Given a group-based Markov model on a tree, one can compute the vertex representation of a polytope which describes the associated toric variety. The half-space representation, however, is not easily computable. In the case of Z2 or Z2 × Z2, these polytopes have applications in the field of phylogenetics. We provide a half-space representation for the m-claw tree where G = Z2 × Z2, which corres...

The lesions of Kimura disease showed slightly high and very high intensity on T2-weighted MR, and low and intermediate intensity, respectively, on T1-weighted images. The degree of enhancement also differed between the two cases. These discrepancies may be attributable to differing degrees of fibrosis and vascular proliferation.

Kimura disease is a chronic inflammatory disorder usually affecting young adults aged between 20-40years , men are affected more commonly than women[1].It involves subcutaneous tissues and lymph nodes predominantly in the head and neck region and is characterized by angiolymphoid proliferation and eosinophilia[2]. It classically presents as a non-tender subcutaneous swelling in the head and nec...

The effective population number estimated in humans is 10,000 (Nei and Gram1984; Nei 1987; Takahata 1993 ) . This rather small number may contradict the fact that humans had been occupying vast areas in Africa and Eurasia for a long time since Homo erectus first migrated out of Africa l-2 Mya (e.g., see Lewin 1984; Fagan 1990). One possible cause is a recent bottleneck, or a sudden reduction in...