Fumitaka Yura

A two-dimensional mathematical model for dynamics of endothelial cells in angiogenesis is investigated. Angiogenesis is a morphogenic process in which new blood vessels emerge from an existing vascular network. Recently a one-dimensional discrete dynamical model has been proposed to reproduce elongation, bifurcation, and cell motility such as cell-mixing during angiogenesis on the assumption of a simple two-body interaction between endothelial cells. The present model is its two-dimensional extension, where endothelial cells are represented as the ellipses with the two-body interactions: repulsive interaction due to excluded volume effect, attractive interaction through pseudopodia and rotation by contact. We show that the oblateness of ellipses and the magnitude of contact rotation significantly affect the shape of created vascular patterns and elongation of branches.

Abstract. We investigate a simple mathematical model for angiogenesis. From recent time-lapse imaging experiments on the dynamics of endothelial cells (ECs) in angiogenesis, we suppose that elongation and bifurcation of neogenetic vessel is determined by only the density of ECs near the tip, and introduce a model described by nonlinear simultaneous differential equations. We also incorporate proliferation of ECs and activation factor such as VEGF and show the exact solutions to that model and numerical simulations.

In this paper, we prove the one-soliton solutions to the solitonic dynamical system over finite fields that may be regarded as an analogue of the box-ball systems. It turns out that the one-soliton solution has a nested structure similar to fractals, and as far as we know such a system seems to be novel. Furthermore, in spite of such a complex internal structure, numerical simulations show stable propagations before and after collisions among multiple solitons with preserving their patterns.

<p>ALife研究などで様々な創発現象を創り出すことに成功しているが，これらは意味のある現象の創発を研究者が観測により採上げて来たものである．生命システムは細胞の創発の後，これを要素としてより大きな個体の創発に成功している．複数段の創発を行うシステムの構築のためには第一段の創発を，人手を介さずに固定できる仕組みが必要である．そのドメインとしてフラクタルネットワークを使う試みについて現状と展望を述べる．</p>

The box-ball system (BBS) is an ultradiscrete system that is studied extensively. From the method and knowledge based on BBS, we define and consider novel analogs of BBS over finite fields.

This paper is devoted to a numerical simulation of a nonlinear ordinary differential equation with periodic coefficients. The equation is one of equations in the parametrically excited systems and is a model for the neutral inversion in electric transmission lines. A contribution of periodic oscillations caused by bifurcations of periodic solutions to dissipation is discussed and we show continuous bounded components are more dominant than impulse conponents in dissipative energy.

In this paper, we analyze the quantum counting under the decoherence, which<br /> can find the number of solutions satisfying a given oracle. We investigate<br /> probability distributions related to the first order term of the error rate on<br /> the quantum counting with the depolarizing channel. We also implement two<br /> circuits for the quantum counting -- the ascending-order circuit and the<br /> descending-order circuit -- by reversing ordering of application of<br /> controlled-Grover operations. By theoretical and numerical calculations for<br /> probability distributions, we reveal the difference of probability<br /> distributions on two circuits in the presence of decoherence and show that the<br /> ascending-order circuit is more robust against the decoherence than the<br /> descending-order circuit. This property of the robustness is applicable to the<br /> phase estimation such as the factoring.

We implement the quantum order-finding circuit for integer factorizing introduced by Beauregard and the existing ones on Quantum Computer Simulation System (QCSS), and do simulation on the scalable distributed-memory parallel computer. The quantum circuit by Beauregard uses 2L+3 qubits to factorize an arbitrary L-bit number. By using this circuit we can implement the whole quantum circuit on the simulator. On this environment we confirm that we can factorize up to 12-bit numbers. In addition, we examine effect of parallelization and investigate the robustness of the circuits for decoherence and operational errors. Moreover, we discuss from the experimental results the applicability of approximate QFT (AQFT) to Beauregard&#039;s circuit.

It is important to calculate numerical integrals in science and engineering. There is a quantum summation algorithm to calculate these fast on a quantum computer. This algorithm is exponentially faster than the best known classical deterministic algorithms and quadratically faster than the best known classical probabilistic algorithms. Thus, there have been many studies of the quantum summation algorithm. However, these studies have focused on analyzing the complexity of the algorithm and no one has investigated the actual behaviors of this algorithm by a quantum computational simulator. In this paper, we estimated the robustness for decoherence errors of this quantum summation circuits. Moreover, we constructed quantum summation circuits robust for decoherence error by improving circuits, showed the difference of the behaviors in the presence of decoherence errors between on the existing circuits and on the improved circuits, and evaluated the usefulness of our improved quantum summation circuits.

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.