Unrooted binary tree enumeration problem on unrooted binary trees is to count the number of trees with "n" labeled leaves and unlabeled internal nodes. An unrooted binary tree on "n" labeled leaves can be formed by connecting the "n"th leaf to a new node in the middle of any of the edges of an unrooted binary tree on "n" − 1 labeled leaves. There are 2"n" − 5 edges at which the "n"th node can be attached; therefore, the number of trees on "n" leaves is larger than the number of trees on "n" − 1 leaves by a factor of 2"n" −
Transfer DNA binary system Transfer DNA binary system A transfer DNA (T-DNA) binary system is a pair of plasmids consisting of a binary plasmid and a helper plasmid. The two plasmids are used together (thus "binary") to produce genetically modified plants. They are artificial vectors that have both been created from the naturally occurring Ti plasmid found in "Agrobacterium tumefaciens". The binary vector is a "shuttle vector", so-called because it is able to replicate in multiple hosts ("E. coli" and "Agrobacterium tumefaciens"). Systems in which T-DNA and vir genes are located on separate replicons are called T-DNA binary systems. T-DNA is located on the