Fumitaka Yura

Fundamental cycle of a periodic box?ball system

We investigate a box–ball system with periodic boundary conditions. Since the box–ball system is a deterministic dynamical system that takes only a finite number of states, it will exhibit periodic motion. We determine its fundamental cycle for a given initial state.

Entanglement cost of antisymmetric states and additivity of capacity of some quantum channels

We study the entanglement cost of the states in the antisymmetric space, which consists of (d − 1) d-dimensional systems. The cost is always log2(d − 1) ebits when the state is divided into bipartite . Combined with the arguments in [6], additivity of channel capacity of some quantum channels is also shown.

On reversibility of cellular automata with periodic boundary conditions

Reversibility of one-dimensional cellular automata with periodic boundary conditions is discussed. It is shown that there exist exactly 16 reversible elementary cellular automaton rules for infinitely many cell sizes by means of a correspondence between elementary cellular automaton and the de Bruijn graph. In addition, a sufficient condition for reversibility of three-valued and two-neighbour cellular automaton is given.

Entanglement cost of three-level antisymmetric states

We show that the entanglement cost of the three-dimensional antisymmetric states is one ebit.

Linearizable cellular automata

The initial value problem for a class of reversible elementary cellular automata with periodic boundaries is reduced to an initial-boundary value problem for a class of linear systems on a finite commutative ring . Moreover, a family of such linearizable cellular automata is given.

Solitons with a nested structure over finite fields

We propose a solitonic dynamical system over finite fields that may be regarded as an analogue of the box–ball systems. The one-soliton solutions of the system, which have nested structures similar to fractals, are also proved. The solitonic system in this paper is described by polynomials, which seems to be novel. Furthermore, in spite of such complex internal structures, numerical simulations exhibit stable propagations before and after collisions among multiple solitons, preserving their patterns.

A Discrete Mathematical Model for Angiogenesis

Angiogenesis is the morphogenetic phenomenon in which new blood vessels emerge from an existing vascular network and configure a new network. In consideration of recent experiments with time-lapse fluorescent imaging in which vascular endothelial cells exhibit cell-mixing behavior even at a tip of newly generated vascular networks, we propose a discrete mathematical model for the dynamics of vascular endothelial cells in angiogenic morphogenesis. The model incorporates two-body interaction between endothelial cells which induces cell-mixing behavior and length of the generating blood vessel shows temporal power-law scaling behavior. Numerical simulation of the model successfully reproduces elongation and bifurcation of blood vessels in the early stage of angiogenesis.