Phases and fractal structures of three-dimensional simplicial gravity

We study phases and fractal structures of three-dimensional simplicial quantum gravity by the Monte-Carlo method. After measuring the surface area distribution (SAD) which is the three-dimensional analog of the loop length distribution (LLD) in two-dimensional quantum gravity, we classify the fractal structures into three types: (i) in the hot (strong coupling) phase, strong gravity makes the space-time one crumpled mother universe with small fluctuating branches around it. This is a crumpled phase with a large Hausdorff dimension d_{\mbox{\tiny H}} \simeq 5. The topologies of cross-sections are extremely complicated. (ii) at the critical point, we observe that the space-time is a fractal-like manifold which has one mother universe with small and middle size branches around it. The Hausdorff dimension is d_{\mbox{\tiny H}} \simeq 4. We observe some scaling behaviors for the cross-sections of the manifold. This manifold resembles the fractal surface observed in two-dimensional quantum gravity. (iii) in the cold (weak coupling) phase, the mother universe disappears completely and the space-time seems to be the branched-polymer with a small Hausdorff dimension d_{\mbox{\tiny H}} \simeq 2. Almost all of the cross-sections have the spherical topology $S^2$ in the cold phase.Comment: 14 pages, latex file, 5 Postscript figures, use psfig.st

Discovery of low thermal conductivity compounds with first-principles anharmonic lattice dynamics calculations and Bayesian optimization

Compounds of low lattice thermal conductivity (LTC) are essential for seeking thermoelectric materials with high conversion efficiency. Some strategies have been used to decrease LTC. However, such trials have yielded successes only within a limited exploration space. Here we report the virtual screening of a library containing 54,779 compounds. Our strategy is to search the library through Bayesian optimization using for the initial data the LTC obtained from first-principles anharmonic lattice dynamics calculations for a set of 101 compounds. We discovered 221 materials with very low LTC. Two of them have even an electronic band gap < 1 eV, what makes them exceptional candidates for thermoelectric applications. In addition to those newly discovered thermoelectric materials, the present strategy is believed to be powerful for many other applications in which chemistry of materials are required to be optimized.Comment: 6 pages, 4 figure

CellTree: an R/bioconductor package to infer the hierarchical structure of cell populations from single-cell RNA-seq data

GO BP Terms for myoblast data. Full table of enriched GO BP terms for each topic in myoblast data. (PDF 36 kb