Recently, data sampling techniques of genome data such as the single-cell RNA sequencing (scRNA-seq) have rapidly been developing. However, genome data is high-dimensional since the number of features (genes) is huge and has some technical noises when its data sampling. Those properties of genome data let conventional data analysis methods sometimes induce incorrect results. Therefore, this research aims to establish the mathematical basements of analyzing genome data via utilizing various mathematical fields such as the high-dimensional statistics, causal discovery, topological analysis, network theory, and dynamical system. Then, this research will contribute to discover the true structures in single-cell resolutions.
Y Imoto, T Nakamura, E G Escolar, M Yoshiwaki, Y Kojima, Y Yabuta, Y Katou, T Yamamoto, Y Hiraoka, M Saitou. Resolution of the curse of dimensionality in single-cell RNA sequencing data analysis. Life Science Alliance, Vol. 5 (12), e202201591, 2022.
Y Imoto. Difference between smoothed particle hydrodynamics and moving particle semi-implicit operators. Computer Methods in Applied Mechanics and Engineering, Vol. 395, 115012, 2022.
M Fujikawa, M Tanaka, N Mitsume and Y Imoto. Hyper-dual number-based numerical differentiation of eigensystems, Computer Methods in Applied Mechanics and Engineering, Vol. 390, 114452, 2022.
Y Imoto, N Yamanaka, T Uramoto, M Tanaka, M Fujikawa and N Mitsume. Fundamental theorem of matrix representations of hyper-dual numbers for computing higher-order derivatives, JSIAM Letters, Vol. 12, pp. 29–32, 2020.
Y Imoto. Truncation error estimates of approximate operators in a generalized particle method. Japan Journal of Industrial and Applied Mathematics, Vol. 37, pp. 565–598, 2020.
Y Imoto, S Tsuzuki, and D Nishiura. Convergence study and optimal weight functions of an explicit particle method for the incompressible Navier–Stokes equations, Computational Particle Mechanics, Vol. 6 (4), pp. 671–694, 2019.
D Morikawa, M Asai, N Idris, Y Imoto, and M Isshiki. Improvements in highly viscous fluid simulation using a fully implicit SPH method. Computational Particle Mechanics, Vol. 6 (4), pp. 529–544, 2019.
Y Imoto. Unique solvability and stability analysis for incompressible smoothed particle hydrodynamics method. Computational Particle Mechanics, Vol. 6 (2), pp. 297–309, 2019.
Y Imoto. Unique solvability and stability of a generalized particle method for a Poisson equation in discrete Sobolev norms. Applications of Mathematics, Vol. 64 (1), pp. 33–43, 2019.
JSIAM Letters Best Paper Award (2020)
MSJ Prize for Excellent Applied Mathematicians (2018)