Topology of Boundary Surfaces in 3D Simplicial Gravity

A model of simplicial quantum gravity in three dimensions(3D) was investigated numerically based on the technique of dynamical triangulation (DT). We are concerned with the genus of surfaces appearing on boundaries (i.e., sections) of a 3D DT manifold with $S^{3}$ topology. Evidence of a scaling behavior of the genus distributions of boundary surfaces has been found.Comment: 3 pages, latex, 4 ps figures, uses espcrc2.sty. Talk presented at LATTICE'97(gravity

Geometry of 4d Simplicial Quantum Gravity with a U(1) Gauge Field

The geometry of 4D simplicial quantum gravity with a U(1) gauge field is studied numerically. The phase diagram shows a continuous transition when gravity is coupled with a U(1) gauge field. At the critical point measurements of the curvature distribution of S^4 space shows an inflated geometry with homogeneous and symmetric nature. Also, by choosing a 4-simplex and fixing the scalar curvature geometry of the space is measured.Comment: 3 pages, 2 eps figure. Talked at Lattice 2000 (Gravity

Phase Transition of 4D Simplicial Quantum Gravity with U(1) Gauge Field

The phase transition of 4D simplicial quantum gravity coupled to U(1) gauge fields is studied using Monte-Carlo simulations. The phase transition of the dynamical triangulation model with vector field ($N_{V}=1$) is smooth as compared with the pure gravity($N_{V}=0$). The node susceptibility ($\chi$) is studied in the finite size scaling method. At the critical point, the node distribution has a sharp peak in contrast to the double peak in the pure gravity. From the numerical results, we expect that 4D simplicial quantum gravity with U(1) vector fields has higher order phase transition than 1st order, which means the possibility to take the continuum limit at the critical point.Comment: 3 pages, latex, 3 eps figures, uses espcrc2.sty. Talk presented at LATTICE99(gravity

Grand-Canonical simulation of 4D simplicial quantum gravity

A thorough numerical examination for the field theory of 4D quantum gravity (QG) with a special emphasis on the conformal mode dependence has been studied. More clearly than before, we obtain the string susceptibility exponent of the partition function by using the Grand-Canonical Monte-Carlo method. Taking thorough care of the update method, the simulation is made for 4D Euclidean simplicial manifold coupled to $N_X$ scalar fields and $N_A$ U(1) gauge fields. The numerical results suggest that 4D simplicial quantum gravity (SQG) can be reached to the continuum theory of 4D QG. We discuss the significant property of 4D SQG.Comment: 3 pages, 2 figures, LaTeX, Lattice2002(Gravity

Will income inequality cause a middle-income trap in Asia? Bruegel Working Paper 2013/06, 10 October 2013

The Asian economy is expected to realise favourable growth during the first half of this century, but there is no guarantee. There is a discussion about a ‘middle-income trap’, which refers to a country that has realised rapid growth to become a middle-income country but is unable to grow further. A middle-income trap could occur not only if there is a delay in shifting the economy toward a productivity-driven structure, but also if there is a worsening of income distribution.We consider this in line with the theories of development economics and through a quantitative analysis. The relationship between income inequality and the trap can be explained by the Kuznets hypothesis and the basic-needs approach. Our quantitative analysis supports the Kuznets hypothesis, and indicates that,although a low-income country can accelerate its economic growth with the worsening of income distribution as an engine, a middle income country would experience a decreasing growth rate if it fails to narrow the income gap between the top and bottom income groups. The results also show that the basic-needs approach is also applicable in practice, and imply that the improvement of access to secondary education is important. A sensitivity analysis for three Asian upper-middle-income countries(China, Malaysia and Thailand) also shows that the situation related to a middle-income trap is worse than average in China and Malaysia. These two countries, according to the result of the sensitivity analysis, should urgently improve access to secondary education and should implement income redistribution measures to develop high-tech industries, before their demographic dividends expire. Income redistribution includes the narrowing of rural urban income disparities, benefits to low-income individuals, direct income transfers, vouchers or free provision of education and health-care, and so on, but none of these are simple to implement

Common Structures in 2,3 and 4D Simplicial Quantum Gravity

Two kinds of statistical properties of dynamical-triangulated manifolds (DT mfds) have been investigated. First, the surfaces appearing on the boundaries of 3D DT mfds were investigated. The string-susceptibility exponent of the boundary surfaces ($\tilde{\gamma}_{st}$) of 3D DT mfds with $S^{3}$ topology near to the critical point was obtained by means of a MINBU (minimum neck baby universes) analysis; actually, we obtained $\tilde{\gamma}_{st} \approx -0.5$. Second, 3 and 4D DT mfds were also investigated by determining the string-susceptibility exponent near to the critical point from measuring the MINBU distributions. As a result, we found a similar behavior of the MINBU distributions in 3 and 4D DT mfds, and obtained $\gamma_{st}^{(3)} \approx \gamma_{st}^{(4)} \approx 0$. The existence of common structures in simplicial quantum gravity is also discussed.Comment: 3 pages, latex, 3 ps figures, uses espcrc2.sty. Talk presented at LATTICE97(gravity

Path-factors involving paths of order seven and nine

In this paper, we show the following two theorems (here $c_{i}(G-X)$ is the number of components $C$ of $G-X$ with $|V(C)|=i$): (i)~If a graph $G$ satisfies $c_{1}(G-X)+\frac{1}{3}c_{3}(G-X)+\frac{1}{3}c_{5}(G-X)\leq \frac{2}{3}|X|$ for all $X\subseteq V(G)$, then $G$ has a $\{P_{2},P_{7}\}$-factor. (ii)~If a graph $G$ satisfies $c_{1}(G-X)+c_{3}(G-X)+\frac{2}{3}c_{5}(G-X)+\frac{1}{3}c_{7}(G-X)\leq \frac{2}{3}|X|$ for all $X\subseteq V(G)$, then $G$ has a $\{P_{2},P_{9}\}$-factor.Comment: 29 pages, 4 figure