Harada's conjecture II for the finite general linear groups

K. Harada conjectured for any finite group $G$, the product of sizes of all conjugacy classes is divisible by the product of degrees of all irreducible characters. We study this conjecture when $G$ is the general linear group over a finite field. We show the conjecture holds if the order of the field is sufficiently large.Comment: 11 pages, 7 table

A neural network system for transformation of regional cuisine style

We propose a novel system which can transform a recipe into any selected regional style (e.g., Japanese, Mediterranean, or Italian). This system has two characteristics. First the system can identify the degree of regional cuisine style mixture of any selected recipe and visualize such regional cuisine style mixtures using barycentric Newton diagrams. Second, the system can suggest ingredient substitutions through an extended word2vec model, such that a recipe becomes more authentic for any selected regional cuisine style. Drawing on a large number of recipes from Yummly, an example shows how the proposed system can transform a traditional Japanese recipe, Sukiyaki, into French style

Self-consistent study of topological superconductivity in two-dimensional quasicrystals

We study two-dimensional $s$-wave topological superconductivity with Rashba spin-orbit coupling and Zeeman field in Penrose and Ammann-Beenker quasicrystals. By solving the Bogoliubov-de Gennes equations self-consistently for not only the superconducting order parameter, but also the spin-dependent Hartree potential, we show the stable occurrence of TSC with broken time-reversal symmetry in both Penrose and Ammann-Beenker quasicrystals. The topological nature of the quasicrystalline system is signified by the Bott index $B$. Topological phase transitions are found to occur, where $B$ changes between 0 and $\pm 1$, as the chemical potential or Zeeman field is varied. In terms of self-consistent solutions, we demonstrate the existence of a Majorana zero mode per edge or vortex when $B=\pm 1$, consistently with the bulk-edge/defect correspondence for periodic systems.Comment: 11 pages, 10 figure

Confined states and topological phases in two-dimensional quasicrystalline π\pi-flux model

Motivated by topological equivalence between an extended Haldane model and a chiral-$\pi$-flux model on a square lattice, we apply $\pi$-flux models to two-dimensional bipartite quasicrystals with rhombus tiles in order to investigate topological properties in aperiodic systems. Topologically trivial $\pi$-flux models in the Ammann-Beenker tiling lead to massively degenerate confined states whose energies and fractions differ from the zero-flux model. This is different from the $\pi$-flux models in the Penrose tiling, where confined states only appear at the center of the bands as is the case of a zero-flux model. Additionally, Dirac cones appear in a certain $\pi$-flux model of the Ammann-Beenker approximant, which remains even if the size of the approximant increases. Nontrivial topological states with nonzero Bott index are found when staggered tile-dependent hoppings are introduced in the $\pi$-flux models. This finding suggests a new direction in realizing nontrivial topological states without a uniform magnetic field in aperiodic systems.Comment: 5+20 pages, 4+19 figures, 1+11 table

A simplified method for power-law modelling of metabolic pathways from time-course data and steady-state flux profiles

BACKGROUND: In order to improve understanding of metabolic systems there have been attempts to construct S-system models from time courses. Conventionally, non-linear curve-fitting algorithms have been used for modelling, because of the non-linear properties of parameter estimation from time series. However, the huge iterative calculations required have hindered the development of large-scale metabolic pathway models. To solve this problem we propose a novel method involving power-law modelling of metabolic pathways from the Jacobian of the targeted system and the steady-state flux profiles by linearization of S-systems. RESULTS: The results of two case studies modelling a straight and a branched pathway, respectively, showed that our method reduced the number of unknown parameters needing to be estimated. The time-courses simulated by conventional kinetic models and those described by our method behaved similarly under a wide range of perturbations of metabolite concentrations. CONCLUSION: The proposed method reduces calculation complexity and facilitates the construction of large-scale S-system models of metabolic pathways, realizing a practical application of reverse engineering of dynamic simulation models from the Jacobian of the targeted system and steady-state flux profiles