2 citations · 5 across the 6 of their papers we have counts for
7 papers
Tropical linearization and stability analysis of discrete dynamical systems at the tropical origin }
Yuki Nishida, Sennosuke Watanabe, Yoshihide Watanabe
The tropical semiring is a semiring of extended real numbers, where the operations of `max' and `+' replace the usual addition and multiplication, respectively. Difference equation…
Independence and orthogonality of algebraic eigenvectors over the max-plus algebra
Yuki Nishida, Sennosuke Watanabe, Yoshihide Watanabe
The max-plus algebra is a semiring with the two operations: addition and multiplication . Roots of the…
A variant of the discrete Burgers equation derived from the correlated random walk and its ultradiscretization
Akiko Fukuda, Etsuo Segawa, Sennosuke Watanabe
In this paper, we show that a variant of the discrete Burgers equation can be obtained through the Cole--Hopf transformation to a generalized discrete diffusion equation correspond…
-VFCA: -state Vector-valued Fuzzy Cellular Automata
Yuki Nishida, Sennosuke Watanabe, Akiko Fukuda +1
Elementary fuzzy Cellular Automata (CA) are known as continuous counterpart of elementary CA, which are 2-state CA, via the polynomial representation of local rules. In this paper,…
A walk on max-plus algebra
Sennosuke Watanabe, Akiko Fukuda, Etsuo Segawa +1
Max-plus algebra is a kind of idempotent semiring over with two operations and .In this paper, we intr…
Network Simplex Algorithm associated with the Maximum Flow Problem
Sennosuke Watanabe, Hodaka Tanaka, Yoshihide Watanabe
In the present paper, we apply the network simplex algorithm for solving the minimum cost flow problem, to the maximum flow problem. Then we prove that the cycling phenomenon which…
Two characteristic polynomials corresponding to graphical networks over min-plus algebra
Sennosuke Watanabe, Yuto Tozuka, Yoshihide Watanabe +2
In this paper, we investigate characteristic polynomials of matrices in min-plus algebra. Eigenvalues of min-plus matrices are known to be the minimum roots of the characteristic p…