由良 文孝

Vascular endothelial cells (ECs) in angiogenesis exhibit inhomogeneous collective migration called "cell mixing", in which cells change their relative positions by overtaking each other. However, how such complex EC dynamics lead to the formation of highly ordered branching structures remains largely unknown. To uncover hidden laws of integration driving angiogenic morphogenesis, we analyzed EC behaviors in an in vitro angiogenic sprouting assay using mouse aortic explants in combination with mathematical modeling. Time-lapse imaging of sprouts extended from EC sheets around tissue explants showed directional cohesive EC movements with frequent U-turns, which often coupled with tip cell overtaking. Imaging of isolated branches deprived of basal cell sheets revealed a requirement of a constant supply of immigrating cells for ECs to branch forward. Anisotropic attractive forces between neighboring cells passing each other were likely to underlie these EC motility patterns, as evidenced by an experimentally validated mathematical model. These results suggest that cohesive movements with anisotropic cell-to-cell interactions characterize the EC motility, which may drive branch elongation depending on a constant cell supply. The present findings provide novel insights into a cell motility-based understanding of angiogenic morphogenesis.

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.

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.

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 Z(2). Moreover, a family of such linearizable cellular automata is given.

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.

We study the entanglement cost of the states in the antisymmetric space, which consists of (d - 1) d-dimensional systems. The cost is always 1092(d - 1) ebits when the state is divided into bipartite C-d circle times (C-d)(d-2). Combined with the arguments in [6], additivity of channel capacity of some quantum channels is also shown.

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

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.

We propose a box and ball system with a periodic boundary condition periodic box and ball system (pBBS). The time evolution rule of the pBBS is represented as a Boolean recurrence formula, an inverse ultradiscretization of which is shown to be equivalent to the algorithm of the calculus for the 2Nth root. The relations to the pBBS of the combinatorial R matrix of U-q' (A(N)((1))) are also discussed.

After reviewing the important roles of excitons in nonlinear optical responses, we demonstrate mutual and quantum-mechanical control of radiation field and excitons on the same footing in a microcavity. First we introduce dressed excitons as bosons interacting coherently and reversibly with a radiation mode in the microcavity. Although the vacuum Rabi splitting of the dressed exciton is the same as that of dressed atom, the emission spectrum under strong pumping shows quartet structure different from the triplet of dressed atom. Secondly, the population dynamics of dressed excitons, i.e., one-dimensional polaritons in the mesoscopic system is solved and the dominant distribution on a single mode is demonstrated above the critical pumping.