Simple assembly graphs characterize the process of DNA recombination in living cells. The number, number distinct Hamiltonian sets polygonal paths, one-sided and middle additivity a graph are important characteristics such graphs. This paper investigates transformations simple that allow one to increase their numbers or obtain additive Also minimum loops must be added edges tangled cord order i...

Given any sequence τ = (τn)n≥1 of positive real numbers and any set E of complex sequences, we write Eτ for the set of all sequences x = (xn)n≥1 such that x/a = (xn/an)n≥1 ∈ E. We define the sets Wτ = (w∞)τ and W 0 τ = (w0)τ , where w∞ is the set of all sequences such that supn (n −1∑n m=1 |xm|) < ∞, and w0 is the set of all sequences such that limn→∞ (n−1 ∑n m=1 |xm|) = 0. Then we explicitly c...

Abstract This paper characterizes a class of regular para-Hermitian transfer matrices and then studies the J-spectral factorization of this class using similarity transformations. A transfer matrix Λ in this class admits a J-spectral factorization if and only if there exists a common nonsingular matrix to similarly transform the A-matrices of Λ and Λ, resp., into 2 × 2 lower (upper, resp.) tria...

We introduce a class of transformations of finite data words generalizing the well-known class of regular finite string transformations described by MSO-definable transductions of finite strings. These transformations map input words to output words whereas our transformations handle data words where each position has a letter from a finite alphabet and a data value. Each data value appearing i...