry trees in Korea as park and roadside trees. A collection of 13 strains of the pathogen in Korea and Japan was characterized by 18S rDNA gene sequence and restriction fragment length polymorphism (RFLP) analysis. In cluster analysis based on 18S rDNA gene sequence the strains were divided into 2 clusters. In RFLP analysis of the rDNA-IGS region using HhaI, the strains were separated into four patterns, B, C, D and G, of which pattern G was new.